Transient Analysis of a Stochastic Inventory System for Serving Eligible Customers with Reworks
Author(s)
Mohammad Ekramol Islam , Md. Sharif Uddin , Mohammad Ataullah ,
Download Full PDF Pages: 58-66 | Views: 1220 | Downloads: 325 | DOI: 10.5281/zenodo.3490341
Abstract
this paper presents an inventory system where eligible customers are screened out at the first stage of service. The arrival of demand for fresh items and for rework items follows the Poisson process with parameter and . From fresh items store, items will be provided to the arrival customer within a negligible service time. We assume that a certain portion of arriving customers will get service with rate and rest of the arriving customer will be rejected to serve with a rate (1- when inventory level for fresh items reaches to the reorder level s an order takes place which follows exponean an ntial distribution with parameter . The defective items will dysfunction before expire date, a service will be provided once it returns to the service center with parameter . If the store of rework items is full then th,e next case will be served at home as early as possible. We considered two stores in the system one for fresh items and another for returned items. When inventory level is zero then ar,rival cu the stomer will be lost forever. A suitable mathematical model is developed and the solution of the developed model using Markov pa rocess with Rate-matrixisderived. Also the sys,,tems characteristics are numerically illustrated. The validation of the result in this model was coded in Mathematica 11
Keywords
Inventory, Stochastic model, Re-order level, Replenishment, Reworks, Poisson process, exponential distribution
References
i. Ammar SI (2015) Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations. Appl Math Comput 260:97–105
ii. Ammar SI (2014a) Transient analysis of a two-heterogeneous servers queue with impatient behavior. J Egypt Math Soc 22(1):90–95
iii. Ammar SI (2014b) Transient behavior of a two-processor heterogeneous system with catastrophes, server failures and repairs. Appl Math Model 38(7–8):2224–2234 Transient analysis of a two-heterogeneous servers queue... 205
iv. Armony M, Ward AR (2010) Fair dynamic routing in large-scale heterogeneous-server systems. Oper Res 58(3):624–637 MR2680568
v. Brojeswar Pal, ShibSankar Sana and KripasindhuChudhuri, A multi-echelon supply chain model for reworkable items in multiple-markets with supply disruption, Economic Modeling,Vol.29,pp.1891-1898.2012
vi. C.K.Sivashankari, S.Panayappan(2014),Production inventory model with reworking of imperfect production, scrap and shortages, International Journal of Management Science and Engineering Management,Vol.9(1),pp.9-20(Taylor’s Francies).
vii. Chiu,Y.S.P.,Liu,S.C.,Chiu,C.L.,Chang,H.M. Mathematical modeling for determining the replenishment policy for a EMQ model with rework and multiple shipments, Mathematical and Computer Modeling,54(9-10),pp.2165-2174,2011.
viii. Chung,K.J., the Economic Product Quantity with rework process in supply chain management, Computers and Mathematics with Application,62(6),pp.2547-2550,2011.
ix. Dharmaraja S (2000) Transient solution of a two-processor heterogeneous system. Math Comput Model 32(10):1117–1123
x. Dharmaraja S, Kumar R (2015) Transient solution of a Markovian queuing model with heterogeneous servers and catastrophes. OPSEARCH (Oct–Dec 2015) 52(4):810–826 .
xi. Huel-Hsin Chang, Feng-TsungChend, Economic Product Quantity model with backordering, rework and machine failure taking place in stock piling time, Wseas Transactions on information scienceand applications,Vol.7Issue4,pp.463-473,2010.
xii. Ibrahima R, LEcuyerb P, Shenc H (2016) Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers. Eur J Oper Res 250(2):480–492 .
xiii. Kumar BK, Madheswari SP, Venkatakrishnan KS (2007) Transient solution of an M/M/2 queue with heterogeneous servers subject to catastrophes. Int J Inform Manag Sci 18(1):63–80
xiv. Krishnamoorthi.C and Panayappan,S.,An EPQ model for an imperfect production system with rework and shortages, International Journal of Operation Research,vol.17(1),pp.104-124, 2013.
xv. Mohammad Ekramol Islam, K.M Safiqul Islam, M Sharif Uddin, Inventory system with postponed demands considering reneging pool’s and rejecting Buffer’s customers, International Conference on Mechanical, Industrial and Materials Engineering 2013 (ICMIME2013), Paper ID: IE-01, 1-3 November, 2013, RUET, Rajshahi, Bangladesh.
xvi. Mohammad Ekramol Islam, M. Sharif Uddin, Mohammad Ataullah, Stochastic Inventory Models with Reworks, Yugoslav Journal of Operations Research 28 (2018), N0. 4, 567-578
xvii. S. K. Goyal and B. C. Giri, Recent trends in modeling of deteriorating inventory, European Journal of Operational Research, vol. 134, no. 1, pp. 1–16, 2001.
xviii. S. Priyan and R. Uthayakumar, An EMQ inventory model for defective products involving rework and sales team’s initiatives-dependent demand, Journal of Industrial Engineering International (2015) 11:517–529, Springer, DOI 10.1007/s40092-015-0118-6
xix. Sanjoi Sharma, S.R. Singh and Mangey Ram, An EPQ model for deteriorating items with price sensitive demand and shortages, International Journal of Operation Research,vol.23(2),pp.245-255, 2015.
xx. Sudhesh R (2010) Transient analysis of a queue with system disasters and customer impatience. Queueing Syst 66(1):95–105
xxi. Yanyi Xu, Arnab Bisi and Maqbool Dada, A Periodic-Review Base-Stock Inventory System with Sales Rejection, Operations Research, vol. 59, No. 3, P.P. 742–753, 2011, ISSN: 0030-364X (Print), ISSN: 1526-5463 (Online).
xxii. Yechiali U (2007) Queues with system disasters and impatient customers when system is down. Queueing Syst 56(3–4):195–202.
xxiii. Y-S.P. Chiu, C-K. Ting, C-B. Cheng, and F-Y. Lin, Alternative approach for realistic lot-sizeproblem with random scrap rate and backlogging, WSEAS Transactions on Mathematics, Vol. 6 (6), 2007, pp. 736-740.
Cite this Article: