MATHEMATICAL MODELING FOR OPTIMIZATION OF FOOD TRANSPORTATION

Abstract

Food transportation is a critical component of the food supply chain because it directly affects delivery cost, product availability, service reliability, and the quality of perishable goods. In many practical situations, food products must be transported from several warehouses, production facilities, or distribution centers to several markets, supermarkets, restaurants, or institutional consumers. The main operational question is how to determine the quantity of goods that should be shipped from each origin to each destination so that total transportation cost is minimized while all supply and demand requirements are satisfied. This paper presents a mathematical modeling approach for optimizing food transportation using the classical transportation problem from linear programming. The problem is formulated through decision variables, an objective function, supply constraints, demand constraints, and non-negativity conditions. A numerical example is developed for the distribution of food pallets from three distribution centers to four retail markets. The example is solved using the transportation simplex method, including the initial feasible allocation and the optimality test based on the MODI method. The results show that mathematical optimization can significantly support decision- making in food logistics by identifying the least-cost distribution plan and by providing a structured basis for operational planning. Knowledge of mathematical modeling techniques provides significant information for simulation and further design and optimization purposes