The multi-plant perishable food production routing with packaging consideration

We investigate a perishable food production routing problem with multiple plants and packaging considerations. The study is inspired by the fact that perishable food products usually have a short shelf life and are frequently sold with discounts. In particular, package selection is for the first time integrated into a supply chain planning problem. We describe and model this new problem by means of a mixed-integer linear program. Then a hybrid matheuristic (HM) is developed to solve it. HM is composed of three components, i.e., a two-phase iterative (TI) method, a fix-and-optimize (FO) procedure, and a route-based optimization (RO) process. In particular, TI generates a potential infeasible solution that is repaired and improved by FO, and RO further enhances the solution by exploiting useful information provided by TI and FO. Two branch-and-cut algorithms are also designed and implemented. Computational experiments on 320 randomly generated instances with up to four plants, 50 retailers, six periods, and three packages are carried out to demonstrate the performance of HM. The results of detailed computational experiments show that HM is effective and efficient, as it achieves solutions in short computing times; moreover, these solutions represent savings both economically and in terms of food spoilage. Extensive computational experiments are conducted to illustrate the benefits for the integration of packaging and the production routing planning. In addition, we explore the impacts of different shapes of price discounts.