An improved mathematical program to solve the simple assembly line balancing problem

The simple assembly line balancing problem (SALBP) has been extensively examined in the literature. Various mathematical programs have been developed to solve SALBP type-1 (minimising the number of workstations, m, for a given cycle time, ct) and SALBP type-2 (minimising ct given m). Usually, an initial pre-process is carried out to calculate the range of workstations to which a task i may be assigned, in order to reduce the number of variables of task-workstation assignment. This paper presents a more effective mathematical program than those released to date to solve SALBP-1 and SALBP-2. The key idea is to introduce additional constraints in the mathematical program, based on the fact that the range of workstations to which a task i may be assigned depends either on the upper bound on the number of workstations or on the upper bound on the cycle time (for SALBP-1 and SALBP-2, respectively). A computational experiment was carried out and the results reveal the superiority of the mathematical program proposed.