Forming minimum-cost machine cells with exceptional parts using zero-one integer programming

Abstract

The value of forming machine cells for efficient job shop operations is well recognized. In practice, machine cells have often been formed based on intuitive guidelines driven by business objectives. For example, the cell design may seek to match the required skills of operator teams to available personnel, simplify material flow patterns, relieve congested areas around key equipment, and minimize the effect of undesirable environmental factors (noise, vibration, heat, and so on). Traditional methods of cell design often use heuristic rules that involve production flow analysis, similarity coefficients, rank-order clustering, or graph-theoretic methods. A more academic approach is to describe the problem as minimizing a constrained objective function written in terms of cost. The cost-minimizing approach has an advantage in that its importance is naturally understood by upper management. However, this approach generally involves using zero-one integer programming (IP) and thus has had limited usage because the IP approach is computationally demanding and relatively inflexible because it does not allow a controlled number of intercellular movements. Recent studies have shown how to reduce the computational demands. This leaves the inflexibility of the IP approach as its major obstacle. The motivation for this research is to show a method for increasing the zero-one IP method's flexibility by removing its prohibition on intercellular operations while minimizing overall operating costs.