Bi-objective model for multi-level supply chain by focusing on quality of agricultural products: a case study
Authors: Khazaeli Sareh , Jabalameli Mohammad Saeed , Sahebi Hadi 
Published: May 2023

PurposeDue to the importance of quality to customers, this study considers criteria of quality and profit and optimizes both in a multi-echelon cold chain of perishable agricultural products whose quality immediately begins to deteriorate after harvest. The two objectives of the proposed cold chain are to maximize profit and quality. Since postharvest quality loss in the supply chain depends on various decisions and factors, in addition to strategic decisions, the authors consider the temperature setting in refrigerated facilities and transportation vehicles due to the unfixed shelf life of the products which is related to the temperature found by Arrhenius formula.Design/methodology/approachThe authors use bi-objective mixed-integer nonlinear programming to design a four-echelon supply chain. The authors integrate the supply chain echelons to detect the sources and factors of quality loss. The four echelons include supply, processing, storage and customer. The decisions, including facility location, assigning nodes of each echelon to corresponding nodes from the adjacent echelon, allocation of vehicles to transport the products from farms to wholesalers, processing selection, and temperature setting in refrigerated facilities, are made in an integrated way. Model verification and validation in the case study are done based on three perishable herbal plants.FindingsThe model obtains a 29% profit against a total cost of 71 and 93% of original quality of the crops is maintained, indicating a 7% quality loss. The final quality of 93% is the result of making a US$6m investment in the supply chain, including the procurement of high-quality raw materials; facility establishment; high-speed, high-capacity vehicles; location assignment; processing selection and refrigeration equipment in the storage and transportation systems, helping to maximize both the final quality of the products and the total profit.Research limitations/implicationsThe proposed supply chain model should help managers with modeling decisions, especially when it comes to cold chains for agricultural products. The model yields these results – optimal location-allocation decisions for the facilities to minimize distances between the network nodes, which save time and maintain the majority of the products’ original quality; choosing the most appropriate processing method, which reduces the perishability rate; providing high-capacity, high-speed vehicles in the logistics system, which minimizes transportation costs and maximizes the quality; and setting the right temperature in the refrigerated facilities, which mitigates the postharvest decay reaction rate of the products.Practical implicationsComparison of the results of the present research with those of the traditional chain (obtained through experts) shows that since the designed chain increases the profit as well as the final quality, it has benefits for the main chain stakeholders, which are customers of agricultural products. This study model is expected to have a positive impact on the environment by placing strong emphasis on quality and preventing excessive waste generation and air pollution by imposing a financial penalty on extra demand production.Social implicationsSince profit and quality of the final product are two important factors in all cultures and communities, the proposed supply chain model can be used in any food industry around the world. Applying the proposed model induces growth in local industries and promotes the culture of prioritizing quality in societies.Originality/valueTo the best of the authors’ knowledge, this is the first research on a bi-objective four-echelon (supply, processing, storage and customer) postharvest supply chain for agricultural products including that integrates transportation logistics and considers the deterioration rate of products as a time-dependent variable at different levels of decision-making.