Analysis of a simple CONWIP system with impatient customers

We study a single-stage, constant work-in-process (CONWIP) production system that produces one product to stock to cope with random demand. During stockout periods, the system incurs three types of potential customer loss: Balking, i.e., arriving customers may be unwilling to place orders and leave immediately. Rejection, i.e., the system rejects new customer orders if its backlog has reached a certain limit, called the base backlog. Reneging, i.e., outstanding customers waiting in queue may become impatient and withdraw their orders. The objective is to determine the CONWIP level and the base backlog that maximize the mean profit rate of the system. This quantity is estimated analytically using a finite capacity M/M/1 queueing model, in which the arrival rate is a decreasing but otherwise arbitrary function of the backlog and customer reneging times have an arbitrary but known distribution. Certain properties of the mean profit rate are established which ensure that the optimal control parameters can be determined in finite time by exhaustive search. Numerical results show that managing inventories and backlog jointly achieves higher profit than other control policies.