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Stability and optimality of a multi-product production and storage system under demand uncertainty

Stability and optimality of a multi-product production and storage system under demand uncertainty
Stability and optimality of a multi-product production and storage system under demand uncertainty

This work develops a discrete event model for a multi-product multi-stage production and storage (P&S) problem subject to random demand. The intervention problem consists of three types of possible decisions made at the end of one stage, which depend on the observed demand (or lack of) for each item: (i) to proceed further with the production of the same product, (ii) to proceed with the production of another product or (iii) to halt the production. The intervention problem is formulated in terms of dynamic programming (DP) operators and each possible solution induces an homogeneous Markov chain that characterizes the dynamics. However, solving directly the DP problem is not a viable task in situations involving a moderately large number of products with many production stages, and the idea of the paper is to detach from strict optimality with monitored precision, and rely on stability. The notion of stochastic stability brought to bear requires a finite set of positive recurrent states and the paper derives necessary and sufficient conditions for a policy to induce such a set in the studied P&S problem. An approximate value iteration algorithm is proposed, which applies to the broader class of control problems described by homogeneous Markov chains that satisfy a structural condition pointed out in the paper. This procedure iterates in a finite subset of the state space, circumventing the computational burden of standard dynamic programming. To benchmark the approach, the proposed algorithm is applied to a simple two-product P&S system.

Dynamic programming, Intervention control, Manufacturing, Markov processes, Stochastic stability
0377-2217
406-427
Arruda, E. F.
8eb3bd83-e883-4bf3-bfbc-7887c5daa911
do Val, J. B.R.
4139d2f5-1439-45d9-a77e-8e7e20ec98b8
Arruda, E. F.
8eb3bd83-e883-4bf3-bfbc-7887c5daa911
do Val, J. B.R.
4139d2f5-1439-45d9-a77e-8e7e20ec98b8

Arruda, E. F. and do Val, J. B.R. (2008) Stability and optimality of a multi-product production and storage system under demand uncertainty. European Journal of Operational Research, 188 (2), 406-427. (doi:10.1016/j.ejor.2007.04.028).

Record type: Article

Abstract

This work develops a discrete event model for a multi-product multi-stage production and storage (P&S) problem subject to random demand. The intervention problem consists of three types of possible decisions made at the end of one stage, which depend on the observed demand (or lack of) for each item: (i) to proceed further with the production of the same product, (ii) to proceed with the production of another product or (iii) to halt the production. The intervention problem is formulated in terms of dynamic programming (DP) operators and each possible solution induces an homogeneous Markov chain that characterizes the dynamics. However, solving directly the DP problem is not a viable task in situations involving a moderately large number of products with many production stages, and the idea of the paper is to detach from strict optimality with monitored precision, and rely on stability. The notion of stochastic stability brought to bear requires a finite set of positive recurrent states and the paper derives necessary and sufficient conditions for a policy to induce such a set in the studied P&S problem. An approximate value iteration algorithm is proposed, which applies to the broader class of control problems described by homogeneous Markov chains that satisfy a structural condition pointed out in the paper. This procedure iterates in a finite subset of the state space, circumventing the computational burden of standard dynamic programming. To benchmark the approach, the proposed algorithm is applied to a simple two-product P&S system.

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More information

Published date: 16 July 2008
Keywords: Dynamic programming, Intervention control, Manufacturing, Markov processes, Stochastic stability

Identifiers

Local EPrints ID: 445867
URI: http://eprints.soton.ac.uk/id/eprint/445867
ISSN: 0377-2217
PURE UUID: a139939c-2fe3-4aff-b330-cd4542eed571
ORCID for E. F. Arruda: ORCID iD orcid.org/0000-0002-9835-352X

Catalogue record

Date deposited: 12 Jan 2021 17:32
Last modified: 18 Feb 2021 17:42

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