Analysis and solution to the single-level batch production smoothing problem

Many companies use mixed-model production systems running under the Just-in-Time philosophy in order to efficiently meet customer demands for a variety of products. Such systems require demand be stable and production sequence be leveled. The production smoothing problem aims at finding level schedules in which the appearances of products are dispersed over the horizon as uniformly as possible. In this paper, the production smoothing problem is extended to a more general manufacturing environment where a single machine can be identified as either the final or the bottleneck stage of the system and products may have arbitrary non-zero setup and processing time requirements on this single machine. An optimization model is built for the problem and a two phase solution methodology is developed. The first phase problem is shown to be NP-hard and a parametric heuristic procedure is proposed for its solution. In contrast, the second phase problem is shown to be efficiently solvable and currently available solution methods are adopted from the literature. A computational study is designed to test the proposed two phase solution methodology and also the parametric heuristic procedure. Computational results show that the proposed two phase solution methodology enables effective and efficient control of the studied manufacturing system, and the heuristic procedure developed for the first phase problem is time efficient and promises near optimal solutions for a variety of test instances.