Purchase and production optimization in a meat processing plant

This paper addresses an optimization problem concerning the purchase and subsequent material processing in a meat processing company. Unlike the majority of existing papers, we do not concentrate on how this problem concerns supply chain management, but we focus on the production stage, primarily the meat cutting. Specifically, we study the operational level of production management, where the company responds to fluctuations in demand and controls the flow of materials, as this level of management significantly affects its profit. The problem involves the concept of alternative ways of material processing, stock of material with different expiration dates, and extra constraints widely neglected in the current literature addressing meat cutting and processing, namely, the minimum order quantity and the minimum percentage in alternatives. We prove that each of these two constraints makes the problem $\mathrm{NP}$-hard, and we design an exact iterative approach based on integer linear programming that allows us to solve real-life instances even using an open-source integer linear programming solver. Another advantage of this approach is that it mitigates numerical issues, caused by the extensive range of data values, we experienced with a commercial solver. The results obtained using real data from the meat processing company showed that our algorithm can find the optimum solution in a few seconds for all considered use cases.