A New Mathematical Formulation for the Classical Assembly Line Balancing Problem

This paper presents a new integer formulation (Type III ALB) for a single model assembly line balancing problem. The objective of the formulation is to minimize the total idle time, which is defined as the product of the number of work stations and the cycle times minus the total work content. This formulation considers currently existing Type I (minimizing the number of work stations for a given cycle time) and type II (minimizing the cycle time for a given number of work stations) formulations as its special cases and provides the global minimum solutions of the cycle time and the number of work stations. This information would be of great value to line designers involved in designing new assembly lines and rebalancing old lines under flexible conditions. Solution methods based on combination of Type I and Type II approaches are also suggested and compared.