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 insignificant