Fuzzy production planning model for fresh tomato packing

A fuzzy mathematical program is formed when the strict requirements within a mathematical program (objective coefficients, right-hand-side values, inequality conditions, etc.) are fuzzified. In general, such fuzzifying is appropriate for situations where the values or conditions are subjects of perception. In tomato packing, uncertain elements attributed to human perception are quite common. Such elements include harvest time, tomato packing rate, and shortage cost. In this paper, we first provide an LP formulation to determine the production schedule for a fresh tomato packinghouse. Then the corresponding fuzzy elements are fuzzified into a fuzzy model which is solved using an auxiliary model (mixed 0–1 LP). Using real-life data, we compare the cost obtained from the LP to that from the fuzzy model. It is found that the cost from the former is substantially higher. We observe that the rigid requirements in the LP result in an unrealistic optimal solution, while the fuzzy programming seeks to realize a desirable solution (as perceived by the user) by relaxing some resource restrictions. It is further observed that such opportunistic relaxation of constraints to achieve a better solution is typical of decision-making behavior in tomato packing.