A Continous-Review (s, S) Inventory System with Arbitrary Interarrival Distribution between Unit Demand

Abstract

For a continuous-review inventory system where demand is defined by a discrete-valued process with units withdrawn from stock one at a time and where the interarrival times between successive demands are independently and identically distributed, the transient and steady-state distribution for the position inventory are derived when operating under an (s, S) policy. This paper shows that the limiting distribution of the position inventory is uniform over the set (s + 1, …, S) and is independent of the distribution of the interarrival times. When instantaneous delivery of orders is allowed, the problem is equivalent to an independent stand-by system consisting of Q = S − s operating elements subject to failure, where, following the failure of the last operating element, all Q failed elements are immediately repaired or replaced by Q new identical elements.

Incorporating a delay mechanism in ordering policies into multi-echelon distribution systems

“…The literature on single-location continuous-review inventory models is extensive and contains studies on the analysis and computation of optimal or near-optimal parameters of the well known (s, S) and (Q, R) policies under different settings (see Hadley and Whitin (1963), Tijms (1972), Sivlazian (1974), Nahmias (1976), Sahin (1979Sahin ( , 1982, Zipkin (1986aZipkin ( , 1986b, Federgruen and Zheng (1992), and Zheng (1992)). It is well known that in single-location systems under continuous review and Poisson demand, the (Q, R) policy, in which orders are placed only at demand epochs is optimal.…”

On exhibiting inventory systems with Erlangian lifetimes under renewal demands

“…Hence following the derivations given before, we obtain Thus the result regarding the limiting inventory level distribution being uniform for an (s, S) system with renewal demands and instantaneous supply (Sivazlin (1974)) would remain true even if we include failure of exhibited items with Erlangian lifetimes in the model. …”

Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems

“…Since then, substantial research has been done on (Q, r) policies and its generalization (s, S) policies. Various authors have analyzed the operating characteristics and the objective functions of (Q, r) and (s, S) policies under different system settings: Browne and Zipkin [3], Sahin [16], Scarf [17], Serfozo and Stidham [20], Simon [22], Sivazlian [23], Veinott [26], and Zipkin [32], among others. In spite of these efforts, major progress towards the development of efficient algorithms and in the sensitivity analysis of these models has been achieved fairly recently.…”