Managing inventories of reusable containers for food take-away at a restaurant

Single-use packaging in the food services sector accounts for a substantial amount of waste, leading some restaurants to offer customers reusable containers for take-away or delivery orders. Once used, customers may return these containers to the same restaurant or another restaurant in the reusable container network or they may not return them at all. The restaurant hence faces both uncertain demand and returns for reusable containers and needs to decide on the number of containers to stock to serve its customers. We formulate this problem by modeling it as a continuous-time Markov Decision Process. Through a numerical study, we investigate the effect that different balances of demand and return intensities and their coupling have on the average total cost for the restaurant. We find that greater demand and return coupling reduces average costs, but the effects are most beneficial when the overall demand and returns of the restaurant are balanced. The restaurant can reduce costs by optimizing the supplier visit frequency in addition to the inventory level of clean containers after the supplier visit. The supplier's choice of the level of the visit cost is important as smaller scale restaurants may be penalized by a larger supplier visit cost, dissuading them from participating in reusable container systems.