Production and set-up control of a failure-prone manufacturing system

The present paper considers a stochastic optimal control problem for a one-machine two-parts manufacturing system, subject to random breakdowns and repairs. The machine under consideration is not completely flexible and hence requires set-up time and cost in order to switch the production from a part type to another. The objective is to find the production plan and sequence of set-ups that minimize the cost function that penalizes inventory/backlog and set-up costs. A continuous dynamic programming formulation of the problem is presented. A numerical scheme is then adopted to solve the obtained optimality conditions equations. The optimal set-up policy is shown numerically, to be described by a modified hedging corridor strategy. A complete heuristic policy, based on the determination of the boundaries of the corridors that describe the optimal policy in positive and negative areas of the state variables, is developed. The usefulness of such a policy is illustrated through experimentation and sensitivity analysis. Extensions to more complex systems are also discussed.