Fuzzy economic production for production inventory
The fuzzy version of the EOQ problem with finite production rate is examined. This means that the optimal production quantity of a single item is sought given that it is produced at a certain rate, its demand is known and constant and shortages are not allowed. Contrary to the classical model, the production quantity is a fuzzy amount with a trapezoidal membership function. The objective is to determine the fuzzy production quantity that minimizes the total storage and fixed production costs per (production) cycle. All problem data are constant over the infinite planning horizon. To obtain the best production quantity \(q_{\ast}\), the centroid of the membership function is determined for each possible value of \(q_{\ast}\) relative to the four points defining the trapezium. Next, defuzzification is performed to convert the fuzzy outputs into a single production quantity. This is accomplished by simply calculating the centroid of the fuzzy outputs. For a small example it is shown that the relative error of using \(q_{\ast}\) instead of the best crisp production quantity is very small. General impression: the paper is not very well written and both the notation and exposition are confusing.
scientific article; zbMATH DE number 1437013