A multi-objective integer mathematical model proposal for agile external milk-run systems

A milk-run system is a cyclical material delivery system that enables frequent small-batch deliveries with short lead times and low inventories. In the literature, milkrun systems are classified into external and internal categories. This study presents a multi-objective integer mathematical model for the cost minimisation of external milkrun tours and discusses agile external milk-run systems, which have yet to receive much attention in the literature. The proposed model was coded using the Lingo software, and its effectiveness was shown using both a real-world problem and randomly generated test problems. The proposed model found the optimal solution for real-world and most test problems in approximately a few seconds. The results have shown that the proposed mathematical model for external milk-run systems in agile environments is useful.