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 procedures.