%0 Journal Article
%T An EPQ Model with Two-Component Demand under Fuzzy Environment and Weibull Distribution Deterioration with Shortages
%A S. Sarkar
%A T. Chakrabarti
%J Advances in Operations Research
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/264182
%X 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 real-life 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 -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. 1. Introduction The classical EOQ (Economic Order Quantity) inventory models were developed under the assumption of constant demand. Later many researchers developed EOQ models taking linearly increasing or decreasing demand. Donaldson [1] discussed for the first time the classical no-shortage inventory policy for the case of a linear, positive trend in demand. Wagner and Whitin [2] developed a discrete version of the problem. Silver and Meal [3] formulated an approximate solution procedure as ¡°Silver Meal heuristic¡± for a deterministic time-dependent demand pattern. Mitra et al. [4] extended the model to accommodate a demand pattern having increasing and decreasing linear trends. Deb and Chaudhuri [5] extended for the first time the inventory replenishment policy with linear trend to accommodate shortages. After some correction in the above model [5], Dave [6] applied Silver¡¯s [7] heuristic to it incorporating shortages. Researchers have also worked on inventory models with time-dependent demand and deterioration. Models by Dave and Patel [8], Sachan [9], Bahari-Kashani [10], Goswami and Chaudhuri [11], and Hariga [12] all belong to this category. In addition to these demand patterns, some researchers use ramp type
%U http://www.hindawi.com/journals/aor/2012/264182/