Simultaneous determination of lot size and production rate at capacity-constrained multiple-product systems

In the capacity constrained manufacturing systems where multiple product types are manufactured, the products are often produced in lots. Although the lot production may increase the system throughput by reducing changeover times, it may also increase production lead time because each item in a large lot has a long waiting time. Hence, a production manager should consider both throughput and lead time at the same time when deciding production lot sizes. This paper, which is an extension to the previous work done in Koo et al. (2007) that assumes homogeneous setup times, addresses a lot sizing problem in the system with multiple product types and unequal setup times. We develop a non-linear optimization model for simultaneous determination of throughput rate and lot size for each product. Since this optimization model cannot be solved analytically, we propose a heuristic solution procedure by analyzing the characteristics of the problem. Some numerical examples are presented to validate the proposed model, and finally the performance of the heuristic procedure is evaluated by comparison with the results of simulation experiments.