The impact of customer impatience on production control

Abstract

Most analyses of make-to-stock production control assume that either all orders are eventually met (complete backordering) or that no customers are willing to wait (lost sales). We consider a more nuanced model of customer behavior, where the fraction of potential customers who place orders depends on the current backlog, and hence the lead time. A continuous one-part-type, single machine model with Markov modulated demand and deterministic production is considered. We show that the impact of customer impatience is captured by one quantity, the mean sojourn time in the backlog states. A simple procedure finds this quantity and the optimal policy, which has hedging point form. In applications, observing the durations of stockouts gives a practical method of incorporating the effect of customer impatience.

Production control with backlog-dependent demand

“…Finally, we find the optimal hedging point numerically and evaluate the system performance measures including throughput (actual production rate), fill rate, and average backlog. Further analysis is given in Veatch (2007), where it is shown that the impact of B() on system performance can be expressed through a single parameter.…”

“…While other functions satisfying (1) could be studied, our numerical results suggest that there is limited sensitivity to the exact shape of B(x). Furthermore, it is shown in Veatch (2007) that the impact of B(x) on system performance, for a given demand and production model, can be expressed through a single parameter. Thus, simple parametric forms of B(x) are appropriate.…”