Modelling and solving the milk collection problem with realistic constraints

The milk collection problem (MCP) is concerned with the collection of raw milk of varying quality at dairy factories via tankers under problem-specific constraints. During this collection process, keeping milk of different levels of quality separate is at least as critically important as production quality because when the milk of different qualities is mixed together, the worst quality determines the final milk quality. In MCP, decisions such as which farms/milk collection centers, quality of milk, types of tankers, storage tanks, and visiting sequences will be used are made. In this study, an integrated mathematical model is proposed for the first time that aims to minimize the total distance and total network costs for tanker assignments and routing problems by simultaneously considering realistic routing, incompatibility, and loading constraints. The problem was formulated as a mixed-integer linear program and the small instances were solved using CPLEX. To solve the larger-scale real-life problems, a variable neighborhood search (VNS) metaheuristic optimization framework is developed. The proposed mathematical model and the VNS framework were evaluated on scenarios based on real-life data from a dairy company. Computational results show that the proposed VNS framework solves the realistic MCP problem efficiently.