A computational study of the influence of the parameter big-M in a time-indexed MILP for assembly flowshop

In this paper, a mixed integer linear programming model was proposed to solve the assembly flowshop scheduling problem. The objective of the study was to evaluate the impact on computational time (CPU) from the variation of the value of the big-M parameter considering three different dimensions. The performance of the mathematical model was evaluated from the application of a commercial solver that has different strategies in search of the optimal solution. 240 test-problems were solved on the optimality in an acceptable computational time, with the number of jobs ranging from 4 to 8, the number of products from 2 to 4 and the number of machines from 1 to 4. The performance profiles of Dolan and More (2002) were employed for a more accurate statistical analysis of the results, which indicated the most efficient value for the big-M parameter in the proposed mathematical formulation.