Testing a new approach for the multi-item dynamic scheduling problem

In this paper a non time discrete model for the multi-item, single-machine dynamic scheduling problem is presented. The objective minimizes total holding and setup costs. In the capacitated production system a production rate of zero or full capacity is possible. Backlog is not allowed and setup-times are included. For this model an algorithm is tested, which consists of a start algorithm and two solvers. The start algorithm is used to find an admissible solution. A sequence solver uses heuristics to get a sequence for all batches. A lot-size solver based on different search directions, Quasi-Newton and projection methods, improves the solution for a fixed sequence by changing the lot-sizes and the batch starting times. With the recently developed algorithm several test instances are solved and compared to solutions of the Bomberger Problem and to the commercial advanced planning system APO from SAP. The developed algorithm yields better solutions and outperforms APO comparing the calculation time.