Dynamic Capacity Allocation to Customers Who Remember Past Service

We study the problem faced by a supplier deciding how to dynamically allocate limited capacity among a portfolio of customers who remember the ll rates provided to them in the past. A customer's order quantity is positively correlated with past ll rates. Customers di er from one another in their contribution margins, in their sensitivities to the past, and in their demand volatilities. By analyzing and comparing policies that ignore goodwill with ones that account for it, we investigate when and how customer memory e ects impact supplier profits. We develop an approximate dynamic programming (ADP) policy that dynamically rationalizes the ll rates the rm provides to each customer. This policy achieves higher rewards than margingreedy and Lagrangian policies and yields insights into how a supplier can e ectively manage customer memories to its advantage.

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