Optimal priority ordering in optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs

Shu and Perkins deals with the problem of minimising the expected sum of quadratic buffer cost when a single, failure-prone machine produces multiple part-types. They restrict the set of control policies to the class of prioritised hedging point (PHP) policies and determine simple, analytical expressions for the optimal hedging points, provided that the priority ordering of the part-types is given. This paper addresses the determination of the optimal priority ordering for PHP policies, and reports the results of a computational experiment. The conclusions are that instances of up to approximately twenty-five part-types can be solved to optimality in short computing times, that it is worthwhile to use dominance relations and that the influence of the values of some parameters is insignifican

Optimal priority ordering in PHP production of multiple part-types in a failure-prone machine

This note deals with the problem of minimising the expected sum of quadratic holding and shortage inventory costs when a single, failure-prone machine produces multiple part-types. Shu and Perkins (2001) introduce the problem and, by restricting the set of control policies to the class of prioritised hedging point (PHP) policies, establish simple, analytical expressions for the optimal hedging points provided that the priority ordering of the part-types is given. However, the determination of an optimal priority ordering is left by the authors as an open question. This leaves an embedded sequencing problem which we focus on in this note. We define a lower bound for the problem, introduce a test bed for future developments, and propose three dynamic programming approaches (with or without the lower bound) for determining the optimal priority orderings for the instances of the test bed. This is an initial step in a research project aimed at solving the optimal priority ordering problem, which will allow evaluating the performance of future heuristic and metaheuristic proceduresPeer ReviewedPostprint (published version

Optimal priority ordering in optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs

Shu and Perkins deals with the problem of minimising the expected sum of quadratic buffer cost when a single, failure-prone machine produces multiple part-types. They restrict the set of control policies to the class of prioritised hedging point (PHP) policies and determine simple, analytical expressions for the optimal hedging points, provided that the priority ordering of the part-types is given. This paper addresses the determination of the optimal priority ordering for PHP policies, and reports the results of a computational experiment. The conclusions are that instances of up to approximately twenty-five part-types can be solved to optimality in short computing times, that it is worthwhile to use dominance relations and that the influence of the values of some parameters is insignifican

Optimal priority ordering in optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs

Shu and Perkins deals with the problem of minimising the expected sum of quadratic buffer cost when a single, failure-prone machine produces multiple part-types. They restrict the set of control policies to the class of prioritised hedging point (PHP) policies and determine simple, analytical expressions for the optimal hedging points, provided that the priority ordering of the part-types is given. This paper addresses the determination of the optimal priority ordering for PHP policies, and reports the results of a computational experiment. The conclusions are that instances of up to approximately twenty-five part-types can be solved to optimality in short computing times, that it is worthwhile to use dominance relations and that the influence of the values of some parameters is insignifican

Commande optimale stochastique appliquée aux systèmes manufacturiers avec des sauts semi-Markoviens

Les travaux de ce mémoire sont constitués de deux parties principales. La première partie tente de formuler un nouveau modèle du problème de commande optimale stochastique de systèmes sur un horizon fini. Les systèmes considérés sont soumis à des phénomènes aléatoires dits sauts de perturbation qui sont modélisés par un processus semi-Markovien. Ces sauts de perturbation traduits par des taux de transition dépendent de l’état du système et du temps. Par conséquent, le problème de commande est formulé comme un problème d’optimisation dans un environnement stochastique. La deuxième partie vise à modéliser des systèmes de production flexible (SPF). Dans ce mémoire, ces SPF se composent de plusieurs machines en parallèles, ou en série, ou d’une station de travail (une machine représentative). Ces machines sont sujettes à des pannes et à des réparations aléatoires. L’objectif de la modélisation est de déterminer les taux de production u(t) de ces machines en satisfaisant les fluctuations de demande d(t) sur un horizon fini. Dans ce mémoire, nous avons : (a) proposé un nouveau modèle du problème d’optimisation dans un environnement stochastique sur un horizon fini pour deux cas; avec taux d’actualisation (ρ > 0) et sans taux d’actualisation (ρ = 0); (b) modélisé des SPF en déterminant une stratégie de commande plus réaliste incluant stratégie de production; (c) présenté des exemples numériques à l’aide d’une méthode de Kushner et Dupuis (2001)