Simple assembly line balancing problem of Type 1 with grey demand and grey task durations

The purpose of this paper is to present a mixed integer programming model for simple assembly line balancing problems (SALBP) with Type 1 when the annual demand and task durations are uncertain and encoded with grey numbers.

Grey theory and grey numbers are used for illustrating the uncertainty of parameters in an SALBP, where the objective is to minimize the total number of workstations. The paper proposes a 0-1 mathematical model for SALBP of Type 1 with grey demand and grey task durations.

The uncertainty of the demand and task durations are encoded with grey numbers and a well-known 0-1 mathematical model for SALBP of Type 1 is modified to find the minimum number of workstations in order to meet both the lower and upper bounds of the uncertain demand. The results obtained from the proposed mathematical model show a task-workstation assignment that does not distribute precedence relations among tasks and workstations and the sum of task durations in each single workstation is less than or equal to the grey cycle time.

The grey theory and grey numbers have not been previously used to identify uncertainties in assembly line balancing problems. Therefore, this study provides an important contribution to the literature.