Coping with uncertainties in production planning through fuzzy mathematical programming: application to steel rolling industry

This paper adopts the approach of fuzzy set theory into the context of a practical production planning problem encountered frequently in steel rolling mills, where the objective is to establish a cost-minimising master production schedule. To better capture the uncertainties associated with the market demand, the problem is formulated as a fuzzy mixed integer bilinear program (FMIBLP) in which the demand constraints are assumed to be rather flexible and characterised by triangular membership functions. The aspiration level for the decision maker is represented by a linear function where the tolerance limits for this function are determined based on the degree of flexibility in demand that the decision maker is willing to undertake. The fuzzy decision set is obtained using two different types of aggregators which, in turn, allows for the transformation of the fuzzy model into a crisp one seeking the maximum value for the aspiration level. A linearisation scheme is first adopted to transform the bilinear model into an equivalent linear model and then an exterior penalty function based algorithm is employed to the linearised version in order to obtain 'near optimal' solutions that minimise deviations from integral batches. Computational experiments are carried out for different problem instances under both aggregation operators and the results are reported.