Aggregate scheduling and network solving of multi-stage and multi-item manufacturing systems

This paper is concerned with the modeling of aggregate scheduling problems in multi-stage and multi-item dynamic manufacturing systems with storage space limitations and production capacity constraints of workstations. The model aims to minimize the total cost which is the sum of all costs incurred in holding, processing, transporting and schedule delay over the whole study horizon. In order to solve this model efficiently, we show that it can be transferred into an equivalent static job assignment problem with multiple job classes over a space-time network which is a temporal expansion of the base workstation network. Then, an adapted network algorithm based on Frank-Wolfe's is proposed to solve the equivalent problem. The results are illustrated with their application to a numerical example. The computation times on several problem types and problem sizes are investigated. The model solution represents a system optimum scheduling pattern and, hence, could help to improve the existing scheduling works.