art-3A10.1007-2Fs40092-015-0115-9 - J Ind Eng Int(2015...

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ORIGINAL RESEARCH Application of queuing theory in production-inventory optimization Reza Rashid 1 Seyed Farzad Hoseini 1 M. R. Gholamian 1 Mohammad Feizabadi 2 Received: 4 December 2014 / Accepted: 29 May 2015 / Published online: 4 July 2015 Ó The Author(s) 2015. This article is published with open access at Abstract This paper presents a mathematical model for an inventory control system in which customers’ demands and suppliers’ service time are considered as stochastic parameters. The proposed problem is solved through queuing theory for a single item. In this case, transitional probabilities are calculated in steady state. Afterward, the model is extended to the case of multi-item inventory systems. Then, to deal with the complexity of this problem, a new heuristic algorithm is developed. Finally, the pre- sented bi-level inventory-queuing model is implemented as a case study in Electroestil Company. Keywords Production inventory ± Queuing theory ± Multi-item inventory ± Heuristic algorithm Introduction Nowadays, supply chains play an important role to meet diverse needs of customers. A supply chain can be defined as a network of organizations that collaborate to control and manage materials and information flow from suppliers to customers (Aitken 1998 ). One of the challenging issues in supply chain management is to find optimal policies for inventory systems. The main objective of inventory man- agement is to balance conflicting goals such as stock costs and shortage costs (Arda and Hennet 2006 ). Day by day, the number of researchers, attracted to production-inventory systems in supply chain, is increas- ing. In inventory management point of view, a manufac- turer with a limited production capacity needs to hold finished goods inventory as safety stocks. For this inven- tory system, if demand is less than service capacity, the manufacturer needs to use different policies for different inventory levels. For instance, it should use two points of inventory level: one for starting and the other for finishing the production line. For better description of the model, Fig. 1 illustrates the inventory level for the system when production rate l and demand rate D are considered deterministic. Actually, in a real-world system, different stochastic parameters may affect the model and increase the complexity of the system. In summary, it is clear that in spite of many contribu- tions to the stock control, there is little consideration regarding production-inventory models in stochastic envi- ronments. For this reason, we represent a mathematical model in which the main contributions of this paper can be summarized as follows: A production inventory system is developed in an uncertain environment.
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