DETERMINISTIC APPROXIMATIONS FOR INVENTORY MANAGEMENT AT SERVICE FACILITIES

Oded Berman · Edward H. Kaplan · DANIEL G. SHEVISHAK

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

Abstract

We consider the problem of finding optimal inventory policies for a service facility where the demand for inventory occurs during the provision of service (e.g., fixing a car in a repair shop). The paper formulates a model where both the demand and service rates are assumed to be constant and deterministic. Consequently a queue forms only during stockouts. In the first of two models analyzed, the service rate is assumed to be fixed and cannot be controlled by the service facility. The ability to use this simple, deterministic model to approximate systems with probabilistic arrival and/or service distributions is also analyzed. The second model relaxes the assumption of a fixed service rate. Optimal inventory policies are derived under linear costs over ordering, inventory holding, customer waiting, and the service rate.

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1964Analysis of Inventory Systems.1979Decision Systems for Inventory Management and Production Planning 1986Decision systems for inventory management and production planning

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1999Stochastic models for inventory management at service facilities 2011A survey on inventory models with positive service time 2000Inventory management at service facilities for systems with arbitrarily distributed service times 2008Inventory Management: An Overview, Canadian Publications, Practical Applications and Suggestions for Future Research 2013Stochastic decomposition in production inventory with service time 2013A revisit to queueing-inventory system with positive service time 2007A perishable inventory system with service facilities and retrial customers 2015Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations

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