Comparison of three vacation policies in discrete time inventory system with postponed demands

Abstract

In this paper, we consider a single server discrete time inventory system with postponed demands and server vacation. Arrival process follows DMAP and ordering policy follows $(s,S)$ policy with geometrically distributed lead time. Due to depletion of inventory in the stock to zero, server may avail vacation immediately or after some random time. Here, we proposed three different vacation policies, namely modified multiple vacation (random idle time before each vacation), single (only one vacation) and multiple (one after another vacation). The demand who arrives during the stock-out period or server vacation period enters the pool of infinite size. These pooled demands are selected one-by-one according to a rule. The vacation time, the server idle time and the inter-selection time follow independent DPH distribution. The joint probability distribution of the number of demands in the pool, the server status, the on-hand inventory level is obtained in the steady-state case. We derived the total expected cost function in the steady-state case for each vacation model. We present some numerical examples and try to justify the best vacation policy for different parameter rates. Also, we analyse the impact of system costs on the total optimal cost of modified multiple vacation policy.

Keywords:

• Vacation policy
• matrix-geometric method
• discrete time inventory system
• postponed demands

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by the University Grants Commission, India, research award no. 42-6/2013(SR).

Notes on contributors

I. Padmavathi

I. Padmavathi received her M.Sc., (Mathematics) from Anna University, Guindy, Chennai, her M.Phil., (Mathematics) and Ph.D., from School of Mathematics, Madurai Kamaraj University, Madurai. Her areas of research interest are Continuous review inventory system, Discrete time inventory system and Vacation inventory system. She has published her articles in journals such as Annals of Operational Research,OPSEARCH and International of Journal of Operational Research. Currently, she is working as an Assistant Professor of Mathematics in the Department of Mathematics, The Madura College (Autonomous), Madurai, Tamilnadu, India.

B. Sivakumar

B. Sivakumar received his M.Sc., (Mathematics) and Ph.D., from Madurai Kamaraj University, Madurai. He has received Young Scientist Award from DST-SERC Fast Track scheme in 2008. He has received major project from DST, UGC, NBHM, etc. His areas of research interest are Continuous review inventory system, Discrete time inventory system and Queueing theory. He has numerous publications in various reputed journals of mathematics and operations research such as European Journal of Operational Research, Computers and Industrial Engineering, International Journal of Production Economics, etc. Currently, he is working as an Assistant Professor of Applied Mathematics in the School of Mathematics, Madurai Kamaraj University, Madurai, Tamilnadu, India.