A min-max policy for multi-item joint inventory replenishment problem: Application to industrial vending machines

Industrial vending machines are often used in manufacturing facilities to offer various items and tools that are required in the manufacturing process. Companies often manage the inventory replenishment for such vending machines based on a min-max or (s, S) policy for each item. When a replenishment arrives, the inventory of all items can be brought up to their maximum levels. This paper studies this unique multi-item joint inventory replenishment problem to determine the optimal min-max policy that maximizes the expected profit in a finite planning horizon. Specifically, a simulation optimization framework is used to determine the optimal inventory decisions. Two discrete-event simulation models are developed in Arena and Python and three optimization approaches are utilized, including OptQuest in Arena simulation, gradient-based methods, and particle swarm optimization algorithms. Moreover, computational experiments are conducted to compare the different solution methods. A simple heuristic is also provided for ease of implementation.