An EPQ Model with Two-Component Demand under Fuzzy Environment and Weibull Distribution Deterioration with Shortages

A single-item economic production model is developed in which inventory is depleted not only due to demand but also by deterioration. The rate of deterioration is taken to be time dependent, and the time to deterioration is assumed to follow a two-parameter Weibull distribution. The Weibull distribution, which is capable of representing constant, increasing, and decreasing rates of deterioration, is used to represent the distribution of the time to deterioration. In many reallife situations it is not possible to have a single rate of production throughout the production period. Items are produced at different rates during subperiods so as to meet various constraints that arise due to change in demand pattern, market fluctuations, and so forth. This paper models such a situation. Here it is assumed that demand rate is uncertain in fuzzy sense, that is, it is imprecise in nature and so demand rate is taken as triangular fuzzy number. Then by using α-cut for defuzzification the total variable cost per unit time is derived. Therefore the problem is reduced to crisp average costs. The multiobjective model is solved by Global Criteria method with the help of GRG Generalized Reduced Gradient Technique. In this model shortages are permitted and fully backordered. Numerical examples are given to illustrate the solution procedure of the two models.