A two-phase approach to solve the synchronized bin–forklift scheduling problem

In this paper, we propose a two-phase approach to solve a combined routing and scheduling problem that occurs in the textile industry: fabrics are dyed by dye-jets and transported by forklifts. The objective is to minimize the cost of the unproductive activities, i.e., the dye-jet setup times and the forklift waiting time. The first phase solves an integer linear program to assign jobs (fabrics) to dye-jets while minimizing the setup cost; we compare an arc-based and a path-based formulation. The second phase uses a mixed-integer linear program for the dye-jet scheduling and both the routing and scheduling of forklifts. Experiments are performed on real data provided by a major multinational company, and larger test problems are randomly generated to assess the algorithm. The tests were conducted using Cplex 12.6.0 and a column generation solver. The numerical results show that our approach is efficient in terms of both solution quality and computational time.