Analysis of a Two-Echelon Inventory Model with Lost Sales and Stochastic Demand using Continuous-Time Markov Chain

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Vasheghani Farahani, Iman | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44974 (01)
University: Sharif University of Technology
Department: Industrial Engineering
Advisor(s): Haji, Rasoul
Abstract:
In this paper, we studied a two-echelon inventory system which consists of one central warehouse and one retailer. All installations follow base stock inventory management policy. The customers arrive at retailer according to Poisson distribution. The demand is satisfied when both central warehouse and retailer have positive on-hand inventory. Otherwise, the demand is lost. The lead time of central warehouse and the time needed to replenish orders of retailer are assumed to be exponentially distributed. The purpose of this study is to minimize the expected long-run total cost of the system per unit time. Total cost of the system includes holding costs of central warehouse and retailer, cost of lost sales and the cost of waiting times of outstanding orders at retailer. We modeled the problem using continuous-time Markov chain and provided an approximation of the steady-state joint probabilities of outstanding orders of retailer in the service of central warehouse and central warehouse’s on-hand inventory. The optimal solutions, properties of the objective function as well as some numerical results are presented. In our numerical results, the maximum error of 1.34% was observed
Keywords:
Lost Sale ; Two Echelon Inventory Model ; Base Stock System ; Stochastic Demand

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