A Sustainable Agri-Food Supply Chain for a Multi-Layer, Multi-Period, Multi-Product Chain Restaurants Planning Problem

This study develops a multi-layer, multi-period, multi-product mixed-integer linear programming model for planning the agri-food supply chain of chain restaurants by integrating farms, processing centers, warehouses, and restaurants within a single optimization framework. The model jointly captures cultivation, processing, transportation, storage, recipe-based ingredient consumption, menu decisions, and restaurant cooking-capacity constraints, with the objective of maximizing total supply chain profit. The proposed framework addresses an important gap in the agri-food supply chain optimization literature by explicitly treating restaurants as an operational decision layer rather than merely as passive demand points. The model is validated through two numerical examples and additional scalability tests solved in GAMS. The two main examples yield optimal objective-function values of 48,430.920 and 336,121.732 monetary units, respectively. The scalability analysis shows that the model remains computationally tractable as problem size increases, solving two small-sized instances in 0.100 and 0.205 seconds, a medium-sized instance in 2.115 seconds, and a large-sized instance with 1,074,510 decision variables and 565,665 constraints in 33.163 seconds. Sensitivity analysis further indicates that food selling price is the most influential parameter. A 50% increase in food selling prices increases the objective value by 63.34%, while a 50% decrease reduces it by 63.34%. In contrast, a 50% increase in farm cultivation costs, restaurant cooking costs, transportation costs, and processing costs reduces the objective value by 8.06%, 3.46%, 1.27%, and 0.54%, respectively. These numerical findings highlight the effectiveness, scalability, and managerial relevance of the proposed framework.