An integrated multitiered supply chain network model of competing agricultural firms and processing firms: The case of fresh produce and quality

Highlights

• We develop an integrated multitiered competitive agricultural supply chain network model where agricultural firms and processing firms compete to sell their differentiated products.

• The focus here is on fresh produce and minimally processed agricultural products in which we capture the quality decay of agricultural products through kinetic functions based on time and temperature at every stage of the supply chain.

• The competition among agricultural firms and processing firms is studied through game theory, where the governing Cournot-Nash equilibrium conditions correspond to a variational inequality problem.

• A numerical study consisting of several supply chain disruption scenarios demonstrates the applicability of our modeling framework.

• The numerical study results suggest that a gricultural firms increase their profit by selling their agricultural products at the demand markets, and to the processing firms.

Abstract

In this paper, we develop an integrated multitiered competitive agricultural supply chain network model in which agricultural firms and processing firms compete to sell their differentiated products. The focus here is on fresh produce and minimally processed such agricultural products, with quality also captured. The competition among agricultural firms and processing firms is studied through game theory, where the governing Cournot–Nash equilibrium conditions correspond to a variational inequality problem. The algorithm, at each iteration, yields explicit closed form expressions for the agricultural product path flows, the agricultural product shipments from agricultural firms to the processing firms, and the Lagrange multipliers. A numerical study consisting of several supply chain disruption scenarios demonstrates the applicability of our modeling framework.

Introduction

Agricultural supply chains (ASCs) are very intricate local, regional, and global networks, creating pathways from farms to consumers, and encompassing the sets of activities such as: farming/production, processing, storage, transportation, and distribution (Chandrasekaran, Raghuram, 2014, Sharma, Shishodia, Kamble, Gunasekaran, Belhadi, 2020, Tsolakis, Keramydas, Toka, Aidonis, Iakovou, 2014, Yu, Nagurney, 2013). The dynamics in the agriculture industry are very complex; the connections between various stakeholders are intertwined, and all the players work towards providing food to the consumers, while maximizing profits under tight competition. The agricultural product industry includes small and large scale farms as well as global commercial food firms such as Tyson Foods, Dole, Cargill, etc., with the latter also involved in the processing of food, as in the form of cutting, canning, freezing, pasteurization, modified atmosphere packaging, etc. Minimally processed ready to eat fresh food such as chopped vegetables, fresh-cut fruits as well as frozen produce, which are the focus in this paper, have gained popularity in recent times due to the convenience of use and health benefits. The market share for minimally processed products such as fresh-cut produce is significant. According to research conducted by Global Market Insights Inc., the processed fruits and vegetables market is projected to cross USD 465 billion by 2027 (Globe Newswire, 2021). In the COVID-19 pandemic, with an increase in home cooking, sales of fresh food increased by 10 percent in 2020, whereas frozen food had an increase of 21 percent (Morrison, 2021). Processing can increase the shelf life of agricultural produce that is often highly perishable. Currently, it is evident that frozen alternatives are providing stiff competition to fresh or minimally processed agricultural products (Renner, Cook, Baker, & Upadhyaya, 2021).

However, when it comes to processed produce there can be concerns regarding the quality of the food. Hence, there have been numerous studies in the field of food science that aim to determine the quality loss or deterioration in agricultural produce under different storage conditions and subjected to different processing techniques (Aamir, Ovissipour, Sablani, Rasco, 2013, Demiray, Tulek, 2015, Goncalves, Abreu, Pinheiro, Brando, Silva, 2020, Labuza, 1984). Quality of fresh and processed agricultural products such as fruits and vegetables can be measured based on various attributes such as color change, texture softening, loss of nutrients such as Vitamin C, etc. Agricultural supply chains exhibit a fundamental difference from other supply chains, which is particularly prevalent with fresh produce and minimally processed products, in that the quality of agricultural products changes continuously from the point of production to the point of consumption (Ahumada, Villalobos, 2009, Aiello, La Scalia, Micale, 2012, Akkerman, Farahani, Grunow, 2010, Blackburn, Scudder, 2009, Lowe, Preckel, 2004, Sloof, Tijskens, Wilkinson, 1996). Quality decay of agricultural products along different stages of the supply chain varies by type of product and environmental conditions such as temperature maintained during storage and transportation (Lejarza & Baldea, 2022) as well as the duration. It has been discovered that the quality of fresh produce can be determined scientifically using chemical formulae, which include both time and temperature (Labuza, 1982, Rong, Akkerman, Grunow, 2011, Taoukis, Labuza, 1989, Tijskens, Polderdijk, 1996).

It is evident that there are several layers of complexity associated with managing agricultural supply chains. For example, agricultural supply chain networks worldwide are predominantly multitiered, underlined by the impact of competition among the various stakeholders including the agricultural firms and the processing firms (cf. Sharma et al., 2020 and the references therein). In this paper, we develop a multitiered competitive agricultural supply chain network model in which agricultural firms and processing firms compete to sell their products at the demand markets, which can include retailers and supermarkets. With the prevalence of multiple options for consumers in terms of fresh, minimally processed and frozen substitutes for agricultural produce that have different levels of quality, it is important to study how the agricultural firms and processing firms compete with each other based on their differentiated products at the demand markets. Hence, we develop in this paper such a model that also integrates the interactions and economic transactions between the supply chains of agricultural firms and processing firms. Below, we list the main contributions of our work to the literature on agricultural supply chains.

• We capture competition at two levels; at the first level, the agricultural firms compete and sell their harvested produce to processing firms and, at the second level, the agricultural and processing firms compete to sell their differentiated but substitutable products at the demand markets.

• We include in our model explicit functions to capture the quality decay of the harvested fresh produce products along the entire, multitiered supply chain since quality is an important factor in agricultural supply chain management.

• In our numerical study, we include supply chains of both fresh and minimally processed produce; specifically, that of carrots, that follow different kinetic functions of quality decay.

• Our numerical study reveals the impacts of various supply chain disruptions in agricultural supply chains. Our results suggest that agricultural firms achieve higher profits when they sell their agricultural products both at the demand markets and to the processing firms.

• We demonstrate quantitatively the impacts of the quality of agricultural products at the demand markets and how the level of quality affects the demand market prices of the products of the agricultural and the processing firms. The results reveal that, when there are temperature and time issues at different stages of the supply chain resulting in lower quality products, the demand market prices and the profits for the associated agricultural and processing firms decrease.

• Although there is a rich literature on optimization approaches to agriculture in the context of supply chains, the literature on the use of game theory for the modeling, analysis, and solution of supply chain network problems associated with agricultural products, including that of fresh produce, is much more limited.

This paper is organized as follows. In Section 2, we provide a literature review of agricultural supply chains, further emphasizing the novelty of our work, and noting papers relevant to our research. In Section 3, we provide preliminaries on quality deterioration. In Section 4, we present the integrated multitiered agricultural supply chain network of competing agricultural firms and processing firms. We state the governing Cournot–Nash equilibrium conditions and derive alternative variational inequality formulations. In Section 5, we present our results for a numerical study on carrot supply chains using the algorithm that is provided in the Appendix. We provide our managerial insights in Section 6, and we summarize and present our conclusions in Section 7.