Multi-objective production planning problem: a case study for optimal production

In this paper, we have formulated a multi-objective production planning model for a hardware firm. This firm produces different types of hardware locks and other items in their production run. The objectives of the firm are to minimise the production cost, minimise the inventory holding cost and maximise the net profit subject to the set of realistic constraints. The production planning problem of a similar type in the past formulated under the certain environment where the input information precisely known to the decision maker (DM). However, in most of the situations, the input information is not precisely known. In such situations, fuzzy set theory plays a vital role in modelling of the problem where the input data has some vagueness. The proposed model of production planning also been formulated under fuzzy environment. Both triangular and trapezoidal fuzzy numbers used to present the vagueness in the input information. The equivalent crisp form of the fuzzy model obtained by two different defuzzification approaches namely ranking function and α-cut approach. Henceforth, the formulated models under the certain and fuzzy environment have been solved by the fuzzy goal programming approach.