A Single Product Cycling Problem Under Brownian Motion Demand

R. G. Vickson

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Supply Chain and Inventory Management Management and Optimization Techniques Advanced Queuing Theory Analysis

Abstract

This paper treats a continuous review, single product stochastic cycling problem with demand modelled as a Brownian motion process. A broad class of production policies is admitted: they may be nonstationary, non-Markovian, or, in fact, almost arbitrary. Control theory is used to show that, within this wide class of policies, a simple, stationary, two-number policy is optimal for the average cost minimization problem. This policy switches production on when it is currently off and net inventory reaches a low critical level, or switches it off when it is on and net inventory reaches a high critical level. Simple methods are developed for obtaining the optimal critical levels numerically. Examples are developed comparing the results with those given by Graves and Keilson for a different demand process having the same mean and variance per unit time.

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References

1971Introduction to stochastic control 1966A continuous time inventory model 1978Optimal control of a Brownian storage system 1980Technical Note—A One-Product Production/Inventory Problem under Continuous Review Policy 1981The Compensation Method Applied to a One-Product Production/Inventory Problem

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2019An economic production quantity model with backlogging and imperfect rework process for uncertain demand 2015Performance analysis of a reflected fluid production/inventory model 2010Production control and supplier selection under demand disruptions 2013Brownian inventory models with convex holding cost, Part 1: Average-optimal controls 2010Production control and supplier selection under demand disruptions

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