Approximation and Optimization of a Multi-Server Impatient Retrial Inventory-Queueing System with Two Demand Classes

Abstract

In this paper, we investigate a multi-server retrial inventory-queueing system with two demand classes. The low priority customers are impatient with Bernoulli reneging probabilities. When the inventory level drops to a re-order level a replenishment order is placed at an external supplier. The order is replenished with a randomly positive lead time. Assume the demand arrival is a Markov arrival process (MAP). We propose two modeling approximations for the original two unbounded level problems. After an economic model is formulated we use combined enumerative and quasi-Newton search to heuristically optimize the number of servers, stock and reorder levels, and retrial and service rates such that the average operating cost per unit time is minimized. Numerical examples are provided to illustrate the application.

Key Words:

• Impatience
• MAP
• matrix geometric method
• quasi-Newton
• retrial inventory-queue.

Additional information

Notes on contributors

Fong-Fan Wang

Fong-Fan Wang is an Associate Professor in the Department of Industrial Engineering and Management at Hsiuping University of Science & Technology, Taiwan. His research interests include queueing, stochastic modeling, and simulation with their supply chain applications.