Heuristic procedures for solving the general assembly line balancing problem with setups

Abstract

The General Assembly Line Balancing Problem with Setups (GALBPS) was recently defined in the literature. It adds sequence-dependent setup time considerations to the classical Simple Assembly Line Balancing Problem (SALBP) as follows: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time, thereby providing the task sequence inside each workstation. This paper proposes heuristic procedures, based on priority rules, for solving GALBPS, many of which are an improvement upon heuristic procedures published to date.

The assembly line balancing and scheduling problem with sequence-dependent setup times: problem extension, model formulation and efficient heuristics

“…They formulate a binary linear program and propose priority-rule-based and GRASP procedures. A large number of additional priority-rule-based procedures are developed and examined by Martino and Pastor (2009). Futhermore, see Arcus (1966), Wilhelm (1999) as well as Bautista and Pereira (2002).…”

“…As a basic result, it could be established for SALBP and SUALBSP as well that the station-oriented scheduling scheme is to be preferred to the task-oriented one (cf. Scholl and Voß, 1996;Martino and Pastor, 2009). Both scheduling schemes order tasks by priority rules and successively assign available tasks, i.e., tasks whose predecessors have already been assigned.…”

Combinatorial Benders cuts for assembly line balancing problems with setups

“…The set of constraints (16) determines the proper orderings within any three tasks, i.e., if task i has been performed before task k and task k has been performed before task j, then task i would be performed before task j. The number of necessary performing orders between tasks in any workstation is calculated by the constraint set (17). The set of constraints (18) guarantees that each task in any workstation would have at most one immediate successor.…”

“…Finally, constraints (23) and (24) determine the backward and forward setup operations in any workstation, respectively. We note that the constraints (17), (23) and (24) are semi-linear due to the absolute value. A way of linearising these constraints are given in Appendix B.…”

“…The absolute value function is a semi-linear function used in constraint sets (17), (23) and (24) into two different forms. Table B.1 provides these forms and the transformation of absolute value function for these forms that we used in the proposed mathematical model.…”