This chapter is concerned with the time-dependent and stationary behavior of the inventory systems introduced in Chapter 1. Details are given for the continuous review system under a compound renewal demand process. The periodic review system is treated as a special case, following the correspondence explained in Chapter 1. Included in the analysis are the stochastic processes representing inventory position, inventory on hand, and demand during a lead time. The investigation is based on the joint distribution of inventory position and demand during a lead time. Time dependent and stationary distributions of lead time demand, inventory position and inventory on hand are derived in section 3.2 from this joint distribution. Section 3.3 is concerned with certain stationary measures of interest that can be constructed from the distributions obtained before. Important among these are the probability that on hand inventory is positive (the fill rate), the cost rate function, and the distribution of the customer waiting time. The chapter is concluded with a discussion of two special cases. This includes an independent treatment of the unit demands model and the specialization of some of the results to the periodic review mode.
KeywordsLead Time Renewal Process Batch Size Fill Rate Inventory Position
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