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May, 1993 Production Control in a Failure-Prone Manufacturing System: Diffusion Approximation and Asymptotic Optimality
Elena V. Krichagina, Sheldon X. C. Lou, Suresh P. Sethi, Michael I. Taksar
Ann. Appl. Probab. 3(2): 421-453 (May, 1993). DOI: 10.1214/aoap/1177005432


We consider a problem of controlling the production rate of a single machine, single product, stochastic manufacturing system in order to minimize the total discounted inventory/backlog costs. The demand has two components: one is deterministic with constant rate $d$ and the other is stochastic with random demand batches. Under heavy loading (or heavy traffic) conditions, that is, when the average production capacity is close to the average demand, the control problem is approximated by a singular stochastic control problem. The approximate problem can be solved explicitly. The solution is then interpreted in terms of the actual manufacturing system and a control policy for this system is derived. We prove that the resulting policy is nearly optimal under the heavy traffic condition. This policy is characterized by a single critical level $z_0$. The commodity should be produced only when inventory is less than or equal to $z_0$: The production rate is maximal if the inventory is less than $z_0$ and equal to the deterministic component $d$ of the demand rate if the inventory is equal to $z_0$.


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Elena V. Krichagina. Sheldon X. C. Lou. Suresh P. Sethi. Michael I. Taksar. "Production Control in a Failure-Prone Manufacturing System: Diffusion Approximation and Asymptotic Optimality." Ann. Appl. Probab. 3 (2) 421 - 453, May, 1993.


Published: May, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0804.90067
MathSciNet: MR1221160
Digital Object Identifier: 10.1214/aoap/1177005432

Primary: 90B30
Secondary: 60F17 , 60J65 , 93E20

Keywords: asymptotic optimality , diffusion approximation , heavy traffic , production planning , reflected Brownian motion , Stochastic manufacturing system

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 2 • May, 1993
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