Service constrained inventory models with random lifetimes and lead times
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Service constrained inventory models with random lifetimes and lead times L Liu and KL Cheung The Hong Kong University of Science and Technology We consider continuous review inventory models with Poisson demands, exponentially distributed lifetimes and replenishment order processing times. The model is unique in that complete backorders, complete lost sales and partial backorders are all addressed. We derive exact expressions of the key operating characteristics. Based on these performance measures, we optimise the system parameters subject to ®ll rate and waiting time constraints. Numerical examples are also provided to validate our models and to generate useful managerial insights. Keywords: inventory; Markov process; random lifetime; service constraints
Introduction Inventory systems with ®nite item lifetimes are known to be dif®cult to analyse when replenishment lead times are positive. This is primarily because the stock depletion rate is a function of the on-hand inventory.1 Furthermore, analytical results are often limited when the probability distributions of the inventory levels are intractable. Despite their complexity, these inventory systems are instrumental in representing realistic systems of retail, maintenance, production and blood bank management. This paper is motivated by the classic (S ÿ 1; S) inventory systems in the context of reparable items, such as METRIC.2 In METRIC, expensive spare parts are managed to replace malfunctioning parts that are brought back from the ®eld to the bases and the depot for repair. METRIC assumes in®nite item lifetimes. In practice, however, many items are subject to aging over time.3 Under such a condition, it would be reasonable to assume that items have only ®nite lifetimes. This paper considers single-item (S ÿ 1; S) inventory models with exponentially distributed lifetimes and order processing times. In many studies of inventory systems, the time-to-failure and time-to-repair are described by exponential distributions. See, for example, Kapakam and Sapna4 and Bielecki and Kumar.5 In our study, the possibilities of partial backorders, complete backorder and complete lost sales are all included. In addition, inventory investment is based on service level criteria rather than on the classic cost minimising approach. This is plausible in view of the current trend that a company's competitive edge Correspondence: Dr L Liu, Department of Industrial Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. E-mail: [email protected]
is characterised by its response times and ®ll rates in meeting customer's demands. Service levels, which are relatively easy to de®ne and measure, should be integrated into companies' operation strategies. The cost minimising approach, on the contrary, may not be feasible when any of the relevant cost elements (such as shortage cost) is dif®cult to evaluate. According to the existing classi®cation scheme of inv
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