Optimal Produciton Control of a Manufacturing System with Customer Balking Behavior

In this paper, we consider a single-stage manufacturing system with one machine, which makes a single product to stock to satisfy random demand. Customers inter-arrival times and production times are all exponential random variables. In order to represent customer impatience behavior caused by backlog, we employ a balking function, which is an arbitrary non-decreasing function of the backlogged number for characterizing the customer’s response to the backlog. First, we formulate the problem as a Markov decision process and use it to characterize the structure of the optimal production policy. We find that the optimal production policy is the base-stock policy. Then, the effects of system parameters on the optimal base-stock level are investigated. Lastly, we illustrate the impacts of customer balking behavior on the system’s cost and optimal base-stock level by the numerical examples in which linear and convex balking functions are employed respectively. Numerical examples show that customer balking has a significant impact on the optimal base-stock level as well as the optimal average cost.