Abstract
The design of assembly lines is an important issue in manufacturing engineering, management and control. The idle time is the most interesting performance index for assembly line design. The classical simple line-balancing problem (SALBP) consists of assigning tasks, necessary for processing a product, to workstations such that the idle time (number of stations, cycle time, cost) is minimized while precedence constraints between tasks are satisfied. From the worst-case analysis point of view, the SALBP problems are NP-hard in strong sense. Nevertheless, in practice, it is also important to be able to compare real instances of SALBP. In this paper, the simple assembly line balancing problem of type 1 (SALBP-1) is considered where the cycle time is fixed and the objective is to minimize the number of stations. Two unconventional ways are proposed to help to estimate the complexity of such a problem instances: reduction of the graph of precedence constraints to planar one and transformation of the problem to a problem of maximization. We show how these techniques can be employed and why they are useful to analysis of assembly line balancing problem instances.
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