Analysis of a two-critical-number production policy in an M/G-type production system with waiting time information

Abstract

ABSTRACT In this paper, a production and inventory system with state-dependent arrival rates is considered under a two-critical-number policy. If the number of products in the inventory reaches the value of a parameter of this policy, the production stops, and if the number of customers who are waiting for products reaches the value of another parameter, the production restarts. In this production and inventory system, the probabilities for the number of products in the inventory and the number of waiting customers in a steady state are developed by using the analytical results of an M/G/1/K queue with state-dependent arrival rates. In addition, the waiting time information policy is investigated. Short waiting time information may decrease the probability that the actual waiting time is shorter than the informed waiting time, which is regarded as a measure of customers’ satisfaction. Sensitivity analysis is conducted via numerical experiments. The numerical examples show that the critical numbers for maximizing the average profit are insensitive to the processing time distributions. They also show that the use of a suitable waiting time information policy is important for the satisfaction of customers, especially if the variance in the processing time is small.