Inventory with service time and transfer of customers and/inventory

Abstract

An inventory system with two parallel service facilities is considered. A certain number of customers are transferred from longer to shorter queue whenever their difference reaches a prescribed quantity. Along with this customer transfer, a certain quantity of inventory is also transferred, depending on availability. Further, if one of the queues has customers, but has no inventoried items whereas the other has at least one inventoried item to spare, then exactly one item is taken to the former and service begins thereby enhancing the efficiency of the system. Stability of the system is analysed. Several performance measures that helps in efficient design of such systems, are computed. Some numerical results are provided.

An ‘(s, S)’ inventory in a queueing system with batch service facility

“…Further, they derived the stationary distributions of joint queue length and inventory processes in product form and obtained various performance measures based on that. For more references we refer to Graves (1982); Sigman and Simchi-Levi (1992); Baron et al (2010Baron et al ( , 2011; He et al (2002); Berman and Kim (1999); Berman and Sapna (2001); Kim (2005); ; Manuel et al (2007); Deepak et al (2008); Nair et al (2013); Saffari et al (2013); Krishnamoorthy et al ( , 2015; Krishnamoorthy and Viswanath (2013).…”

A survey on inventory models with positive service time

“…Lead times for replenishment in them are independent but nonidentical exponentially distributed random variables. Deepak et al [12] discuss this inventory model. In addition to transfer of customers as in He and Neuts [41], the authors introduce transfer of inventory subject to availability.…”

Analysis of a Multiserver Queueing-Inventory System

“…Krishnamoorthy and Viswanath [6] subsume Schwarz et al [5] by extending the latter to production inventory with positive service time. References [7] of Sivakumar and Arivarignan, [8] of Krishnamoorthy and Narayanan, [9] of Deepak et al, [10] of Schwarz and Daduna, [11] of Schwarz et al, and [12] of Krenzler and Daduna are a few other significant contributions to inventory with positive service time. Protection of production and service stages in a queueing-inventory model, with Erlang distributed service and interproduction time, is analyzed by Krishnamoorthy et al [13].…”