Optimal Replenishment Policies for Industrial Vending Machines

Abstract: Industrial Vending Machines (IVMs) automate the dispensing of a variety of supplies like safety equipment and tools at customer sites, providing 24/7 access while tracking inventory in real-time. Industrial distribution companies typically manage the replenishment of IVMs using periodic schedules, which do not take advantage of these advanced real-time monitoring capabilities. We develop two approaches to optimize the long-term average cost of replenishments and stockouts per unit time: a state-dependent optimal control policy that jointly considers all inventory levels (referred to as trigger set policy) and a fixed cycle policy that optimizes replenishment frequency. We prove the monotonicity of the optimal trigger set policy and leverage it to design a computationally efficient approximate online control framework. Unlike existing methods, which typically handle a very limited number of items due to computational constraints, our approach scales to hundreds of items while achieving near-optimal performance. Leveraging transaction data from our industrial partner, we conduct an extensive set of numerical experiments to demonstrate this claim. Our results show that optimal fixed cycle replenishment reduces costs by 61.7 to 78.6% compared to current practice, with our online control framework delivering an additional 4.1 to 22.9% improvement. Our novel theoretical results provide practical tools for effective replenishment management in this modern vendor-managed inventory context.