Multi-Server Queuing Production Inventory System with Emergency Replenishment

Dhanya Shajin, Achyutha Krishnamoorthy, Agassi Z. Melikov and Janos Sztrik ()
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Dhanya Shajin: Department of Mathematics, S. N. College, Chempazhanthy 695587, Kerala, India
Achyutha Krishnamoorthy: Centre for Research in Mathematics, CMS College, Kottayam 686001, Kerala, India
Agassi Z. Melikov: Institute of Control Systems, National Academy of Science, AZ 1141 Baku, Azerbaijan
Janos Sztrik: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2022, vol. 10, issue 20, 1-24

Abstract: We consider a multi-server production inventory system with an unlimited waiting line. Arrivals occur according to a non-homogeneous Poisson process and exponentially distributed service time. At the service completion epoch, one unit of an item in the on-hand inventory decreases with probability δ , and the customer leaves the system without taking the item with probability ( 1 − δ ) . The production inventory system adopts an ( s , S ) policy where the processing of inventory requires a positive random amount of time. The production time for a unit item is phase-type distributed. Furthermore, assume that an emergency replenishment of one item with zero lead time takes place when the on-hand inventory level decreases to zero. The emergency replenishment is incorporated in the system to ensure customer satisfaction. We derive the stationary distribution of the system and some main performance measures, such as the distribution of the production on/off time in a cycle and the mean emergency replenishment cycle time. Numerical experiments are conducted to illustrate the system performance. A cost function is constructed, and we examine the optimal number of servers to be employed. Furthermore, we numerically calculate the optimal values of the production starting level and maximum inventory level.

Keywords: ( s , S ) production inventory system; non-homogeneous Poisson process; multi-server; emergency replenishment; cost function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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