An Optimal Condition and Approximation Algorithm for Mixed-model Sequencing Problems

Abstract

There exist many studies for mixed-model sequencing problems. The goal of many of these studies is to level the workload at each workstation on the assembly line in order to minimize the line stoppage time. The sequencing method of the real mixed-model assembly lines of vehicles uses the total workload of each vehicle in order to level the workload at each workstation. This is the same as an assembly line having only one workstation. The reason for assuming the number of workstations in the vehicle assembly line is only one is as follows. It is very difficult to maintain the data for all of the processing time of each workstation because: (1) There are many workstations in vehicle assembly lines. Moreover, the number of specifications for a vehicle is very large. (2) Improvements in the operation of workstations and assembly line balancing are ongoing. Therefore, assembly line balancing is usually performed such that the workload at each workstation for each specification of a vehicle is kept constant as much as possible. As a result, the workload at each workstation can be leveled approximately, though the sequencing method uses the total workload of each specification for a vehicle, not the workload at each workstation. Consequently, we approach a sequencing problem for mixed-model assembly lines with only one workstation. There have been very few studies regarding this problem. Therefore, we have investigated it and obtained related characteristics. Specifically, we have obtained the necessary condition for an optimal solution. We propose an approximation algorithm using this condition. It is shown by numerical examples that the proposed algorithm can find an optimal solution for almost all sequencing problems.