A branch, bound and remember algorithm for maximizing the production rate in the simple assembly line balancing problem

Abstract

The simple assembly line balancing problem is a classical optimization problem. It aims at efficiently assigning elementary operations to the workstations of a paced assembly line to optimize some efficiency measure. In this paper, we deal with the type-2 version of the problem in which the efficiency measure is the maximization of throughput with a given number of workstations. This problem has been scarcely studied compared to its type-1 counterpart, in which the throughput is fixed and the objective is to minimize the number of workstations. This has led to the development of indirect methods using type-1 exact solution methods to tackle the type-2 case.In this paper, we provide lower bounds, logical tests, and dominance rules for the type-2 problem and adapt the state-of-the-art method for the type-1 problem to develop a direct approach for solving the type-2 problem with a direct approach. Computational results show the effectiveness of the direct method, which can outperform recent type-1-based indirect approaches. The proposed method is able to close all instances from the classical instance set and solves to optimality over 90% of the large (100 tasks) and 76.5% of the very large (1000 tasks) instances derived from the current reference set for its type-1 counterpart. The average gaps between the upper and lower bounds on the optimal cycle time are also tight and are less than 0.13% (0.4%) for large (very large) instances. Finally, our results show that direct and indirect methods are comparable in terms of solution quality, but the direct method outperforms its indirect counterpart in terms of running time and optimality gaps. Moreover, we identify that instances averaging two to three tasks per workstation and featuring large variability between task times pose significant challenges to solve to optimality.