Waiting Time in an S − 1, S Inventory System with Arbitrarily Distributed Lead Times

Wilfried Kruse

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Supply Chain and Inventory Management Advanced Queuing Theory Analysis Age of Information Optimization

Abstract

The customer waiting time distribution is derived for an S − 1, S continuous review inventory system experiencing Poisson demands and general independent identically distributed lead times. The analysis uses results from the infinite server Poisson queue. Some comparisons are made with an approximation to the waiting time distribution due to Higa et al.

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1975Waiting Time in an (S − 1, S) Inventory System

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1992Waiting time distribution in (T, S) inventory systems 1997Service constrained inventory models with random lifetimes and lead times 2009Approximation of the probability distribution of the customer waiting time under an (r, s, q) inventory policy in discrete time 2018Optimal allocation of spares to maximize the window fill rate in a two-echelon exchangeable-item repair system 2012Base stock policy with retrial demands 1990On the optimality of the (S — 1,S) policy

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