Transient analysis of an inventory model with instantaneous replenishment and Catastrophes
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Abstract
We consider an $(\mathrm{s}, \mathrm{S})$ inventory model with instantaneous replenishment and catastrophes. Inventory is replenished according to $(\mathrm{s}, \mathrm{S})$ policy, replenishment being instantaneous. Further no shortage is permitted. We have derived explicit expressions for the transient probabilities using Laplace Transform method and have computed such probabilities numerically. The various performance like number of customers in the system, variance of number of customers in the system, expected inventory level, effective flush out rate, etc. are measured. Steady state probabilities and stability conditions are also derived. Numerical illustrations are used to discuss the system performance measures.
Keywords:
Inventory model, Transient and steady state analysis, Laplace Transform method, CatastrophesMathematics Subject Classification:
Mathematics- Pages: 896-901
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
[I] O.Berman,E.Kim and D.G Shimshack, Deterministic approximations for inventory management at service facilities, IIE Transactions 5(1993), no:5, 98-104.
O.Berman and E.Kim .Stochastic models for inventory management at service facilities, Communication in Statistics. Stochastic Models 15(1999), no.4, 695-718.
O.Berman and K.P Sapna, Inventory management at service facilities for systems with arbitrarily distributed service times, Communications in Statistics. Stochastic Models $16(2000)$, no.3-4, 343-360.
TG Deepak, A.Krishnamoorthy ,C.N Viswanath and K. Vineetha ;Inventory with service time and transfer of customers and/inventory; Annals of Operations Research ,PP.191-213, Volume 160,Number 1/April 2008.
A.Krishnamoorthy,TG Deepak,C.N Viswanath and K.Vineetha; Effective utilization of idle time in an $(mathrm{s}, mathrm{S})$ inventory with positive service time,Journal of Applied Mathematics and Stochastic Analysis(JAMSA), vol.2006, Article ID 69068, 13 pages,2006.doi10.1155/IAMSA/2006/69068
A.Krishnamoorthy,ME Islam and C.N Viswanath; Retrial inventory with Batch Markovian Arrival and Positive Service Time, Stochastic Modelling and Applications Vol 9, Number 2,pp. 38-53,2006.
A.Krishnamoorthy, K.P Jose and C.N Viswanath; Numerical investigation of a $mathrm{PH} / mathrm{PH} / 1$ Inventory system with Positive service time and Shortage; Neural, Parallel & Scientific Computations; Volume 16,Number 4,December 2008 ,Dynamic Publishers, USA.
[א] A.Krishnamoorthy, S.N Sajeev and C.N Viswanath; An Inventory Model with Retrial and Orbital Search; Bulletin of Kerala Mathematical Association ,Special Issue,4765,October 2009; Guest Editor: S.R.S Varadhan FRS.
A.Krishnamoorthy, C.N Viswanath,T.G Deepak and K.Vineetha; Control Policies for Inventory with Service Time; Stochastic analysis and Applications; Volume 24, Number 4/2006, PP.889-899.
A.Krishnamoorthy, C.N Viswanath and M.E Islam; On a Production Inventory with Service Time and retrial of Customers; Proceedings of the 11 th International Conference on Analytical and Stochastic Modelling Techniques and Analysis; ASMTA 2004; pp.238-247-Publishing Company- Magdeburg
A.Krishnamoorthy, C.N Viswanath and M.E Islam;Retrial Production Inventory with MAP and Service Times ; Queues, Flows, Systems, Networks. Proceed- ings of the International Conference "Modern Mathematical Methods of Analysis and Optimization of Telecommunication Networks", Gomel, 2003, pp.148-156.
C.N Viswanath,T.G Deepak ,A.Krishnamoorthy and B.Krishnakumar; On an (s,S) Inventory system with service time vacation on the server an correlated lead time; Quality Technology and Quantitative Management (QTQM), PP.129-143, Volume 5, Number 2 June 2008.
Krishna Kumar B, Arivudainambi D.Transient solution of an $mathrm{M} / mathrm{M} / 1$ queue with catastrophes. Comput Math Appl 2000; 40:1233-1240.
B. Krishna Kumar, A. Krishnamoorthy, S. Pavai MadheswarieS. Sadiq Basha :Transient analysis of a single server queue with catastrophes, failures and repairs, Queueing Systems 2007.
ChaoX.Aqueueing network model with catastrophes and product form solution. OR Lett 1995;18:75-79.
A.Krishnamoorthy, Dhanya Shajin, ViswanathC. Narayanan: Inventory with Potive Service Time: A SurveyQueueing Theory 2, coordinated by Vladimir ANISIMOV, Nikolaos LIMNIOS. (c) ISTE Editions 2020
Atencia I, Moreno P. The discrete time Geo/Geo/1 queue with negative customers and disasters. Comput Oper Res 2004; 31(9): $1537-1548$.
Di Crescenzo A, Giorno V, Nobile AG, Ricciardi LM. On the $mathrm{M} / mathrm{M} / 1$ queue with catastrophes and its continuous approximation.Queueing Syst2003; 43:329-347.
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