The M/M/1 queue with a production-inventory system and lost sales

被引:32
作者
Baek, Jung Woo [1 ]
Moon, Seung Ki [1 ]
机构
[1] Nanyang Technol Univ, Sch Mech & Aerosp Engn, Singapore 639798, Singapore
关键词
Queueing model; Production-inventory model; Lost sales; Cost optimization; M/G/1; QUEUE; MODEL; DRIVEN;
D O I
10.1016/j.amc.2014.02.033
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study an M/M/1 queue with an attached production-inventory system. Customers arrive in the system according to a Poisson process, and a single server serves the customers. The service times are assumed to be i.i.d. exponential random variables. The customers leave the system with exactly one item from the inventory at his service completion epoch. If there is no inventory item, all arriving customers are lost. The stocks are replenished by (1) an external order under (r, Q)-policy, or (2) an internal production. The internal production process is assumed to be a Poisson process. We first derive the stationary joint distribution of the queue length and the on-hand inventory in product form. Using the joint distribution, we introduce long-run performance measures and a cost model. Then, we show numerical examples, which minimize the long-run cost per unit time. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:534 / 544
页数:11
相关论文
共 17 条
[1]   Analysis of an M/M/1 driven fluid queue with multiple exponential vacations [J].
Ammar, Sherif I. .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 227 :329-334
[2]   KITTING VERSUS LINE STOCKING - A CONCEPTUAL-FRAMEWORK AND A DESCRIPTIVE MODEL [J].
BOZER, YA ;
MCGINNIS, LF .
INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, 1992, 28 (01) :1-19
[3]   Design and performance of kitting and order picking systems [J].
Brynzer, H ;
Johansson, MI .
INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, 1995, 41 (1-3) :115-125
[4]  
Cox DR., 1962, Metrheun's Monograph
[5]   STOCHASTIC DECOMPOSITIONS IN THE M/G/1 QUEUE WITH GENERALIZED VACATIONS [J].
FUHRMANN, SW ;
COOPER, RB .
OPERATIONS RESEARCH, 1985, 33 (05) :1117-1129
[6]   The transient solution to M/Ek/1 queue [J].
Griffiths, JD ;
Leonenko, GM ;
Williams, JE .
OPERATIONS RESEARCH LETTERS, 2006, 34 (03) :349-354
[7]   ASSEMBLY-LIKE QUEUES [J].
HARRISON, JM .
JOURNAL OF APPLIED PROBABILITY, 1973, 10 (02) :354-367
[8]  
Lipper E. H., 1986, Queueing Systems Theory and Applications, V1, P67, DOI 10.1007/BF01149328
[9]  
LUCHAK G, 1958, J ROY STAT SOC B, V20, P176
[10]   Fluid model driven by an M/G/1 queue with multiple exponential vacations [J].
Mao, Bing-wei ;
Wang, Fu-wei ;
Tian, Nai-shuo .
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (08) :4041-4048