An approach for integrated scheduling and lot-sizing

In this paper a non time discrete approach is developed for an integrated planning procedure, applied to a multi-item capacitated production system with dynamic demand. The objective is to minimize the total costs, which consist of holding and setup costs for one period. The model does not allow backlog. Furthermore, a production rate of zero or full capacity is the only possibility. The result is a schedule, lot-sizes and the sequences for all lots. The approach is based on a specific property of the setup cost function, which allows for replacement of the integer formulation for the number of setup activities in the model. In a situation where the requirements for the multi-item continuous rate economic order quantity, the so-called economic production lot (EPL) formula, are fulfilled, both the EPL as well as the presented model results are identical for the instances dealt with. Moreover, with the new model problems with an arbitrary demand can be solved.