Optimal control of assembling complexes under predetermined maintenance conditions

This paper discusses a continuous-time approach to production control of parallel assembling complexes under maintenance activities specified in advance in order to avoid machine failures along the planning horizon. Every complex includes multiple machines and a tandem storage and retrieval station. Each machine performs a number of assembling operations with negligible setups and controllable production rates subject to time windows in which predetermined maintenance actions are to be carried out. The objective is to control simultaneous assembling of different items in every complex in order to track dynamic demands for the items as closely as possible, without exceeding the capacity of the tandem storage and retrieval stations. With the aid of the maximum principle, optimal production regimes are derived and a fast iterative time-decomposition algorithm is developed to locate those regimes along the planning horizon with a given accuracy.