Modelling the effects of machine breakdowns in the generalized cell formation problem

Machines are key elements in manufacturing systems and their breakdowns can dramatically affect system performance measures. This paper proposes a new multi-objective pure integer linear programming approach for the cell formation problem with alternative process routings and machine reliability consideration. The model minimizes total cost and maximizes system reliability simultaneously. Traditional reliability evaluation approaches attempt to model the reliability of the manufacturing system as a function of its elements. These approaches have some negative aspects; therefore, instead of modeling the system reliability as an explicit objective function, we use an approach to model the effects of the machine unreliability in terms of cost and time-based effects. Using the epsilon-constraint method as an optimization tool for multi-objective programming, a numerical example is solved to demonstrate the capability of the proposed model in evaluating various effects of the reliability consideration.