Multi-objective approaches to balance mixed-model assembly lines for model mixes having precedence conflicts and duplicable common tasks

The existence of common tasks for model mixes is the main characteristic of the mixed-model assembly lines. The decision problem considered in this study is how some common tasks can be duplicated to improve the efficiency of a mixed-model assembly line under the assumption that some of the precedence relationships among common tasks for different products are conflicting. This decision problem is called by the authors as mixed-model assembly line balancing with precedence conflicts and duplicable common tasks (MALB-CD). Although precedence conflicts have been mentioned in some of the earlier studies, to the best knowledge of the authors, this is the first study that deals with precedence conflicts by mathematical modeling. In the first step of this study, a new binary mathematical model with single objective for MALB-CD is developed where the single-objective is to minimize the number of workstations. Three goals relevant to MALB-CD are then incorporated into this single-objective model to give rise to two pre-emptive goal programming models, one with precise and the other with fuzzy goals. Minimizing the number of workstations, the cycle time and the total cost required to duplicate common tasks are the goals in question. The proposed mathematical models are illustrated and validated by means of a number of numerical illustrations.