Aggregate Production Planning with Fuzzy Demand and Penalty Costs

Uncertainty due to imprecise data and linguistically expressed information is inherent to real-life problems. Tactical production planning cannot neglect the presence of uncertainty due to the length of the planning horizon and the multitude of interacting factors affecting the manufacturing environment. Quantities expressed linguistically are best described by fuzzy sets to capture vagueness and to facilitate decision making in an uncertain context. This work considers developing an aggregate production plan with fuzzy demand and fuzzy cost elements. A fuzzy linear programming model is proposed that aims to minimize the total production costs and penalty costs caused by the unutilized capacity and unsatisfied demand. The proposed model is illustrated via a numerical example reflecting different cases that may occur in industry. The obtained results determine the optimum aggregate production plan while giving the decision-maker the flexibility to select the degree of satisfaction of constraints.