In this paper, the problem of minimizing the smoothness index for an assembly line given a fixed cycle time and the number of workstations is studied. This problem which is known as the workload smoothing line balancing problem (WSLBP) is a mixed-integer quadratic programming problem. Until recently, this problem has only been tackled using heuristic approaches. Recently, there have been some attempts to solve this problem exactly using mixed-integer linear programming (MILP). The MILP formulations, however, are not usually capable of solving large size problem instances. In this paper, the aim is to solve the WSLBP using mathematical programming formulations by using off-the-shelf solvers. Differently from the literature some non-MILP formulations are also considered for the problem. For this purpose, three MILP formulations, one from the literature, and two non-MILP formulations are compared. The two non-MILP formulations include a mixed-integer second order cone programming formulation and a constraint programming model. The superiority of the non-MILP formulations over the considered MILP formulations is experimentally shown.

在本文中，研究了在给定循环时间和工作站数量的情况下，最小化装配线平滑度指标的问题。这个被称为工作负载平滑线平衡问题 (WSLBP) 的问题是一个混合整数二次规划问题。直到最近，这个问题只能使用启发式方法来解决。最近，已经有一些尝试使用混合整数线性规划 (MILP) 来精确解决这个问题。然而，MILP 公式通常不能解决大型问题实例。在本文中，目的是通过使用现成的求解器使用数学规划公式来求解 WSLBP。与文献不同的是，一些非 MILP 公式也被考虑用于该问题。为此，三种 MILP 配方，一种来自文献，并比较了两种非 MILP 配方。两个非 MILP 公式包括混合整数二阶锥规划公式和约束规划模型。实验显示了非 MILP 配方优于所考虑的 MILP 配方。