A Continuous Review of (S - s) Inventory Systems in which Depletion is Due to Demand and Failure of Units

Kumaraswamy, S.; Sankarasubramanian, E.

doi:10.2307/2581853

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“…Various stochastic models of inventory systems have been studied recently by Yadavalli and Joubert [13], Yadavalli et al [12]. Studies on perishable product inventory systems have gained much importance in literature (Kumaraswamy and Sankarasubramanian [7], Kalpakam and Arivarignan [4], Pal [9], Liu [8], Raafat [10] and Kalpakam and Sapna [5,6]). In the stochastic analysis of such inventory systems, it is generically assumed that the distributions of the random variables representing the number of demands over a period of time, the lifetime of the product and the lead-time remain the same and do not change throughout the domain of the analysis.…”

Section: Introductionmentioning

confidence: 99%

A Perishable Product Inventory System Operating in a Random Environment

Yadavalli¹,

Schoor²

2012

The South African Journal of Industrial Engineering

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A model of a perishable product inventory system operating in a random environment is studied. For the sake of simplicity, the stochastic environment is considered to alternate randomly over time between two states 0 and 1 according to an alternating renewal process. When the environment is in state k , the items in the inventory have a perishing rate k µ , the demand rate is k λ and the replenishment cost is k CR. Assuming instantaneous replenishment at the epoch of the first demand after the stock-out and associating a Markov renewal process with the inventory system, the stationary distribution of the inventory level and the performance of various measures of the system evolution are obtained. Numerical examples illustrate the results obtained. OPSOMMING 'n Model van 'n voorraadsisteem van 'n bederfbare produk wat aangehou word in 'n toevalsomgewing word voorgehou. Die stogastiese omgewing word vir doeleindes van vereenvoudiging beskryf deur twee toestande, nul en een, wat op toevalswyse die wisselende hernuwingsproses behandel. Wanneer die omgewing in toestand k is, is die bederftempo k µ , die vraagtempo k λ , en die aanvullingskoste k CR. As aanvulling oombliklik plaasvind na vooraaduitputting en Markov-hernuwings geassosieer word met die voorraadsisteem, word die stasionêre verdeling van voorraadvlak en ander prestasiemaatstawe van die sisteem verkry. 'n Numeriese voorbeeld ondersteun die resultate wat verkry is.

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