Supplier Selection with Multi-Scenario Inputs and Outputs, Using Data Envelopment
Analysis
Sonali Maldini Rajasekara (2234344)
University Canada West
MBAR 661 Academic Research Project (ONS-Summer 24-05)
Dr. Mazyar Zahedi-Seresht
July 30, 2024

Table of Content
Abstract ……………………………………...……………………………………………………2
Introduction……………………………………………………………………………..…………3
Supply Chain Management………………………………………………………………….…….4
Data Envelopment Analysis…………………………………………………………………….....6
Data Envelopment Analysis in Supply Chain…………………………………………………....14
Supplier Selection using data envelopment Analysis…………………………...……………….16
Multi-Scenario Data Envelopment Analysis in Supply Selection …………………………...….21
Data of Interest …………………………………………………………………………………..28
Overview for Data…………………………………………………………..………..28
Recent Statistics…………………………………………………………….………..30
COVID vs Greenhouse Revenue…………………………………………………….32
Inputs and Outputs for DEA…………………………………………………...…… 36
Input - Specialized greenhouse producers' operating expenses………………….…..36
Output- Total value of greenhouse products ………………………………………...43
Developing the Mathematical Model for each DMU……………………………………………45
Conclusions………………………………………………………………………………………51
Limitations of the study ………………………………………………………………..………..52
Future Potential of the study………………………………………………………………..……53
References………………………………………………………………………………………..54
Appendix………………………………………………………………………………..………..60

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Abstract
Data Envelopment Analysis (DEA) is a powerful tool for assessing the relative
efficiency of Decision-Making Units (DMUs) by comparing their input-output ratios. Traditional
DEA models typically address crisp data but may not fully capture scenarios involving
uncertainty in inputs and outputs. This research expands on DEA by applying it to multiple
scenarios to account for varying conditions in farms across Canada. This research applies DEA
to assess the operational efficiency of greenhouse, sod, and nursery operations across Canada,
using a multi-scenario approach over the period from 2019 to 2023. The study focuses on three
key provinces, British Columbia, Ontario, and Quebec, making the sample size as 3, examining
their performance based on various input variables, such as operating expenses for specialized
greenhouse vegetables and flowers, and output variables, including the total value of greenhouse
products produced. This model, derived from traditional DEA formulations but adapted for
multiple scenarios, remains linear and computationally efficient, overcoming common
limitations of non-linear models. Results indicate that Quebec consistently achieved full
efficiency, while Ontario and British Columbia improved over time but did not reach Quebec's
level. This study introduces a new application of DEA with the incorporation of a multi-scenario
approach in order to capture the variation and uncertainty within the greenhouse, sod, and
nursery operations in Canada which will improve the quality and strength of efficiency analyses
relevant to agricultural settings. Despite its advancements, the study acknowledges limitations,
including static analysis, homogeneity assumptions, and the exclusion of qualitative factors.
Keywords
Data Envelopment Analysis (DEA), Efficiency, Ranking, Multiple Scenario, Supplier Selection,
Green House, Decision Making Unit (DMU)
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Introduction
It is observed that the efficient selection of suppliers is a critical factor in gaining
competitiveness and sustainability in the dynamic environment of supply chain management.
Supplier selection is a process for assessing potential suppliers and choosing the most
appropriate ones based on multiple criteria and constraints. Traditional methods are subjective,
intuitive, or limited to some simple metrics, hence generally leading to poor decisions. Data
Envelopment Analysis is one of the most commonly applied techniques in Operations and
Supply Chain Management for measuring the relative efficiency of DMUs, like suppliers, based
on several inputs and outputs. It is particularly useful when traditional methods will likely miss
complexities and nuances in supplier selection within dynamic supply chain environments.
It does this by comparing the input-output ratios of each DMU to that of its peers to
evaluate their relative efficiency. This technique simultaneously supports several inputs like cost,
quality, and delivery time, as well as outputs such as customer satisfaction and product
innovation. In doing this, DEA can give an overall assessment of supplier performance.
One of the critical advantages of DEA is its ability to deal with different scenarios and
variations in inputs and outputs. This is critical in supply chain management, where factors like
fluctuations in market demand, resource availability, or even regulatory changes may
considerably impact supplier performance. In different scenarios, DEA helps establish strong
choices of suppliers resistant to uncertainties and business environment fluctuations.
This research aims to investigate the application of DEA in supplier selection for the
supply chain industry, considering multiple scenario inputs and outputs. By developing and
implementing DEA models tailored to the complexities of supply chain dynamics, the study
3

seeks to enhance the decision-making process, enabling organizations to make informed and
robust supplier selections.
Supply Chain Management
The concept of a supply chain has changed many times and evolved through changes in
business concepts, information technology, and globalization. The Council of Supply Chain
Management Professionals (CSCMP) defines it as managing all procurement, production, and
logistical services. It is about seamlessly knitting together the core business functions with other
operational aspects across various stakeholder companies.
This collaboration involves suppliers, intermediaries, and customers synchronizing
efforts across sales, marketing, finance, production, procurement, and logistics. Additionally,
prior research, such as Tang (2006), characterizes SCM as coordinating material, information,
and financial flows within a network of entities aiming to create and deliver consumer products
or services.
The supply chain is a system of resources, processes, and stakeholders that manage the
flow of materials, information, and finances from raw material sourcing to final product delivery
to meet customer demand. It brings together different perspectives hitherto isolated by scholars:
Athaudage et al. (2022) and Tang (2006).
Business activities are becoming more complex as globalization progresses. The value
and reach of supply chains are increasing fast, and so are the associated stakeholders reaching
out and engaging from all over the world. The supply chain is increasingly prone to disruption,
and the market competition is getting tighter. All companies are eyeing strategies that will make
them better placed in terms of efficiency as competitive forces rise. This is particularly true for
multinational companies that are always looking to adapt and improve to remain competitive in
4

the global market that continues to change. With the increasing significance of supply chains in
enterprise operations, firms focus more on continuous improvement initiatives.
Supply chains are getting complex, and modern supply networks involve many
participants across many industries and parts of the world. Various challenges arise when dealing
with this highly competitive global market today (Vishnu et al., 2019). Many types of risks and
threats, such as demand side, internal uncertainties, and supply, led to several pragmatic but
prevalent and contemporary supply chain practices.
Companies have been suffering from several catastrophic events in the recent past
caused by terrorist attacks, pandemics, and natural disasters, which broke or slowed down supply
chains. Changing business trends, globalization, complexity, and specialization increase the risks
but reduce managerial control of the operations (Urciuoli & Hintsa, 2018).
The concept of supply chains has its earliest discussions in logistics literature, dating
back to the middle of the 20th century. The first contributions that brought out the integration of
many different organizational functions to work out an efficient and low-cost operation in
business were provided by Joseph Juran and W. Edwards Deming. However, their nature and
focus were purely internal and did not extend to the network of suppliers, manufacturers,
distributors, and customers.
During the 1980s, the decade we witnessed an astonishing movement toward the
integrated approach to supply chain management. Concepts developed for Just-In-Time by
Japanese manufacturers, especially Toyota, drew worldwide attention to the need to synchronize
with customer demand, avoiding the high cost entailed by inventory carrying and storing. It also

5

set the fundamentals of partnering between companies and their suppliers and would be the basis
of modern-day supply chain partnerships.
We have seen extremely rapid growth in world trade in the second half of the 20th
century. Transportation and communications improvements and trade liberalization have brought
new challenges and complexities to supply chain management regarding extended lead times,
stronger rivalry, and more significant supply chain risks. At this time, scholars and practitioners
began to feel the need for more sophisticated strategies to deal with such challenges.
Since its inception, information technology has also contributed to changing the face of
supply chain management. When ERP systems began to proliferate in companies in the 1990s,
they provided better integration and smoother internal processes, making it easier to coordinate
and communicate up and down the supply chain, as Davenport observed in 1998. It was also an
era when concepts like Vendor-Managed Inventory and Collaborative Planning, Forecasting, and
Replenishment took shape further to increase the visibility and responsiveness of supply chains.
The trends that appear to be building over the years are sustainability, digitalization, and
omnichannel retailing. Sustainability and corporate social responsibility are fast being perceived
as pertinent issues in the conduct of supply chain operations due to raised awareness by
consumers and regulations (Seuring, 2012). Moreover, e-commerce and digital technologies
have reset consumers' expectations toward ever-faster visibility, raising levels of personalization
and seamless integrations between online and offline channels. (Chopra, 2015).
Data Envelopment Analysis
DEA is a method that calculates efficiency based on operational processes with multiple
inputs and outputs solved within linear programming problems. Charnes et al. introduced this
6

approach in 1978, transforming the multiple inputs and outputs into a single efficiency score.
The process begins by identifying the best-performing units, forming what is known as the
efficient frontier. Other units are then evaluated based on their proximity to this frontier.
Over time, DEA has evolved into various models like the CRS(constant returns to scale)
and VRS(variable-returns-to-scale) models, each suited to different measurement needs. Its
applications span industries such as banking, education, and healthcare (Avkiran, 2011).
Furthermore, research on DEA extends globally, including countries like China (Zhong et al.,
2011), Greece (Demirbag et al., 2010), and the UAE (Seiford & Thrall, 1990).
Various authors have examined the broad DEA literature and offered insights into the
evolution of DEA methodology over different periods and from various perspectives. These
surveys generally fall into bibliography listings, qualitative analyses, and quantitative
assessments.
For instance, Seiford (1990) and Gattoufi et al. (2004) compiled extensive bibliographies
of DEA literature. On the qualitative side, Seiford and Thrall (1990), Cooper et al. (2007), and
Cook and Seiford (2009) offer in-depth discussions. For example, Seiford and Thrall (1990)
delve into the early stages of DEA development, while Seiford (1996) tracks its evolution from
1978 to 1995, highlighting key milestones and conceptual shifts.
One notable aspect of Seiford's (1996) work is the visual evolution map, which
graphically represents major events' timing and new ideas' emergence. This visualization aids in
understanding the interconnectedness of ideas and tracing the genesis of novel concepts.
From a theoretical standpoint, Cooper et al. (2007) analyze various DEA models and
metrics, while Cook and Seiford (2009) offer a comprehensive review of methodological
7

advancements since 1978. Their review covers various topics, including generic DEA models,
multilevel models, constraints on multipliers, variable status considerations, and handling of data
variations.
Gattoufi et al. (2004) and Emrouznejad et al. (2008) conducted quantitative surveys and
provided analyses of publication statistics using DEA. Gattoufi et al. (2004) sourced their data
from six online professional databases, while Emrouznejad et al.(2008) maintained a regularly
updated DEA literature database with community support.
As already pointed out, the DEA model was introduced as far back as 1978 by Charnes,
Cooper, and Rhodes, though Farrell had put forth the efficiency concept as early as 1957. First,
the CCR model, later extended in 1984 by Banker, Charnes, and Cooper to yield the so-called
Banker, Charnes, and Cooper model, introduced constant returns to scale and variable returns to
scale concepts, respectively.
Today, DEA has become an essential tool for decision-making, helping to evaluate
efficiency and identify production capabilities. DEA is a methodology based on linear
programming used to determine the production efficiency of suppliers by employing multiple
input and output variables (Hosseini-Nasab & Ettehadi, 2023). This approach allows for
distinguishing vendors based on their efficiency levels. DEA is a mathematical method for
calculating an economic unit's relative productivity or efficiency, enabling the measurement of
efficiency for a set of Decision-Making Units (DMUs). A DMU refers to a homogeneous entity
or productive unit offering similar products or services.

8

Additionally, DMUs can produce multiple output variables based on various input
variables. DEA's mathematical programming technique helps identify which DMU has the
highest efficiency score, aiding supplier selection.
After defining a set of DMUs, the next step is to specify the input and output variables.
The DEA model accommodates multiple input and output variables (Cikovic et al., 2022), and
the number of input variables can differ from the number of output variables. In DEA, all DMUs
use the same input and output variables.
To assess each DMU's efficiency, a weighted ratio is assigned to each input and output
variable for each DMU. By applying these weight ratios, the efficiency rate of each DMU can be
calculated under optimal conditions to achieve maximum efficiency. The efficiency rate of a
DMU can be expressed as the weighted sum of outputs divided by the weighted sum of inputs.
Maximize
r

θ q = ∑ uk ykq
k =1

Subject to;
r

m

1, 2,..., n,
∑ uk ykj − ∑ vi xij ≤ 0, j =

=
k 1 =i 1
m

∑ v x = 1,
i =1

i iq

uk ≥ ε , vi ≥ ε .
𝑣𝑣𝑖𝑖 – Input weight of the ith input

uk – Output weight of the kth output
Non-Archimedean element 𝜀𝜀 > 0,

𝑣𝑣𝑖𝑖 and 𝑢𝑢𝑘𝑘 represent input and output weights for the i-th input and k-th output. On the other

hand, 𝜀𝜀 > 0 is a non-Archimedean element, smaller than any positive real number.

9

The optimal objective function value 𝑞𝑞𝑞𝑞∗=1 demonstrates the efficiency of the evaluated

unit. Units with values less than one are considered inefficient. Reducing the number of inputs
can help achieve the efficiency threshold (Cengage, 2022).
A set of input and output variables is necessary to determine the efficiency score using
DEA. Inputs are any resources consumed by a DMU, while outputs are the results or
performance measures of transforming these inputs into products or services (Wong, 2021).
The choice between input and output orientation depends on the objective. An inputoriented DEA model examines the capability to produce a given output level with the least
amount of inputs and resources (Alidrisi, 2021). Conversely, an output-oriented DEA model
evaluates how effectively a DMU maximizes its output with a fixed level of inputs.

Consider Ranch House, Inc., a fast-food restaurant chain with operations in five different
locations. To determine the most efficient restaurant in the chain, they have collected input and
output data to develop a Data Envelopment Analysis (DEA) model. The inputs measured include
weekly hours of operation, the number of full-time equivalent staff, and weekly supply expenses.
The outputs are the average weekly contribution to profit, market share, and annual growth rate.
Tables 1 and 2 below display the collected input and output data, respectively (Cengage, 2022).
Table 1- Input measures
Restaurant

Hours of Operation

FTE Staff

Supplies ($)

Bardstown

96

16

850

Clarksville

110

22

1400

Jeffersonville

100

18

1200

New Albany

125

25

1500

St. Matthews

120

24

1600

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Table 2 - Output measures
Restaurant

Weekly Profit ($)

Market Share(%)

Growth Rate (%)

Bardstown

3800

25

8.0

Clarksville

4600

32

8.5

Jeffersonville

4400

35

8.0

New Albany

6500

30

10.0

St. Matthews

6000

28

9.0

Developing the Mathematical Model for each DMU:
DEA model for Bardstown:
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 3800𝑢𝑢1 + 25𝑢𝑢2 + 8𝑢𝑢3
Subject to
3800𝑢𝑢1 + 25𝑢𝑢2 + 8𝑢𝑢3 − 96𝑣𝑣1 − 16𝑣𝑣2 − 850𝑣𝑣3 ≤ 0
4600𝑢𝑢1 + 32𝑢𝑢2 + 8.5𝑢𝑢3 − 110𝑣𝑣1 − 22𝑣𝑣2 − 1400𝑣𝑣3 ≤ 0
4400𝑢𝑢1 + 35𝑢𝑢2 + 8𝑢𝑢3 − 100𝑣𝑣1 − 18𝑣𝑣2 − 1200𝑣𝑣3 ≤ 0
6500𝑢𝑢1 + 30𝑢𝑢2 + 10𝑢𝑢3 − 125𝑣𝑣1 − 25𝑣𝑣2 − 1500𝑣𝑣3 ≤ 0
6000𝑢𝑢1 + 25𝑢𝑢2 + 9𝑢𝑢3 − 120𝑣𝑣1 − 24𝑣𝑣2 − 1600𝑣𝑣3 ≤ 0
96𝑣𝑣1 + 16𝑣𝑣2 + 850𝑣𝑣3 = 1
𝑢𝑢1 , 𝑢𝑢2 , 𝑢𝑢3 , 𝑣𝑣1 , 𝑣𝑣2 , 𝑣𝑣3 ≥ 𝜀𝜀
DEA model for Clarksville:
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 4600𝑢𝑢1 + 32𝑢𝑢2 + 8.5𝑢𝑢3
Subject to
3800𝑢𝑢1 + 25𝑢𝑢2 + 8𝑢𝑢3 − 96𝑣𝑣1 − 16𝑣𝑣2 − 850𝑣𝑣3 ≤ 0
4600𝑢𝑢1 + 32𝑢𝑢2 + 8.5𝑢𝑢3 − 110𝑣𝑣1 − 22𝑣𝑣2 − 1400𝑣𝑣3 ≤ 0
4400𝑢𝑢1 + 35𝑢𝑢2 + 8𝑢𝑢3 − 100𝑣𝑣1 − 18𝑣𝑣2 − 1200𝑣𝑣3 ≤ 0
6500𝑢𝑢1 + 30𝑢𝑢2 + 10𝑢𝑢3 − 125𝑣𝑣1 − 25𝑣𝑣2 − 1500𝑣𝑣3 ≤ 0
6000𝑢𝑢1 + 25𝑢𝑢2 + 9𝑢𝑢3 − 120𝑣𝑣1 − 24𝑣𝑣2 − 1600𝑣𝑣3 ≤ 0
110𝑣𝑣1 + 22𝑣𝑣2 + 1400𝑣𝑣3 = 1
𝑢𝑢1 , 𝑢𝑢2 , 𝑢𝑢3 , 𝑣𝑣1 , 𝑣𝑣2 , 𝑣𝑣3 ≥ 𝜀𝜀
DEA model for Jeffersonville:
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 4400𝑢𝑢1 + 35𝑢𝑢2 + 8𝑢𝑢3
Subject to
3800𝑢𝑢1 + 25𝑢𝑢2 + 8𝑢𝑢3 − 96𝑣𝑣1 − 16𝑣𝑣2 − 850𝑣𝑣3 ≤ 0
4600𝑢𝑢1 + 32𝑢𝑢2 + 8.5𝑢𝑢3 − 110𝑣𝑣1 − 22𝑣𝑣2 − 1400𝑣𝑣3 ≤ 0
4400𝑢𝑢1 + 35𝑢𝑢2 + 8𝑢𝑢3 − 100𝑣𝑣1 − 18𝑣𝑣2 − 1200𝑣𝑣3 ≤ 0
6500𝑢𝑢1 + 30𝑢𝑢2 + 10𝑢𝑢3 − 125𝑣𝑣1 − 25𝑣𝑣2 − 1500𝑣𝑣3 ≤ 0
6000𝑢𝑢1 + 25𝑢𝑢2 + 9𝑢𝑢3 − 120𝑣𝑣1 − 24𝑣𝑣2 − 1600𝑣𝑣3 ≤ 0
100𝑣𝑣1 + 18𝑣𝑣2 + 1200𝑣𝑣3 = 1

11

𝑢𝑢1 , 𝑢𝑢2 , 𝑢𝑢3 , 𝑣𝑣1 , 𝑣𝑣2 , 𝑣𝑣3 ≥ 𝜀𝜀

DEA model for New Alberny:
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 6500𝑢𝑢1 + 30𝑢𝑢2 + 10𝑢𝑢3
Subject to
3800𝑢𝑢1 + 25𝑢𝑢2 + 8𝑢𝑢3 − 96𝑣𝑣1 − 16𝑣𝑣2 − 850𝑣𝑣3 ≤ 0
4600𝑢𝑢1 + 32𝑢𝑢2 + 8.5𝑢𝑢3 − 110𝑣𝑣1 − 22𝑣𝑣2 − 1400𝑣𝑣3 ≤ 0
4400𝑢𝑢1 + 35𝑢𝑢2 + 8𝑢𝑢3 − 100𝑣𝑣1 − 18𝑣𝑣2 − 1200𝑣𝑣3 ≤ 0
6500𝑢𝑢1 + 30𝑢𝑢2 + 10𝑢𝑢3 − 125𝑣𝑣1 − 25𝑣𝑣2 − 1500𝑣𝑣3 ≤ 0
6000𝑢𝑢1 + 25𝑢𝑢2 + 9𝑢𝑢3 − 120𝑣𝑣1 − 24𝑣𝑣2 − 1600𝑣𝑣3 ≤ 0
125𝑣𝑣1 + 25𝑣𝑣2 + 1500𝑣𝑣3 = 1
𝑢𝑢1 , 𝑢𝑢2 , 𝑢𝑢3 , 𝑣𝑣1 , 𝑣𝑣2 , 𝑣𝑣3 ≥ 𝜀𝜀
DEA model for St. Matthews:
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 6000𝑢𝑢1 + 25𝑢𝑢2 + 9𝑢𝑢3
Subject to
3800𝑢𝑢1 + 25𝑢𝑢2 + 8𝑢𝑢3 − 96𝑣𝑣1 − 16𝑣𝑣2 − 850𝑣𝑣3 ≤ 0
4600𝑢𝑢1 + 32𝑢𝑢2 + 8.5𝑢𝑢3 − 110𝑣𝑣1 − 22𝑣𝑣2 − 1400𝑣𝑣3 ≤ 0
4400𝑢𝑢1 + 35𝑢𝑢2 + 8𝑢𝑢3 − 100𝑣𝑣1 − 18𝑣𝑣2 − 1200𝑣𝑣3 ≤ 0
6500𝑢𝑢1 + 30𝑢𝑢2 + 10𝑢𝑢3 − 125𝑣𝑣1 − 25𝑣𝑣2 − 1500𝑣𝑣3 ≤ 0
6000𝑢𝑢1 + 25𝑢𝑢2 + 9𝑢𝑢3 − 120𝑣𝑣1 − 24𝑣𝑣2 − 1600𝑣𝑣3 ≤ 0
120𝑣𝑣1 + 24𝑣𝑣2 + 1600𝑣𝑣3 = 1
𝑢𝑢1 , 𝑢𝑢2 , 𝑢𝑢3 , 𝑣𝑣1 , 𝑣𝑣2 , 𝑣𝑣3 ≥ 𝜀𝜀

The following table shows the results of implementing and solving the above mathematical
models using Excel. (Cengage, 2022).
Table 3 - Optimal Efficiency Score
Restaurant
Optimal Efficiency Score
Bardstown

1

Clarksville

0.96

Jeffersonville

1

New Albany

1

St. Matthews

0.99

An efficiency score of 1 represents optimal efficiency, while a score less than 1 indicates
inefficiency. We can rank DMUs based on their efficiency scores from highest to lowest.
(Zahedi-Seresht et al., 2023b)

12

There are no strict guidelines for determining input and output variables in a DEA model.
Operational indicators such as total assets, capital, current liabilities, operating expenses, number
of staff, and overhead expenses can be treated as input variables. Likewise, operating income, net
profit, net sales, or revenue can be viewed as output variables (Wong, 2021) when using the
DEA method to calculate the efficiency score for comparative purposes.
Despite its foundational role, traditional DEA models like CCR and BCC often rely on
crisp data representations, overlooking the prevalent uncertainty in real-world datasets. O’Neal,
Ozcan, and Yanqiang (2002) suggested excluding data with uncertainties, impacting the relative
efficiency scores. Alternative approaches, like imputation techniques, have been proposed, yet
they risk distorting efficiency scores.
Stochastic programming, dating back to Dantzig (1955) and Beale (1955), offers another
avenue for uncertain data in DEA, albeit challenged by the lack of empirical evidence for
probability distribution functions. Kuosmanen (2009) proposed using dummy variables for
missing data, but this method has limitations in accurately reflecting reality.
Fuzzy methodologies, pioneered by Sengupta (1992) and Cooper, Park, and Yu (1999),
offer a promising avenue by accommodating uncertain data through fuzzy logic and intervalbased approaches. Despite challenges in assessing upper and lower bounds of efficiency,
researchers like Despotis and Smirlis (2002) and Kao (2006) have made strides in developing
interval methods.
Fuzzy DEA, explored by researchers like Guo and Tanaka (2001) and Hatami-Marbini
and Saati (2009), offers an intricate yet effective means of evaluating DMU efficiency amidst
uncertainty. Despite the method's complexity, it holds promise for practical applications.
13

In recent years, scholars like Toloo and Ertay (2014) have introduced novel approaches
like CE-DEA to address uncertainties in input prices, while Sadjadi and Omrani (2008) proposed
robust DEA models for evaluating performance under output uncertainty. Shokouhi et al. (2010)
and Hafezalkotob et al. (2015) have also contributed robust optimization models to address
uncertainty in input and output parameters.
Further advancements include methods proposed by Arabmaldar, Jablonsky, and
Saljooghi (2017) and Zahedi-Seresht, Mehrabian, and Jahanshahloo (2016), aiming to enhance
efficiency evaluation in uncertain environments.
While traditional DEA models paved the way, emerging methodologies like fuzzy DEA
and robust optimization offer promising avenues for addressing uncertainty and enhancing
efficiency evaluations in diverse decision-making contexts. However, challenges remain in
balancing computational complexity with real-world applicability.
Data Envelopment Analysis in Supply Chain
Supply chain management refers to coordinating material, information, and financial
flows that satisfy customers' demands efficiently and at low costs, maximizing the supply chains'
overall profitability. Data envelopment analysis has been an extremely fundamental
mathematical tool in assessing performance in the supply chain over the years. Despite numerous
DEA models proposed for this purpose, systematic literature reviews are lacking.
Researchers have conducted a comprehensive review using the PRISMA method to
address this gap, analyzing 75 articles from 1996 to 2016 across 35 scholarly journals and
conferences. They categorized these articles based on author, publication year, technique,
application area, country, scope, purpose, research gap, contribution, and outcome. (Soheilirad et
al., 2017).
14

The findings highlight that supplier selection, supply chain efficiency, and sustainable
practices are the most frequently studied areas. DEA proves promising as an evaluative tool,
especially when traditional production function data is scarce or difficult to obtain. Its ability to
handle multiple inputs and outputs makes it attractive for researchers in supply chain
management and various organizational and industrial contexts.
For example, Li et al. (2012) have used DEA to measure the supply chain efficiency of
the Chinese manufacturing industry. In their findings, DEA highlights where the chain is
inefficient and provides suggestions on how it can be enhanced for leaner and more costeffective supply chain operations.
Furthermore, in sustainable supply chain practices, Wu et al. (2013) used DEA to
measure the environmental efficiency of supply chains. Their research illustrated how DEA
could integrate environmental factors into the efficiency analysis, promoting sustainable
practices by identifying which supply chains achieve a balance between economic and
environmental performance.
Furthermore, Chen et al. (2016) applied DEA to measure the operational efficiency of
logistics companies from a supply chain perspective. Their findings further underscored the
ability of DEA to pinpoint those logistics companies with the opportunity and potential to
improve their operations to improve the supply chains' overall efficiency.
A more advanced application is reported in an article published by the European Journal
of Operational Research, where a two-stage DEA model was applied to evaluate the performance
of a three-tier supply chain involving suppliers, manufacturers, and distributors. This approach

15

helps measure efficiency with respect to the whole chain and various components at every level;
therefore, it does a more detailed analysis. (Tavana, 2015).
Another significant study in the International Journal of Systems Science explored how
DEA can be adapted to consider environmental factors in supply chain performance evaluation.
Their model incorporates undesirable outputs, such as emissions or waste generation, alongside
traditional metrics to provide a holistic assessment that integrates sustainability (Liu et al., 2012).
In conclusion, DEA is, in general, a potent tool in supply chain management, as it can
provide a very robust framework for evaluating and improving performance across several
dimensions, such as supplier selection, overall efficiency, and sustainability. Its flexibility and
the possibility of handling multiple inputs and outputs make it an invaluable resource for
researchers and practitioners seeking to optimize supply chain operations.
Supplier Selection Using Data Envelopment Analysis
Supplier evaluation is a heavily researched topic in the field of purchasing, with various
methodologies ranging from theoretical to empirical and modeling approaches. This paper will
not cover all these studies in detail, as it focuses on quantitative models for supplier evaluation.
Empirical research about supplier evaluation emerged in the 1960s. In this regard, a
seminal study was published by Dickson (1966), which analyzed the factors that industrial
purchasing managers perceive as relevant in supplier evaluation. The findings highlighted cost,
quality, and delivery performance as the top three criteria. Subsequent research has supported
this and developed it further, all about the strategic importance of supplier evaluation and the
trade-offs between cost, quality, and delivery. Other studies have focused on the issue of the
relative importance of supplier attributes. Monczka et al. (1981), Moriarity (1983), Woodside
16

and Vyas (1987), Chapman and Carter (1990), Tullous and Munson (1991), and Weber et al.
(1991) are some of the studies conducted toward this end.
In their review of 74 articles, Weber et al. (1991) found that quality was the most critical
factor, followed by delivery performance and cost. These studies collectively indicate that
supplier evaluation should consider multiple factors rather than focusing solely on cost.
However, they have not developed specific decision models for supplier evaluation.
In a thorough review of supplier selection methods, Weber et al. (1991) found that 47 out
of 74 articles reviewed used multiple criteria. Traditional multi-criteria approaches have included
factors like cost, quality, and delivery, which have gained importance with the focus on Just-InTime (JIT) manufacturing philosophy (Chapman, 1989; Chapman & Carter, 1990). However,
these measures are mainly operational. Table 4 shows the supplier evaluation techniques
categorized by methodological area. Table 4 shows the supplier selection techniques followed by
different methodologies.
Table 4 -Supplier Selection and Evaluation Techniques
Evaluation technique

Authors

Grouping methods

Hinkle et al. (1969)

Weighted linear models

Lamberson et al. (1976)

Weighted linear models

Timmerman (1986)

Matrix method

Gregory (1986)

Analytic hierarchy process

Narasimhan (1983)

Linear programming

Turner (1988)

Linear programming

Pan (1989)
17

Analytic hierarchy process

Hill and Nydick (1992)

Mixed integer programming

Weber and Current (1993)

Multi-objective programming

Weber and Ellram (1993)

Interpretive structural modeling

Mandal and Deshmukh (1994)

Total cost of ownership

Ellram (1995)

DEA

Weber and Desai (1996)

Statistical analysis

Mummalaneni et al. (1996)

Analytic hierarchy process

Barbarosoglu and Yazgac (1997)

Neural networks

Siying et al. (1997)

DEA

Weber et al. (1998)

Discrete choice analysis experiments

Verma and Pullman (1998)

Principal component analysis

Petroni and Braglia (2000)

DEA

Narasimhan et al. (2001)

As depicted in Table 4, Several techniques have employed multiple criteria for evaluating
suppliers. However, many of these techniques face issues such as the absence of objective
methods for assigning factor weights, the lack of relative comparisons of alternative suppliers for
benchmarking and Supplier Development Initiatives (SDI), insufficient emphasis on strategic
level capabilities or practices, and not addressing the issues and reasons behind ineffective
supplier performance.
The use of Data Envelopment Analysis (DEA) as a tool for strategic sourcing of suppliers
has been limited. Few studies have applied DEA for supplier evaluation. For instance,
Kleinsorge et al. (1992) used DEA for performance monitoring of a single supplier over time,
18

but their research did not address strategic supplier selection or benchmarking issues. Weber and
Desai (1996) and Weber et al. (1998) addressed supplier selection and negotiation using DEA,
but they focused solely on operational metrics and relied on a traditional DEA model, which has
certain limitations. Narasimhan et al. (2001) applied DEA for the strategic evaluation of
suppliers by considering various strategic and operational factors. While their approach offered
useful insights into supplier evaluation and rationalization, it was also constrained by traditional
DEA model evaluations. Additionally, their work did not explore the reasons behind differences
in suppliers' efficiency scores and therefore did not propose supplier improvement strategies
A study by Talluri and Narasimhan (2004), DEA was employed to assess the
performance of suppliers by considering multiple input and output criteria. The study revealed
that DEA could effectively identify efficient suppliers and provide insights into improving the
performance of inefficient ones, demonstrating its practical applicability in supplier selection
processes. The study was conducted for a major global telecommunications company. Several
meetings were held to determine the specific product line to be analyzed and to identify the input
and output dimensions for Data Envelopment Analysis (DEA).
Inputs include Quality management practices and systems (QMP), Documentation and
self-audit (SA), Process/manufacturing capability (PMC), Management of the firm (MGT),
Design and development capabilities (DD), Cost reduction capability (CR). The outputs included
Quality, Price, Delivery, Cost reduction performance (CRP) and Other factors. A sample of the
data structure is depicted in Table 5 as follows.

19

Table 5- Data Structure of the DEA used by Talluri and Narasimhan (2004) for supplier
selection research for a large telecommunication entity.

Source: Talluri, S., & Narasimhan, R. (2004). A methodology for strategic sourcing. European
Journal of Operational Research, 154(1), 236–250
One limitation of the study is that it considered only one respondent for each supplier. This
approach may not capture the full spectrum of perspectives and experiences related to the
supplier's performance. Therefore, this study may have a bias of only one respondent or
incomplete information since this is also the view and knowledge of one respondent and not a
comprehensive assessment by different stakeholders of the supplier organization. Thus, this may
influence the accuracy and reliability of the findings and conclusions of the present study.
A study by Zahedi-Seresht et al. (2017) proposed using the area's magnitude under the
efficient curve. In order to estimate this magnitude, they suggest using Monte Carlo simulation
for the complete ranking of originally efficient DMUs to overcome the problems arising from
other ranking methods, which is very simple, computationally. This method generates random
weights for the inputs and outputs in the feasible region and finally derives probability the
DMUs are efficient.

20

Another research by Jahanshahloo & Zahedi Seresht, (2015), utilizes monte carlo method
for ranking extreme efficient units in data envelopment analysis. They highlighted that there
have been so many attempts in the literature which have their pros and cons in ranking extreme
efficient units. They attempt to present a method which does not have any problems and can be
utilized to calculate the rank of extreme efficient units through using the Hit or Miss Monte
Carlo method
Multi-Scenario Data Envelopment Analysis in Supply Selection
The previous section shows that supplier selection in supply chain management is very
important. If properly done, it can influence an organization's ability to be competitive and
sustainable. Traditionally, supplier selection has been approached using different methods, most
of which are normally based on some simplistic metrics or subjective evaluation. Modern-day
supply chains are usually complex, while the traditional assessment methods are too inadequate
to capture the multidimensionality of supplier performance. A major problem in supplier
selection could be that multiple scenarios exist for both inputs and outputs within DMUs.
Multiple responses for inputs and outputs in DMUs are commonplace due to several
factors inherent in supply chain dynamics. Firstly, suppliers may offer various products or
services with characteristics and attributes. For instance, a supplier may deliver multiple raw
materials or components that would differ by quality, cost, and lead time. Alternatively, suppliers
can also have a good many customer segments they sell to, or even operate in various geographic
regions, so their performance may vary across different markets or product lines at different
points in time.

21

Multiple responses pose challenges and opportunities in supplier selection using Data
Envelopment Analysis (DEA). DEA is a non-parametric method that evaluates the relative
efficiency of DMUs based on their input-output relationships. When multiple responses are
available for inputs and outputs, DEA allows for the simultaneous consideration of these diverse
dimensions, providing a comprehensive assessment of supplier performance.
For example, a manufacturing company is to choose the suppliers for one of its critical
components. That company will have to evaluate potential suppliers against multiple criteria,
including cost, delivery time, quality, and flexibility. Each supplier may have different
performance levels across different product lines or regions for each criterion. For example, a
Supplier might offer lower costs but longer lead times in one region while providing high-quality
goods. Conversely, the same supplier might offer a high cost and short lead time with the same
quality for the goods. So there will be two costs values and two lead times which we have to
taken in to account when we incorporate the responses for DEA.
In supply chain management, DMUs such as suppliers may exhibit variability or multiple
responses in their performance for a single input or output due to various factors. For example, a
supplier may offer different price points for the same product or service, reflecting variations in
negotiation strategies, market conditions, or production costs. Similarly, a supplier's delivery
performance may vary across orders or customers, influenced by transportation logistics,
inventory management, or order complexity.
For example, supplier price variability is a common phenomenon influenced by
negotiation tactics, market dynamics, and production costs. Chen and Paulraj (2004) highlight
that suppliers, as a single decision-making unit, may adopt different pricing strategies based on
customer segments, order quantities, and competitive pressures. This pricing variability reflects
22

not merely cost structures but also strategic decisions made to maximize competitive advantage
and market share. For example, a supplier might offer lower prices to large-volume buyers or
strategically essential customers, while higher prices may be quoted to smaller, less frequent
buyers. This variability impacts a firm's procurement decisions and overall supply chain costs,
necessitating sophisticated price analysis, and negotiation strategies to optimize procurement
performance.
The variability in delivery performance among suppliers stems from factors such as
transportation logistics, inventory management practices, and order complexities. Sodhi and
Tang (2012) argue that suppliers' ability to meet delivery commitments fluctuates due to transit
times, production schedules, and inventory availability uncertainties resulting in different values
of responses for a single input/output in a single DMU at different time points. This variability
can manifest in several ways, such as differing lead times for the same product across different
orders, inconsistencies in meeting delivery deadlines, and varying reliability in the quality of
delivered goods. These fluctuations pose quite a challenge to inventory management, production
planning, and customer service as firms have to constantly vary their operations while dealing
with uncertain delivery schedules. For instance, a supplier may reliably manage to meet their
delivery schedules to one client but not another because the order sizes are different, the shipping
routes are different, or priority has been accorded to different clients.
For example, some component in the automotive industry may be received from different
suppliers by a manufacturer. All the suppliers' performances vary because of differences in
production capacity, geographical location, and efficiency of logistic management. One may
deliver high-quality components on time but at higher prices than others, while another has better
prices but less reliable delivery schedules. These multiple factors must be evaluated to optimize
23

the supply chain for cost, quality, and reliability. Also, a single supplier can have different
components in quality and price at different times, leading to multi-scenario responses for data
analysis. In such situations, which data to consider for supply evaluation matters. Should we take
the average of the responses, the maximum, the minimum, or the mode is questionable?
In this multi-scenario context, DEA can be employed to assess the efficiency of each
supplier by considering each scenario separately. This method provides a more granular supplier
performance analysis, highlighting strengths and weaknesses across different conditions. For
instance, DEA can be used to create efficiency frontiers for each scenario, allowing the company
to understand how each supplier performs under varying conditions and to identify which
suppliers consistently perform well across multiple scenarios (Li et al., 2019).
Thus, addressing the variability in supplier performance requires a multi-scenario
analysis approach. This approach evaluates multiple potential outcomes or responses for a single
input /output from a single DMU under different conditions, allowing firms to anticipate and
manage uncertainties better. By doing so, the firm can develop more robust supplier selection
strategies and procurement, inventory management, and production planning strategies.
Thus multi-scenario analysis enables firms to prepare for various kinds of disruptions and
come up with contingency plans that are important in building the capability of maintaining
operations under adverse conditions. Collaborative relationships with suppliers and techniques of
risk management, like dual-sourcing, safety stock, and flexible contracts, become critical in
increasing the ability of supply chains to withstand variability.
As mentioned above, DEA models typically handle precise data and do not account for
uncertain input and output situations. Many scholars have explored these scenarios, considering
24

fuzzy data, interval data, probabilistic data, and other forms of uncertainty in datasets. They have
proposed various approaches to address this, including mean value and variance models, robust
DEA, multiple criteria decision-making (MCDM) models, and several other techniques.
A study by Zahedi-Seresht et al. (2021) addresses cases where multiple alternative
scenarios represent uncertainty in the dataset. The initial model for problems featuring various
alternative scenarios in their inputs and outputs is developed directly from the definition of the
relative efficiency formula, akin to those used in traditional DEA models. Their model was
illustrated using a numerical example with 10 DMUs and three scenarios for input and output
values as depicted in Table 6. They considered single scenarios for inputs which are manpower
and Assets of a engineering company, but multiple scenarios for Output.
Table 6 – Inputs and Outputs for different scenarios

The key contribution of their paper is the development of models to assess efficiency,
considering the existence of multiple alternative scenarios, each with a specified probability of
occurring. Initially, the paper introduces a model based on the traditional CCR framework. This
25

model considers an aggregated Decision Making Unit (DMU), which is defined as the weighted
sum of all possible alternative scenarios.
Also, there can be DMUs with different internal structures. The two-stage DEA model is
a unique version designed to assess the efficiency of Decision-Making Units (DMUs) with a
two-step internal process. In this model, initial inputs are first converted into intermediate
outputs. These intermediate outputs are transformed into the final outputs in the subsequent
stage. A study by M. Alimohammadi Ardekani (2016) emphasizes that traditional Data
Envelopment Analysis (DEA) models assess efficiency based solely on inputs and outputs,
without considering the internal structure of Decision-Making Units (DMUs). Consequently,
these conventional models cannot pinpoint the specific reasons and origins of inefficiency within
the DMUs.
A two-stage DEA model is a specific type of network DEA model designed to measure
the relative efficiency of Decision Making Units (DMUs) with a two-stage internal structure. In
this model, the initial inputs are first transformed into intermediate outputs, which are then
converted into final outputs in the subsequent sub-process. The two-stage DEA model allows for
the decomposition of the overall efficiency of DMUs into the efficiencies of each individual
stage. The authors propose a general method for estimating network efficiency, illustrated
through a case study of the Regional Electricity Company of Iran. The two stages of the DMU
are the Production stage and the Distribution stage. The following is sample data that is used in
their Analysis.

26

Table 7- The results of two-stage DEA models for Iranian Electricity Company

As per table 7, DMUs 2, 4, 7, 9, 11, and 12 have excelled in the production stage, while
DMU1 has performed the worst. In the distribution stage, DMUs 2, 3, and 6 have achieved top
ranks, with DMU8 performing the worst. Despite their top ranks in production, DMUs 4 and 7
did not reach the efficiency frontier in the distribution stage, placing them in an unfavorable
position overall. Further, They emphasize that, even though the traditional two-stage DEA model
assumes that the input/output and intermediate output vectors are free from any uncertainty, realworld scenarios often involve data that is noisy or subject to perturbations, making it necessary
to develop a two-stage DEA model that can handle such variations. Robust optimization (RO)
has emerged as a popular method for addressing data uncertainty. While stochastic programming
(SP) has traditionally been used to manage uncertainty, their paper utilizes the RO which is used
as an alternative for performing sensitivity analysis and addressing the challenges of stochastic
27

programming. Table 8 shows the results of the robust two stage model where the perturbations
are set to 0.05 and 0.10, respectively.
Table 8- The results of robust two-stage DEA models for Iranian Electricity company

The findings show that incorporating perturbations into the data led to changes in the efficiency
rankings of decision-making units. This underscores the significant influence that data
uncertainty can have on these rankings.
Data of Interest
Overview for Data
Canada has one of the most sophisticated and innovative indoor agriculture industries in
the world, with global market successes. The greenhouse vegetable and mushroom industries are
substantive parts of Canadian agriculture and a major economic driver for Canada as a whole.
According to the Statistical overview of the Canadian greenhouse vegetable and mushroom
industry, in 2023, these two sectors saw $2.2 billion in farm gate sales in 2022, thereby
28

underlining the economic importance of the businesses in question. The export value also
reached approximately $1.9 billion, which clearly underlined Canada's leading position in the
world markets. Of the large number of crops produced in Canadian greenhouses, tomatoes,
peppers, and cucumbers hold top places. In 2022, these three vegetables represented 96% of the
total production of greenhouse vegetables. This significant concentration illustrates the
specialized focus and expertise within the industry, ensuring high-quality produce that meets
domestic and international demand. The continued successes and growth are thus a reflection of
the commitment to ensure that Canada remains competitive based on insemination of technology
and agricultural innovation
Canadian greenhouse growers have been making huge investments in modern
greenhouses to raise volumes and answer demands for fresh vegetables throughout the year.
Nowadays, a significant portion of greenhouse facilities across Canada is highly automated. This
trend reflects a widespread commitment among growers to adopt the latest technological
advancements continually. By doing so, they aim to enhance production efficiency, minimize
labor costs and inputs, and improve the quality of their products. The drive towards embracing
innovative technologies has empowered farmers to extend the natural harvest seasons, thereby
achieving continuous gains in efficiency. These improvements have significantly boosted the
competitiveness of Canadian greenhouse growers and led to noticeable enhancements in product
quality.
The Canadian vegetable greenhouse industry is strategically concentrated near the
southern border with the United States. Notable regions include the Fraser Valley in British
Columbia, Southern Ontario, and Quebec. These locations offer several advantages: they are

29

close to major consumer markets, have access to efficient transportation networks, and provide
favorable growing conditions. This strategic positioning not only supports the logistics of
distributing fresh produce but also optimizes growing conditions, contributing to the overall
success and sustainability of the industry.
Recent Statistics
There were 934 commercial greenhouse vegetable operations in Canada in 2022. These
produced a remarkable 752,685 metric tons of vegetables. This indicates an increase of 5% in the
number of operations and 7% in production from 2021, the year prior. Ontario continued to
dominate the industry regarding the production of greenhouse vegetables, contributing about
71% of the country's total output. British Columbia was next in contribution at 14.5%, followed
by Quebec at 8%. The remaining 6.5% of greenhouse vegetable production was distributed
among the other provinces. The data indicates the continuing growth of Canada's greenhouse
vegetable industry and regional distribution.
These producers cultivate a wide variety of crops, including tomatoes, cucumbers,
lettuce, bell peppers, green and yellow beans, eggplants, strawberries, various herbs, and
microgreen vegetables. However, tomatoes, cucumbers, and bell peppers are the main crops
grown by the majority of producers; these are the three major greenhouse vegetable crops
produced in Canada.
Tomatoes occupy the largest share and contribute 36% to sales in the greenhouse
vegetable sector. The next in line are cucumbers, with 33%, and finally, bell peppers with 25%
of the sales. All three of these crops together build the foundation of Canada's greenhouse
vegetable market, defining their role for the entire farmed produce.
30

The economic impact of this greenhouse production of fruits and vegetables has been
high. In 2022, total sales in that sector were up 11 percent over the previous year to a record $2.2
billion. To further put this change into perspective, these increases are part of a longer trend of
yearly rises beginning all the way back in 2013, which speaks to the solid and continued growth
and escalating importance of greenhouse agriculture to Canada's economy. This steady increase
is a pointer to increased demand for greenhouse-grown produce, coupled with better
technologies and farming practices that achieve productivity and efficiency gains in the industry.
In 2022, the value of greenhouse vegetable exports from Canada increased significantly
from 2021 by 7.5 percent to over $1.4 billion, making it the most valuable category of all fresh
produce exports in the country, including fruits, mushrooms, field vegetables, and potatoes, and
accounting for 39% of the total value of all fresh produce exports. Cucumbers, peppers, and
tomatoes dominated the greenhouse vegetable production market. Each of these types of
vegetables held quite a share of export value: cucumbers and peppers had 34%, while tomatoes
had 32%.
Mushroom production, like greenhouse vegetables, occurs in a controlled environment
and is a year-round activity. In this dark, specially climatized setting, growing conditions are
optimized by controlling temperature and humidity. Mushroom growing is a continuous process
with 24 hours a day, 7 days a week harvesting. Canadian mushroom growers produced 139,090
metric tonnes of mushrooms in 2022, up 0.9 percent from the previous year. The gain was
supported by a 1.8 percent increase in cultivated area and 7.2 percent increase in harvested area.
Improvement to the financial performance of the mushroom industry occurred in 2022.
The total value of mushrooms sold leaped by 6.3 percent to $694.5 million as fresh and
31

processed prices went up. Ontario and British Columbia continue to be Canada's leading
mushroom-producing provinces, with the two accounting for about 93 percent of the total value
of Canadian mushrooms. Ontario alone accounted for over half of the country's volume.
Regarding exports, the United States continued to be the largest market for Canadian
mushrooms, much like the trend for greenhouse vegetable exports. Over 97% of the value of
fresh mushroom exports was destined for the U.S. Over the past five years, the value of
mushroom exports increased by 66% to USD 446.0 million in 2022. This clearly indicates the
rise in demand and market value for Canadian mushrooms in the global market, particularly in
the United States.
COVID vs Greenhouse Revenue
Food security is becoming of critical importance to society, driven by the challenge of
feeding a global population that is projected to be 9.6 billion by the year 2050. This is further
complicated by the continued decrease in the availability of arable land. Recent disruptions to
international trade, largely a product of responses to the COVID-19 pandemic, have again
brought into focus the need for countries to be self-sufficient in food production.
In the case of Canada, the country is nearly self-sufficient in terms of most foodstuffs
specified—including, of course, meat and dairy. At the same time, in terms of fresh vegetables, it
relies on international imports. This dependency on global supply chains really exposes
Canadian food security to several international trade disruption scenarios.
One of the most promising solutions to this vulnerability is in the expansion of the
greenhouse vegetable industry. All year round, greenhouses can credibly produce fresh
32

vegetables, independent of climatic conditions outside. With advanced agricultural technologies,
greenhouses can stake a claim to provide fresh produce on a stable and continuous basis. This
move toward localizing food production will significantly increase Canada's self-sufficiency in
food and minimize the risks associated with reliance upon international imports.
This could add further to the benefits accruing from the development of the greenhouse
industry in terms of the number of jobs it could create within the agricultural value chain,
stimulating the economy while helping the environment with a reduced carbon footprint from the
transportation of food over long distances. Therefore, by investing and expanding its greenhouse
vegetable production, Canada can take giant steps toward ensuring that it has a food supply
resilient to the next global shocks.
The COVID-19 pandemic has evidenced how the application of adapted supplier
selection criteria will go a long way in ensuring supply chain resilience. Given changes that were
happening in consumer behavior and disruptions to supply chains, many operators in Canada had
to adapt rapidly during the outbreak of COVID-19.
This adaptability included selecting suppliers who can ensure timely and reliable
deliveries despite global transport challenges. With that, the selection of suppliers has moved
further towards local suppliers to drive down risks in international shipping delays and border
restrictions. This move also impinged directly on the efficiency indicators, where the dependency
on local suppliers reduced lead times and transportation costs, improving overall supply chain
efficiency.

33

Coming off the challenges of 2020, there is an obvious question for the Canadian
greenhouse sector. Will 2021, declared by the United Nations to be the International Year of
Fruits and Vegetables, be as successful? Based on Farm Credit Canada, greenhouse sales in 2020
showed a 9.4% year-over-year increase, thanks to a good fruit and vegetable crop. A number of
challenges, though, may keep this growth from carrying over into 2021. Rising operational costs,
plus appreciation of the Canadian dollar, may prove to be the most significant challenge to
producers.
In a year ruled by the COVID-19 pandemic, greenhouse-grown fresh vegetables have notched up
their fastest growth in receipts since 2012. For the eighth year in a row, greenhouse-grown fresh
vegetables recorded a 12.3% jump to $1.8 billion in 2020 (as seen in Figure 1). This spectacular
growth was off the back of a solid performance in 2019, where sales grew 5.0% to end at $1.6
billion.
As soon as the pandemic arrived, operators in greenhouses had to adapt to new ways of
consumer behavior such as curbside pickup and online shopping, boosting farm cash receipts by
an astonishing 19.8% year-over-year in the first quarter of 2020. That continued into second and
third quarters, all suggesting that one key factor to sustaining growth was quick adaptation in the
sector to the challenges posed by the pandemic. These changes underscored the sector's agility in
response to the pandemic, emphasizing the importance of having a flexible supply chain and
efficient supplier selection processes.

34

Figure 1 – Canadian Greenhouse fresh vegetable cash receipts

Source- Despite remarkable greenhouse sales in 2020 – uncertainty lies in the year ahead | FCC.
(n.d.). https://www.fcc-fac.ca/en/knowledge/economics/greenhouse-sales
Within the period of 2015-2020, greenhouse areas allocated for fruit and vegetable production
increased drastically by 23.9%. Last year, it rose to a total capacity of 1,809 hectares. This
growth was reflected in the increased production of peppers and cucumbers, which are two of the
three primary fresh vegetables produced in large quantities. In contrast, tomato production,
despite being the largest in terms of both value and volume, experienced a slight decline of 3.2%.
Nevertheless, tomatoes continued to lead sales growth, pulling off an impressive 12.1% increase.
Next came cucumbers with a sales rise of 9.4%, followed by peppers with 7.3%. The trio of
tomato, cucumber, and pepper sales accounted for 92.5%, thereby giving strong support to their
leading position in the market.
The bottom line is that the COVID-19 pandemic accelerated the need for a supply chain in the
agriculture sector to be both efficient and resilient. Notably, it concerns greenhouse vegetable
production. Investment in local suppliers and more efficient supply chain practices would
accordingly enhance Canada's food security by lessening its reliance on international imports and
saving up a resilient supply of food for whatever global shock might come.
35

Inputs and Outputs for DEA
To illustrate the proposed mathematical model for multi-scenario Data Envelopment
Analysis (DEA), we will use data from greenhouse, sod, and nursery operations across Canada,
sourced from Statistics Canada in 2024. This model focuses on evaluating the efficiency of these
operations over multiple years. The output variable in our analysis is the total value of
greenhouse products produced. The input variables comprise various operating expenses
incurred by specialized greenhouse producers. These expenses are categorized into several
distinct types, which we will treat as separate inputs in the DEA model. Specifically, we consider
expenses related to specialized greenhouse vegetables and specialized greenhouse flowers and
plants.
Our multi-scenario approach involves analyzing data collected over five years: 2019,
2020, 2021, 2022, and 2023. This longitudinal dataset allows us to assess trends and changes in
efficiency over time. The data serves a crucial role for federal and provincial agricultural
departments, as well as producer associations, by aiding in market trend analysis and examining
domestic production with a particular focus on import dynamics. Additionally, this survey
contributes to the agricultural receipts program of Statistics Canada, ultimately feeding into the
System of National Accounts.
Agriculture and Agri-Food Canada, along with other federal departments, utilize this
information to develop and administer agricultural policies. Provincial departments leverage the
data for production and price analysis, as well as for economic research. The survey is
administered under the Integrated Business Statistics Program (IBSP), which consolidates
approximately 200 individual business surveys into a cohesive master survey program. The IBSP
36

aims to collect detailed industry and product information at the provincial level while
minimizing redundancy across different survey questionnaires.
For the purpose of this analysis, we will focus on three key provinces: British Columbia,
Ontario, and Quebec. These provinces will serve as the three decision-making units (DMUs) in
our DEA model. Within each province, farms are classified into one of four categories based on
their involvement in greenhouse, sod, and nursery activities, as well as their primary North
American Industry Classification System (NAICS) code. The four categories are:
1.

Greenhouse - Floriculture

2.

Greenhouse - Other

3.

Sod

4.

Nursery

Farms that produce multiple commodities are assigned to a category based on the
predominant contribution of each commodity at the provincial level. The combination of these
categories and provinces forms what is known as the sampling cell for our analysis.
The target population for this study includes all entities operating greenhouse, sod, or
nursery operations that meet Statistics Canada's definition of a farm. A farm is defined as an
operation that produces at least one agricultural product and reports revenue and/or expenses
related to that production to the Canada Revenue Agency. Certain small populations are
excluded from the target population of the Annual Greenhouse, Sod, and Nursery Survey. These
exclusions include farms in Canada's three territories, institutional farms, community farms,
greenhouses that produce marijuana, and greenhouses or nurseries that produce tree seedlings for
reforestation.

37

Input - Specialized greenhouse producers' operating expenses
There are primarily two categories of greenhouse producers: those that specialize in greenhouse
vegetables and those that specialize in greenhouse flowers and plants. These categories exclude
mixed operations (involving both vegetables and flowers/plants) and cannabis operations. The
total expenses for each category are determined by summing several specific types of costs.
For greenhouse vegetable producers, the total expenses encompass the following:
•

Plant Material Purchases for Growing On: This includes the cost of acquiring flowers,
plants, cuttings, seedlings, seeds, and bulbs that are intended to be grown on-site. The value
is calculated before any sales tax is applied.

•

Plant Material Purchases for Resale: This covers the expense of buying flowers, plants,
cuttings, seedlings, seeds, and bulbs for the purpose of resale, also before sales tax.

•

Gross Yearly Payroll: This accounts for the total wages paid to both seasonal and
permanent laborers employed by the greenhouse operation.

•

Electricity Costs: These are the expenses related to electricity usage for various purposes
such as lighting, running airflow fans, and heating within the greenhouse.

•

Fuel Costs: This includes all fuel-related expenses incurred for the operation of the
greenhouse.

•

Other Crop Expenses: This category encompasses a wide range of costs associated with
crop production, including fertilizers, pesticides, pollination services, irrigation, containers,
packaging, bioprograms, and growing mediums like soil, peat moss, vermiculite, perlite,
sand, Styrofoam, and sawdust.

38

•

Other Operating Expenses: These are additional expenses necessary for running the
greenhouse operation. They include interest payments, land taxes, insurance premiums,
advertising costs, repairs to farm buildings, machinery, agricultural equipment, and vehicles,
costs of contract work, and expenses related to telephone and telecommunications services.

Similarly, for greenhouse flower and plant producers, the total expenses include the same
categories as listed above:
•

Plant Material Purchases for Growing On: The value of flowers, plants, cuttings,
seedlings, seeds, and bulbs purchased for cultivation, calculated before sales tax.

•

Plant Material Purchases for Resale: The cost of flowers, plants, cuttings, seedlings, seeds,
and bulbs bought for resale, also before sales tax.

•

Gross Yearly Payroll: The total wages paid to both seasonal and permanent employees.

•

Electricity Costs: Expenses for electricity used for lighting, airflow fans, and heating.

•

Fuel Costs: All fuel-related expenses for the operation of the greenhouse.

•

Other Crop Expenses: Costs related to fertilizers, pesticides, pollination, irrigation,
containers, packaging, bioprograms, and growing mediums such as soil, peat moss,
vermiculite, perlite, sand, Styrofoam, and sawdust.

•

Other Operating Expenses: Additional operational costs including interest payments, land
taxes, insurance, advertising, repairs to buildings, machinery, agricultural equipment, and
vehicles, contract work, and telephone and telecommunications services.

By considering all these specific types of expenses, we can accurately determine the total
expenses for both specialized greenhouse vegetable and specialized greenhouse flower and plant
operations.
39

Producers

Table 9 – Greenhouse Producers Operating Expenses in British Colombia (in Dollars)
Geography
Expenses

British Colombia
2019

2020

2021

2022

2023

Specialized greenhouse flower and plant

Specialized greenhouse vegetable

Plant material
purchases for
21,519,817
27,276,523 23,317,772
22,990,864
20,606,968
growing on
Plant material
purchases for
0
0
0
0
0
resale
Gross yearly
67,227,559
73,003,694 79,709,266
80,127,442
80,431,798
payroll
Electricity
5,240,308
5,984,723
6,099,920
6,871,855
6,228,145
Fuel
29,186,819 29,363,914 28,435,349
32,494,227
32,708,966
Other crop
46,177,481
60,015,564 59,962,203
63,810,630
64,695,604
expenses
Other
operating
60,823,849
53,045,269 54,839,394
57,937,017
58,009,193
expenses
Total
operating
230,175,833 248,689,687 252,363,903 264,232,035 262,680,674
expenses
Plant material
purchases for
39,412,071
48,923,400 53,778,894
55,817,591
52,798,755
growing on
Plant material
purchases for
11,500,828
11,982,077 17,598,720
17,793,794
15,406,573
resale
Gross yearly
55,038,249
65,754,148 71,524,705
72,593,871
77,511,029
payroll
Electricity
5,866,190
7,096,710
6,806,997
7,462,695
7,593,961
Fuel
8,491,207
9,639,198 10,582,885
11,431,840
12,857,194
Other crop
28,105,213
30,682,080 33,808,409
34,812,582
35,439,222
expenses
Other
operating
32,829,159
28,883,018 32,467,212
33,094,951
39,058,410
expenses
Total
operating
181,242,917 202,960,631 226,567,822 233,007,324 240,665,144
expenses
Source- Statistics Canada. Table 32-10-0025-01 Specialized greenhouse producers' operating expenses

40

Specialized greenhouse flower and plant

Specialized greenhouse vegetable

Producers

Table 10 - Greenhouse Producers Operating Expenses in Ontario (in Dollars)
Geography
Expenses

Ontario
2019

2020

2021

2022

2023

Plant material
purchases for
96,398,673 107,006,294
122,041,230
132,697,073
137,179,630
growing on
Plant material
purchases for
0
0
0
0
0
resale
Gross yearly
258,822,641 289,405,268
354,291,694
377,127,111
389,508,955
payroll
Electricity
22,236,382 26,221,262
36,253,539
37,494,931
43,494,120
Fuel
99,888,431 103,064,533
115,796,766
120,708,555
129,462,119
Other crop
167,517,248 180,527,603
207,903,337
247,370,590
269,598,142
expenses
Other
operating
209,826,056 260,323,454
268,258,835
292,804,007
330,275,890
expenses
Total
operating
854,689,431 966,548,414 1,104,545,402 1,208,202,267 1,299,518,856
expenses
Plant material
purchases for
116,984,393 117,114,919
124,736,489
128,424,019
131,377,771
growing on
Plant material
purchases for
78,565,367 79,058,179
58,086,222
60,078,075
69,239,946
resale
Gross yearly
165,233,241 158,110,005
156,074,932
159,735,990
182,702,743
payroll
Electricity
13,736,008 14,011,733
10,146,487
12,472,842
14,976,041
Fuel
29,440,026 22,218,312
23,458,257
25,172,680
30,652,589
Other crop
90,533,964 91,949,279
98,325,549
126,304,382
132,312,398
expenses
Other
operating
113,517,481 126,025,519
132,308,286
137,429,016
150,329,879
expenses
Total
operating
608,010,480 608,487,946
603,136,222
649,617,004
711,591,369
expenses
Source- Statistics Canada. Table 32-10-0025-01 Specialized greenhouse producers' operating expenses
41

Producers

Table 11 - Greenhouse Producers Operating Expenses in Quebec (in Dollars)
Geography
Expenses

Quebec
2019

2020

2021

2022

2023

Specialized greenhouse flower and plant

Specialized greenhouse vegetable

Plant material
purchases for
6,017,566
6,455,788
7,074,880
7,990,710
7,959,193
growing on
Plant material
purchases for
0
0
0
0
0
resale
Gross yearly
30,909,289
38,585,698
49,847,384
51,268,987 51,750,570
payroll
Electricity
7,471,815
7,699,720
11,586,660
11,867,188 12,055,220
Fuel
9,211,085
8,469,340
10,131,665
10,628,727 11,344,359
Other crop
16,953,893
19,183,207
27,314,033
27,937,367 24,936,979
expenses
Other
operating
19,327,580
22,762,635
31,169,028
31,847,033 24,705,908
expenses
Total
operating
89,891,228 103,156,388 137,123,650
141,540,012 132,752,229
expenses
Plant material
purchases for
25,969,415
25,706,469
17,413,924
22,411,362 23,252,384
growing on
Plant material
purchases for
7,294,212
9,328,448
12,965,656
13,096,244 12,108,571
resale
Gross yearly
38,240,437
36,869,261
39,385,096
39,962,938 45,693,275
payroll
Electricity
2,791,885
2,239,668
2,072,583
2,197,625
2,747,157
Fuel
10,554,802
9,406,911
7,793,968
8,002,060
9,314,974
Other crop
17,541,982
19,135,521
18,233,712
21,152,594 21,878,127
expenses
Other
operating
21,237,890
20,408,729
21,789,628
22,534,052 23,180,953
expenses
Total
operating
123,630,623 123,095,007 119,654,567
129,356,875 138,175,442
expenses
Source- Statistics Canada. Table 32-10-0025-01 Specialized greenhouse producers' operating expenses
42

Output- Total value of greenhouse products
The output considered in the study is the Total value of sales, which comprises two main
components: Fruit and vegetable sales, and Flower and plant sales and resales.
1. Fruit and vegetable sales: This category represents the value of produce sold directly from
farms, excluding taxes. It encompasses a variety of items, including greenhouse Chinese
vegetables, herbs, and sprouts.
2. Flower and plant sales and resales:
o

Flower and plant sales: The value of flowers and plants sold directly from farms,
excluding sales tax. Notably, this category does not include sales related to cannabis.

o

Flower and plant resales: This include the resale value of flowers and plants, representing
transactions where previously sold items are sold again.

In summary, the study analyzes the overall sales revenue generated from these agricultural
sectors, distinguishing between direct sales of fruits, vegetables, flowers, and plants from farms,
and subsequent resale activities within the flower and plant market.
Table 12- consists of the Output data components for British Colombia (in Dollars)
Geography

British Columbia
2019

Scenario
Fruit and vegetable sales
Flower and plant sales and
resales
Flower and plant sales
Flower and plant resales
Total greenhouse sales

2020

2021

2022

2023

306,335,083

329,623,922 322,817,515 349,544,705

369,109,987

342,733,310

400,565,796 452,481,666 487,795,340

514,430,769

316,254,990
26,478,320

365,706,725 410,072,083 440,756,031
34,859,071 42,409,583 47,039,309

455,614,010
58,816,759

649,068,393

730,189,718 775,299,181 837,340,045

883,540,756

Source- Statistics Canada. Table 32-10-0023-01 Total value of greenhouse products
43

Table 13- Output data components for Ontario (in Dollars)
Geography
Ontario
Scenario
2019
2020
2021
2022
2023
Fruit and
1,067,387,947 1,190,662,602 1,300,512,754 1,509,966,196 1,667,977,048
vegetable sales
Flower and plant
817,586,186
839,461,539
913,740,368 1,007,274,383 1,047,366,136
sales and resales
Flower and plant
705,592,622
724,641,118
804,652,953
894,655,878
924,105,092
sales
Flower and plant
111,993,564
114,820,421
109,087,415
112,618,505
123,261,044
resales
Total greenhouse
1,884,974,133 2,030,124,141 2,214,253,122 2,517,240,579 2,715,343,184
sales
Source- Statistics Canada. Table 32-10-0023-01 Total value of greenhouse products
Table 14 - Output data components for Quebec (in Dollars)
Geography
Quebec
Scenario
2019
2020
2021
2022
2023
Fruit and vegetable
146,811,420
174,061,503 211,307,863
248,311,808 269,349,188
sales
Flower and plant
215,194,730
240,733,354 267,282,090
271,714,624 273,384,629
sales and resales
Flower and plant
193,479,561
215,999,546 238,621,177
245,331,325 248,375,888
sales
Flower and plant
21,715,169
24,733,808 28,660,913
26,383,299
25,008,741
resales
Total greenhouse
362,006,150
414,794,857 478,589,953
520,026,432 542,733,817
sales
Source- Statistics Canada. Table 32-10-0023-01 Total value of greenhouse products
The following tables consist of the summarized data, including inputs and outputs for each
scenario and each DMU collectively.

44

966,548,414
1,104,545,402 252,363,903
1,208,202,267 264,232,035
1,299,518,856 262,680,674
608,010,480
608,487,946
603,136,222
649,617,004
711,591,369

1,884,974,133 649,068,393
2,030,124,141 730,189,718
2,214,253,122 775,299,181
2,517,240,579 837,340,045
2,715,343,184 883,540,756

103,156,388
137,123,650
141,540,012
132,752,229
123,630,623
123,095,007
119,654,567
129,356,875
138,175,442
362,006,150
414,794,857
478,589,953
520,026,432
542,733,817

240,665,144

233,007,324

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 730,189,718𝑢𝑢1
Subject to
730,189,718𝑢𝑢1 − 248,689,687𝑣𝑣1 − 202,960,631𝑣𝑣2 ≤ 0
2,030,124,141𝑢𝑢1 − 966,548,414𝑣𝑣1 − 608,487,946𝑣𝑣2 ≤ 0
414,794,857𝑢𝑢1 − 103,156,388𝑣𝑣1 − 123,095,007𝑣𝑣2 ≤ 0
2023

2022

Input 2
2021

2020

2019

2023

2022

2021

2020

2019

2023

2022

2021

2020

2019

Scenarios DMU

Input 1

226,567,822

202,960,631

181,242,917

248,689,687

230,175,833

854,689,431

89,891,228

BC

Ontario

Quebec

Table 15- Input data for all the DMU’s

Output

Developing the Mathematical Model for each DMU

DEA model for BC 2019

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 649,068,393𝑢𝑢1
Subject to
649,068,393𝑢𝑢1 − 230,175,833𝑣𝑣1 − 181,242,917𝑣𝑣2 ≤ 0
1,884,974,133𝑢𝑢1 − 854,689,431𝑣𝑣1 − 608,010,480𝑣𝑣2 ≤ 0
362,006,150𝑢𝑢1 − 89,891,228𝑣𝑣1 − 123,630,623𝑣𝑣2 ≤ 0
230,175,833𝑣𝑣1 + 181,242,917𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for BC 2020

45

DEA model for BC 2021

248,689,687𝑣𝑣1 + 202,960,631𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 775,299,181𝑢𝑢1
Subject to
775,299,181𝑢𝑢1 − 252,363,903𝑣𝑣1 − 226,567,822𝑣𝑣2 ≤ 0
2,214,253,122𝑢𝑢1 − 1,104,545,402𝑣𝑣1 − 603,136,222𝑣𝑣2 ≤ 0
478,589,953𝑢𝑢1 − 137,123,650𝑣𝑣1 − 119,654,567𝑣𝑣2 ≤ 0
252,363,903𝑣𝑣1 + 226,567,822𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for BC 2022

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 837,340,045𝑢𝑢1
Subject to
837,340,045𝑢𝑢1 − 264,232,035𝑣𝑣1 − 233,007,324𝑣𝑣2 ≤ 0
2,517,240,579𝑢𝑢1 − 1,208,202,267𝑣𝑣1 − 649,617,004𝑣𝑣2 ≤ 0
520,026,432𝑢𝑢1 − 141,540,012𝑣𝑣1 − 129,356,875𝑣𝑣2 ≤ 0
264,232,035𝑣𝑣1 + 233,007,324𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for BC 2023

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 883,540,756𝑢𝑢1
Subject to
883,540,756𝑢𝑢1 − 262,680,674𝑣𝑣1 − 240,665,144𝑣𝑣2 ≤ 0
2,715,343,184𝑢𝑢1 − 1,299,518,856𝑣𝑣1 − 711,591,369𝑣𝑣2 ≤ 0
542,733,817𝑢𝑢1 − 132,752,229𝑣𝑣1 − 138,175,442𝑣𝑣2 ≤ 0
262,680,674𝑣𝑣1 + 240,665,144𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Ontario 2019

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 1,884,974,133𝑢𝑢1
Subject to
649,068,393𝑢𝑢1 − 230,175,833𝑣𝑣1 − 181,242,917𝑣𝑣2 ≤ 0
1,884,974,133𝑢𝑢1 − 854,689,431𝑣𝑣1 − 608,010,480𝑣𝑣2 ≤ 0
362,006,150𝑢𝑢1 − 89,891,228𝑣𝑣1 − 123,630,623𝑣𝑣2 ≤ 0
854,689,431𝑣𝑣1 + 608,010,480𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Ontario 2020
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 2,030,124,141𝑢𝑢1

46

Subject to
730,189,718𝑢𝑢1 − 248,689,687𝑣𝑣1 − 202,960,631𝑣𝑣2 ≤ 0
2,030,124,141𝑢𝑢1 − 966,548,414𝑣𝑣1 − 608,487,946𝑣𝑣2 ≤ 0
414,794,857𝑢𝑢1 − 103,156,388𝑣𝑣1 − 123,095,007𝑣𝑣2 ≤ 0
966,548,414𝑣𝑣1 + 608,487,946𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀

DEA model for Ontario 2021

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 2,214,253,122𝑢𝑢1
Subject to
775,299,181𝑢𝑢1 − 252,363,903𝑣𝑣1 − 226,567,822𝑣𝑣2 ≤ 0
2,214,253,122𝑢𝑢1 − 1,104,545,402𝑣𝑣1 − 603,136,222𝑣𝑣2 ≤ 0
478,589,953𝑢𝑢1 − 137,123,650𝑣𝑣1 − 119,654,567𝑣𝑣2 ≤ 0
1,104,545,402𝑣𝑣1 + 603,136,222𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Ontario 2022

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 2,517,240,579𝑢𝑢1
Subject to
837,340,045𝑢𝑢1 − 264,232,035𝑣𝑣1 − 233,007,324𝑣𝑣2 ≤ 0
2,517,240,579𝑢𝑢1 − 1,208,202,267𝑣𝑣1 − 649,617,004𝑣𝑣2 ≤ 0
520,026,432𝑢𝑢1 − 141,540,012𝑣𝑣1 − 129,356,875𝑣𝑣2 ≤ 0
1,208,202,267𝑣𝑣1 + 649,617,004𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Ontario 2023
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 2,715,343,184𝑢𝑢1
Subject to
883,540,756𝑢𝑢1 − 262,680,674𝑣𝑣1 − 240,665,144𝑣𝑣2 ≤ 0
2,715,343,184𝑢𝑢1 − 1,299,518,856𝑣𝑣1 − 711,591,369𝑣𝑣2 ≤ 0
542,733,817𝑢𝑢1 − 132,752,229𝑣𝑣1 − 138,175,442𝑣𝑣2 ≤ 0
1,299,518,856𝑣𝑣1 + 711,591,369𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Quebec 2019

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 362,006,150𝑢𝑢1
Subject to
649,068,393𝑢𝑢1 − 230,175,833𝑣𝑣1 − 181,242,917𝑣𝑣2 ≤ 0
1,884,974,133𝑢𝑢1 − 854,689,431𝑣𝑣1 − 608,010,480𝑣𝑣2 ≤ 0
362,006,150𝑢𝑢1 − 89,891,228𝑣𝑣1 − 123,630,623𝑣𝑣2 ≤ 0

47

89,891,228𝑣𝑣1 + 123,630,623𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀

DEA model for Quebec 2020

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 414,794,857𝑢𝑢1
Subject to
730,189,718𝑢𝑢1 − 248,689,687𝑣𝑣1 − 202,960,631𝑣𝑣2 ≤ 0
2,030,124,141𝑢𝑢1 − 966,548,414𝑣𝑣1 − 608,487,946𝑣𝑣2 ≤ 0
414,794,857𝑢𝑢1 − 103,156,388𝑣𝑣1 − 123,095,007𝑣𝑣2 ≤ 0
103,156,388𝑣𝑣1 + 123,095,007𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Quebec 2021

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 478,589,953𝑢𝑢1
Subject to
775,299,181𝑢𝑢1 − 252,363,903𝑣𝑣1 − 226,567,822𝑣𝑣2 ≤ 0
2,214,253,122𝑢𝑢1 − 1,104,545,402𝑣𝑣1 − 603,136,222𝑣𝑣2 ≤ 0
478,589,953𝑢𝑢1 − 137,123,650𝑣𝑣1 − 119,654,567𝑣𝑣2 ≤ 0
137,123,650𝑣𝑣1 + 119,654,567𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Quebec 2022

𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 520,026,432𝑢𝑢1
Subject to
837,340,045𝑢𝑢1 − 264,232,035𝑣𝑣1 − 233,007,324𝑣𝑣2 ≤ 0
2,517,240,579𝑢𝑢1 − 1,208,202,267𝑣𝑣1 − 649,617,004𝑣𝑣2 ≤ 0
520,026,432𝑢𝑢1 − 141,540,012𝑣𝑣1 − 129,356,875𝑣𝑣2 ≤ 0
141,540,012𝑣𝑣1 + 129,356,875𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀
DEA model for Quebec 2023
𝑀𝑀𝑀𝑀𝑀𝑀 𝜃𝜃 = 542,733,817𝑢𝑢1
Subject to
883,540,756𝑢𝑢1 − 262,680,674𝑣𝑣1 − 240,665,144𝑣𝑣2 ≤ 0
2,715,343,184𝑢𝑢1 − 1,299,518,856𝑣𝑣1 − 711,591,369𝑣𝑣2 ≤ 0
542,733,817𝑢𝑢1 − 132,752,229𝑣𝑣1 − 138,175,442𝑣𝑣2 ≤ 0
132,752,229𝑣𝑣1 + 138,175,442𝑣𝑣2 = 1
𝑢𝑢1 , 𝑣𝑣1 , 𝑣𝑣2 , ≥ 𝜀𝜀

48

The above mathematical equations were solved using Python's Pyomo Library (queries attached
in the Appendix), and the results are reported in the following table.
Table 16- Efficiency score of each DMU for different scenarios
DMU

Scenario

BC

Ontario

Quebec

2019

1

1

1

2020

1

0.927356472

1

2021

0.880219281

0.917862352

1

2022

0.893915332

0.963898794

1

2023

0.934667996

0.971489329

1

0.941760522

0.956121389

1

Average Efficiency

The table displays the efficiency scores for each DMU across five different years, from
2019 to 2023, as well as their average efficiency over this period. An efficiency score of 1
indicates that the DMU is operating on the efficiency frontier, meaning it is fully efficient
relative to the other DMUs being evaluated. Scores below 1 indicate inefficiency, with the value
representing the proportion of maximum possible efficiency achieved.
In 2019, all three DMUs, namely BC, Ontario, and Quebec, achieved an efficiency score
of 1. This result indicates that during this year, all three provinces were operating at maximum
efficiency. Moving into 2020, Quebec and BC remained fully efficient with scores of 1.
However, Ontario's efficiency dropped slightly to 0.927356472. This change suggests that
Ontario was operating at approximately 92.74% of its potential efficiency during this period. In

49

2021, Quebec maintained its efficiency score of 1, whereas BC and Ontario experienced declines
in their efficiency. BC's efficiency score fell to 0.880219281, and Ontario's efficiency score
dropped to 0.917862352. These scores indicate that BC and Ontario were less efficient in 2021
than Quebec. By 2022, Quebec sustained its full efficiency with a score of 1. BC and Ontario
showed improvements, with efficiency scores rising to 0.893915332 and 0.963898794,
respectively. This improvement suggests a positive trend in the efficiency of these provinces.
Finally, in 2023, Quebec again achieved a score of 1, reflecting full efficiency. BC and Ontario
continued to improve, with their scores increasing to 0.934667996 and 0.971489329,
respectively. These results indicate a consistent upward trend in the efficiency of BC and
Ontario.
Table 17- Ranking of DMU’s according to the efficiency measure
DMU

Average Efficiency

Rank

Quebec

1

1

Ontario

0.956121389

2

BC

0.941760522

3

Table 17 presents the average efficiency scores and rankings for three provinces over the
specified period. Quebec achieved the highest average efficiency score of 1, securing the 1st
rank. Ontario followed with an average efficiency score of 0.956121389, placing it in the 2nd
rank. British Columbia had the lowest average efficiency score of 0.941760522, resulting in the
3rd rank. This indicates that Quebec consistently performed at full efficiency, while Ontario and
BC, though improving over time, still have some efficiency gaps to address.
50

Conclusions
This paper is aimed at applying DEA in supplier selection in the supply chain industry in
the presence of multiple scenarios. DEA is a non-parametric approach for assessing the relative
efficiency of DMUs based on input–output ratios relative to their peers.
The research uses data from greenhouse, sod, and nursery operations across Canada,
sourced from Statistics Canada in 2024. The DEA model evaluates the efficiency of these
operations over multiple years, specifically focusing on three key provinces: British Columbia,
Ontario, and Quebec.
The output variable in the analysis is the total value of greenhouse products produced,
while the input variables include various operating expenses incurred by specialized greenhouse
producers, such as expenses related to specialized greenhouse vegetables and flowers.
The DEA results indicate that Quebec has consistently been the most efficient province
from 2019 to 2023, achieving full efficiency each year. While Ontario and British Columbia
have experienced periods of inefficiency, they have shown improvement over time. However,
their average efficiency scores suggest that there is still room for enhancement to reach the level
of efficiency consistently maintained by Quebec.
As this study introduces a new application of DEA with the incorporation of a multiscenario approach in order to capture the variation and uncertainty within the greenhouse, sod,
and nursery operations in Canada which will improve the quality and strength of efficiency
analyses relevant to agricultural settings.

51

Limitations of the study
The research employs a static analysis approach by evaluating efficiency over multiple
years but treating each year as a separate scenario. This method may not fully capture the
dynamic nature of supplier performance and supply chain operations over time. A longitudinal
analysis considering the evolution of efficiency scores could provide deeper and more
meaningful insights.
Another limitation is that, with regard to the DMUs under analysis, homogeneity needs to
be assumed. In this case, the provinces of British Columbia, Ontario, and Quebec are presumed
to be homogeneous and comparable. However, regional policy differences, market conditions, or
other contextual features may be such that their efficiency scores really are incomparable. If
these contextual differences are not accounted for, then skewed results may appear.
Moreover, the research has only been targeted at greenhouse, sod, and nursery operations.
While this gives an insight into this particular industry in great depth, generalization cannot be
made for other industries or sectors that diverge in characteristics and dynamics.
The inherent assumptions of the DEA model also present limitations. DEA assumes the
convexity of the production possibility set and that all DMUs operate under similar conditions.
These assumptions may not always hold true, potentially affecting the robustness and reliability
of the results. Moreover, DEA primarily deals with quantitative data, which means that
qualitative factors such as supplier relationships, strategic importance, and innovation
capabilities are not directly considered. These qualitative aspects can be crucial in making
informed supplier selection decisions.

52

The geographical scope of the research is also limited to three provinces in Canada.
Expanding the geographical scope to include more regions or countries could provide a broader
understanding of efficiency in greenhouse operations. Finally, the temporal relevance of the data
is a concern, as the data used is up to 2023. There may have been significant changes in the
industry or external environment since then, and continuous updating of the data and reevaluation of the models are necessary to maintain the relevance and accuracy of the findings.
Future Potential of the study
Looking ahead, the research on the application of Data Envelopment Analysis (DEA) in
supplier selection when multiple scenarios exists, offers substantial potential for future
development and application. Future studies will be able to provide much better and more timely
insights into the efficiency of suppliers if they can leverage real-time data and enhance the
dynamic capabilities of DEA. This broader geographical scope, along with the increased
diversity of industries, will enhance the generalizability of findings and, hence, provide more
complete insights into supplier performance across contexts. This would lead to a more holistic
evaluation framework, one in which the qualitative factors of relationships with suppliers,
strategic importance, and innovation capabilities are integrated with quantitative metrics.
Moreover, employing advanced methodologies to handle multiple scenarios and
uncertainties in inputs and outputs, such as stochastic DEA models or hybrid approaches
combining DEA with other decision-making techniques, can further refine the assessment of
supplier performance. By continuously updating the data and incorporating external factors like
economic conditions and regulatory changes, future research can maintain relevance and provide
actionable insights, ultimately aiding organizations in making more informed and resilient
supplier selection decisions.
53

References
Alidrisi, H. (2021). The Development of an Efficiency-Based Global Green Manufacturing Innovation
Index: An Input-Oriented DEA Approach. Sustainability (Switzerland), 13(22).
https://doi.org/10.3390/su132212697
Ansari, A., Modarress, B., 1986. Just-in-time purchasing: Problems and solutions. Journal of Purchasing
and Materials Management 22 (2), 19–26.
Arabmaldar, A., Jablonsky, J., & Saljooghi, F. H. (2017). A new robust DEA model and superefficiency measure. Optimization, 66(5), 723–736.
Avkiran, N. K. (2011). Association of DEA super-efficiency estimates with financial ratios:
Investigating the case for Chinese banks. Omega, 39(3), 323–334.
https://doi.org/10.1016/j.omega.2010.08.001
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale
efficiencies in data envelopment analysis. Management Science, 30 (9), 1078–1092.
Benton, W.C., Krajeski, L., 1990. Vendor performance and alternative manufacturing environments.
Decision Sciences 21, 403–415.
Bernard, P., 1989. Managing vendor performance. Production and Inventory Management Journal 30,
1–7
Bier, T., Lange, A., & Glock, C. H. (2020). Methods for mitigating disruptions in complex supply chain
structures: a systematic literature review. International Journal of Production Research, 58(6),
1835–1856. https://doi.org/10.1080/00207543.2019.1687954
Browning, J.M., Zabriskie, N.B., Huellmantle, A.B., 1983. Strategic purchasing planning. Journal of
Purchasing and Materials Management 19 (1), 19–24
Burton, T.T., 1988. JIT/Repetitive sourcing strategies: Tying the knot with your suppliers. Production
and Inventory Management Journal (4th Quarter), 38–41
Chapman, S.N., Carter, P.L., 1990. Supplier/customer inventory relationships under just-in-time.
Decision Sciences 21, 35–51
Chapman, S.N., 1989. Just-in-time supplier inventory: An empirical implementation model.
International Journal of Production Research 27 (12), 1993–2007.
Charnes, A., Cooper, W., & Rhodes, E. (1978). Measuring the efficiency of decision-making units.
European Journal of Operational Research, 2(6), 429–444. https://doi.org/10.1016/03772217(78)90138-8
Chen, I. J., & Paulraj, A. (2004). Towards a theory of supply chain management: The constructs and
measurements. Journal of Operations Management
54

Chen, Y., Liang, L., Yang, F., & Zhu, J. (2016). Evaluation of China's logistics industry development: A
DEA approach. Journal of Management Science and Engineering
Choi, T. Y., & Krause, D. R. (2006). The supply base and its complexity: Implications for transaction
costs, risks, responsiveness, and innovation. Journal of Operations Management
Chopra, S., & Meindl, P. (2015). Supply Chain Management: Strategy, Planning, and Operation
Christopher, M. (2016). Logistics & Supply Chain Management.
Christopher, M., & Peck, H. (2004). Building the resilient supply chain. International Journal of
Logistics Management
Cook WD, Seiford LM. Data envelopment analysis (DEA) – thirty years on. European Journal of
Operational Research 2009;192(1):1–17.
Cooper WW, Seiford LM, Tone K, Zhu J. Some models and measures for evaluating performances with
DEA: past accomplishments and future prospects. Journal of Productivity Analysis
2007;28(3):151–63.
Cooper, W. W., Park, K. S., & Yu, G. (1999). IDEA and AR-IDEA: Models for dealing with imprecise
data in DEA. Management Science, 45(4), 597–607
Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1 (3–4), 197–206.
Davenport, T. H. (1998). Putting the Enterprise into the Enterprise System.
Deming, W. E. (1986). Out of the Crisis.
Demirbag, M., Tatoglu, E., Glaister, K. W., & Zaim, S. (2010). Measuring strategic decision making
efficiency in different country contexts: A comparison of British and Turkish firms. Omega,
38(1–2), 95–104. https://doi.org/10.1016/j.omega.2009.05.001
Despotis, D. K., & Smirlis, Y. G. (2002). Data envelopment analysis with imprecise data. European
Journal of Operational Research, 140(1), 24–36
Dickson, G., 1966. An analysis of vendor selection systems and decisions. Journal of Purchasing 2, 28–
41
Ellram, L.M., 1990. The supplier selection decision in strategic partnerships. Journal of Purchasing and
Materials Management 26 (4), 8–14.
Emrouznejad A, Parker BR, Tavares G. Evaluation of research in efficiency and productivity: a survey
and analysis of the first 30 years of scholarly literature in DEA. Socio-Economic Planning
Sciences 2008;42(3):151–7.
Emrouznejad, A., & Yang, G. (2010). A survey and analysis of the first 40 years of scholarly literature
in DEA: 1978-2009. Socio-Economic Planning Sciences
55

Emrouznejad, A., Parker, B.R., & Tavares, G. (2010). Evaluation of research in efficiency and
productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. SocioEconomic Planning Sciences, 42(3), 151-157.
Essentials of Statistics for Business and Economics, 10th Edition - 9780357716014 - Cengage. (2022)
Fagundes, M. V. C., Teles, E. O., Vieira de Melo, S. A. B., & Freires, F. G. M. (2020). Supply chain risk
management modelling: A systematic literature network analysis review. IMA Journal of
Management Mathematics, 31(4), 387–416. https://doi.org/10.1093/imaman/dpaa019
Gattoufi S, Oral M, Kumar A, Reisman A. Epistemology of data envelopment analysis and comparison
with other fields of OR/MS for relevance to applications. Socio-Economic Planning Sciences
2004;38(2–3):123–40
Guo, P., & Tanaka, H. (2001). Fuzzy DEA: A perceptual evaluation method. Fuzzy Sets and Systems,
119(1), 149–160.
Hafezalkotob, A., Haji-Sami, E., & Omrani, H. (2015). Robust DEA under discrete uncertain data: A
case study of Iranian electricity distribution companies. Journal of Industrial Engineering
International, 11(2), 199–208.
Hahn, C.K., Pinto, P.A., Bragg, D.J., 1983. Just-in-time production and planning. Journal of Purchasing
and Materials Management 19 (3), 2–10.
Hatami-Marbini, A., & Saati, S. (2009). Stability of RTS of efficient DMUs in DEA with fuzzy under
fuzzy data. Applied Mathematical Sciences, 3(44), 2157–2166.
Hosseini-Nasab, H., & Ettehadi, V. (2023). Development Of Open-Network Data Envelopment Analysis
Models Under Uncertainty. Journal of Industrial and Management Optimization, 19(3), 1963–
1982. https://doi.org/10.3934/jimo.2022027
Hwang, C. L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. New
York: Springer-Verlag.
Jahanshahloo, gh.r., & Zahedi Seresht, m.. (2015). Utilizing Monte Carlo method for ranking extremely
efficient units in data envelopment analysis. Journal of new researches in mathematics, 1(1), 2340. Sid.
Juran, J. M. (1951). Quality Control Handbook.
Kao, C. (2006). Interval efficiency measures in data envelopment analysis with imprecise data.
European Journal of Operational Research, 174(2), 1087–1099.
Kleinsorge, I.K., Schary, P.B., Tanner, R.D., 1992. Data envelopment analysis for monitoring customer
supplier relationships. Journal of Accounting and Public Policy 11, 357–372
Kralijic, P., 1983. Purchasing must become supply management. Harvard Business Review 61, 109–117
Kuosmanen, T. (2009). Data envelopment analysis with missing data. Journal of the Operational
Research Society, 60(12), 1767–1774.
56

Li, Y., Liu, X., & Wang, X. (2012). DEA efficiency evaluation of the Chinese manufacturing industry.
International Journal of Production Research
Li, Y., Shi, W., & Deng, H. (2019). A data envelopment analysis model for supplier evaluation and
selection in the presence of incomplete information. Journal of Business Research
Liu, S., Luo, L., & Zhu, Q. (2012). Development of Data Envelopment Analysis for the Performance
Evaluation of Green Supply Chain with Undesirable Outputs. International Journal of Systems
Science
Monczka, R.M., Giunipero, L.C., Reck, R.F., 1981. Perceived importance of supplier information.
Journal of Purchasing and Materials Management 17, 21–29.
Moriarity, R.T., 1983. Industrial Buying Behavior. Lexington Books, Lexington, Massachusetts.
M. AlimohammadiArdekani, H. Hoseininasab, H. khademizare, M. Fakhrzad, A Robust Two-stage Data
Envelopment
Analysis Model for Measuring Efficiency: Considering Iranian Electricity Power Production and
Distribution Processes, International Journalof Engineering (IJE), TRANSACTIONS B:
Applications Vol. 29, No. 5, (May 2016) 646-653
Narasimhan, R., Talluri, S., Mendez, D., 2001. Supplier evaluation and rationalization via data
envelopment analysis: An empirical examination, working paper, Michigan State University.
O’Neal, P. V., Ozcan, Y. A., & Yanqiang, M. (2002). Benchmarking mechanical ventilation services in
teaching hospitals. Journal of Medical Systems, 26(3), 227–240.
Saaty, T. L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.
Sadjadi, S. J., & Omrani, H. (2008). Data envelopment analysis with uncertain data: An application for
Iranian electricity distribution companies. Energy Policy, 36(11), 4247–4254.
Seiford, L. M., & Thrall, R. M. (1990). Recent developments in DEA. Journal of Econometrics, 46(1–2),
7–38. https://doi.org/10.1016/0304-4076(90)90045-u
Seiford LM. Data envelopment analysis: the evolution of the state of the art (1978–1995). Journal of
Productivity Analysis 1996;7(2–3):99–137
Seuring, S., & Gold, S. (2012). Sustainability management beyond corporate boundaries: from
stakeholders to performance.
Shokouhi, A. H., Hatami-Marbini, A., Tavana, M., & Saati, S. (2010). A robust optimization approach
for imprecise data envelopment analysis. Computers & Industrial Engineering, 59(3), 387–397.
Sodhi, M. S., & Tang, C. S. (2012). Managing supply chain risk. Springer Science & Business Media.
Soheilirad, S., Govindan, K., Mardani, A., Zavadskas, E. K., Nilashi, M., & Zakuan, N. (2017).
Application of data envelopment analysis models in supply chain management: a systematic
57

review and meta-analysis. Annals of Operation Research/Annals of Operations Research, 271(2),
915–969. https://doi.org/10.1007/s10479-017-2605-1
Talluri, S., & Narasimhan, R. (2004). A methodology for strategic sourcing. European Journal of
Operational Research
Tang, C. S. (2006). Perspectives in supply chain risk management. International Journal of Production
Economics, 103(2), 451–488. https://doi.org/10.1016/j.ijpe.2005.12.006
Tavana, M. (2015). A two-stage data envelopment analysis model for measuring performance in threelevel supply chains. European Journal of Operational Research
Toloo, M., & Ertay, T. (2014). The most cost efficient automotive vendor with price uncertainty: A new
DEA approach. Measurement, 52(1), 135–144.
Treleven, M., 1987. Single sourcing: A management tool for the quality supplier. Journal of Purchasing
and Materials Management 23 (1), 19–24
Tullous, R., Munson, J.M., 1991. Trade-offs under uncertainty: Implications for industrial purchasers.
International Journal of Purchasing and Materials Management 27, 24–31
Urciuoli, L., & Hintsa, J. (2018). Improving supply chain risk management - Can additional data help?
International Journal of Logistics Systems and Management, 30(2), 195–224.
https://doi.org/10.1504/IJLSM.2018.091962
Vishnu, C. R., Sridharan, R., & Kumar, P. N. R. (2019). Supply chain risk management: Models and
methods. International Journal of Management and Decision Making, 18(1), 31–75.
https://doi.org/10.1504/ijmdm.2019.096689
Weber, C.A., Current, J.R., Benton, W.C., 1991. Vendor selection criteria and methods. European
Journal of Operational Research 50, 2–18
Weber, C.A., Desai, A., 1996. Determination of paths to vendor market efficiency using parallel
coordinates representation: A negotiation tool for buyers. European Journal
of Operational Research 90, 142–155.
Womack, J. P., Jones, D. T., & Roos, D. (1990). The Machine That Changed the World.
Wong, W. P. (2021). A Global Search Method for Inputs and Outputs in Data Envelopment Analysis:
Procedures and Managerial Perspectives. Symmetry, 13(7).
https://doi.org/10.3390/sym13071155
Woodside, A.G., Vyas, N., 1987. Industrial purchasing strategies. Lexington Books, Lexington,
Massachusetts.
Wu, H.-J., Dunn, S. C., & Forman, H. (2013). Measuring the environmental efficiency of
manufacturing: A DEA approach. International Journal of Production Economics

58

Xu, Z., Elomri, A., Kerbache, L., & El Omri, A. (2020). Impacts of COVID-19 on Global Supply
Chains: Facts and Perspectives. IEEE Engineering Management Review, 48(3), 153–166.
https://doi.org/10.1109/EMR.2020.3018420
Zahedi-Seresht, M., Athaudage, G. N. P., Lee, W. K., & Khosravi, S. (2023). Sustainable/Robust
supplier selection in the Post-Pandemic Era: Using data envelopment analysis. American Journal
of Industrial and Business Management, 13(08), 865–887.
Zahedi-Seresht, M., Mehrabian, S., & Jahanshahloo, G. R. (2016). A new method for ranking
distribution companies with several scenarios data by using DEA/MADM. International Journal
of Applied Operational Research, 6(3), 11–24.
Zahedi-Seresht, M., Jahanshahloo, G., Jablonsky, J., & Asghariniya, S. (2017). A new Monte Carlo
based procedure for complete ranking efficient units in DEA models. Numerical Algebra Control
and Optimization, 7(4), 403–416.
Zahedi-Seresht, M., Khosravi, S., Jablonsky, J., & Zykova, P. (2021). A data envelopment analysis
model for performance evaluation and ranking of DMUs with alternative scenarios. Computers
& Industrial Engineering, 152, 107002. https://doi.org/10.1016/j.cie.2020.107002
Zhong, W., Yuan, W., Li, S. X., & Huang, Z. (2011). The performance evaluation of regional R&D
investments in China: An application of DEA based on the first official China economic census
data. Omega, 39(4), 447–455. https://doi.org/10.1016/j.omega.2010.09.004
Zhu, J., Sarkis, J., & Lai, K. (2014). Institutional-based antecedents and performance outcomes of
supplier selection in emerging economies. International Journal of Production Economics
Zhu, J. (2003). Quantitative models for performance evaluation and benchmarking: Data envelopment
analysis with spreadsheets and DEA Excel Solver. Springer Science & Business Media.

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Appendix

60