Optimal supplier inventory control policies when buyer purchase incidence is driven by past service

A buyer exposed to a stockout may lose goodwill and be less inclined to select the same supplier in his next procurement. Reversely, an in-stock experience may restore the supplier’s prospect of being selected in the future. What should the supplier’s inventory control policy be in this situation? To address this question, we develop a multiperiod model of a buyer who selects a supplier with a probability that depends on the supplier’s rating. This rating reflects the buyer’s goodwill towards the supplier based on past service, measured in terms of in-stock/out-of-stock incidents, and is updated by the buyer after each service. The supplier’s optimal inventory policy partitions the inventory space in order-up-to and do-not-order intervals for each rating. The optimal decision depends on whether ordering reduces the supplier’s risk of being downgraded enough to offset the increase in her ordering and inventory costs. We derive and evaluate bounds on the optimal policy and expose some of its properties. We obtain conditions for the optimality of basestock policies and show that such policies are optimal if there are only two ratings or if the buyer’s demand is constant. Using our model, we impute the stockout cost in a newsvendor setting. Numerical experiments suggest that (i) the supplier may benefit from holding more inventory in intermediate than in extreme ratings, and from dealing with a buyer who responds less erratically to service, (ii) basestock policies are efficient, and (iii) using an arbitrary stockout cost in the newsvendor setting can significantly hurt profits.