The type E simple assembly line balancing problem: a mixed integer linear programming formulation

Although the simple assembly line balancing problem (SALBP) is the topic of many studies, typically they either consider minimizing the number of stations for a given cycle time (called type one), or minimizing the cycle time for a given number of stations (called type two). Rarely, type E of the problem has been considered. In the type E, cycle time and number of stations are both decision variables, and the objective is to maximize the line efficiency. This paper presents a mixed integer linear programming formulation for the type E simple assembly line balancing problem. Moreover, to further strengthen the presented formulation, two enhancement techniques in the form of valid inequalities and auxiliary variables are proposed. As the secondary objectives of the problem, minimization of the number of stations, the cycle time, and the smoothness index are studied as well. In the case of workload smoothing, three different linearization methods are employed and compared for minimizing the smoothness index. The results of computational study on the benchmark data set demonstrate the efficacy of the improved formulation