Modelling and solving an FMS part selection problem

This paper discusses a part selection problem for a flexible manufacturing system with versatile machine tools but with no tool transportation devices. We propose a maximal network flow model with two side constraints. The model can be relaxed to either a maximal network flow problem or two independent 0-1 knapsack problems. Our computational results show that the latter relaxation significantly outperforms the former. Other factors affecting the solvability of the model are also examined. Finally, we show that our model can efficiently solve real-world part selection problems.