Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model

• We aim at developing a MILP model for MMALBPS-I.
• The MILP model handles sequence dependent setup times for mixed-model assembly lines.
• The MILP model also considers parallel workstations and zoning constraints.
• The capability of our MILP is tested through a set of computational experiments.
• Our MILP is able to solve problems up to 14 tasks instances to optimality.

This paper is the first one of the two papers entitled “modeling and solving mixed-model assembly line balancing problem with setups”, which has the aim of developing the mathematical programming formulation of the problem and solving it with a hybrid meta-heuristic approach. In this current part, a mixed-integer linear mathematical programming (MILP) model for mixed-model assembly line balancing problem with setups is developed. The proposed MILP model considers some particular features of the real world problems such as parallel workstations, zoning constraints, and sequence dependent setup times between tasks, which is an actual framework in assembly line balancing problems. The main endeavor of Part-I is to formulate the sequence dependent setup times between tasks in type-I mixed-model assembly line balancing problem. The proposed model considers the setups between the tasks of the same model and the setups because of the model switches in any workstation. The capability of our MILP is tested through a set of computational experiments. Part-II tackles the problem with a multiple colony hybrid bees algorithm. A set of computational experiments is also carried out for the proposed approach in Part-II.