Production control with backlog-dependent demand

Abstract

A manufacturing firm that builds a product to stock to meet a random demand is studied. Production time is deterministic, so that if there is a backlog, customers are quoted a lead time that is proportional to the backlog. In order to represent the customers' response to waiting, a defection functionthe fraction of customers who choose not to order as a function of the quoted lead timeis introduced. Unlike models with backorder costs, the defection function is related to customer behavior. Using a continuous flow control model with linear holding cost and Markov modulated demand, it is shown that the optimal production policy has a hedging point form. The performance of the system under this policy is evaluated, allowing the optimal hedging point to be found.