Abstract
Possibility, necessity, and credibility measures play a significant role to measure the chances of occurrence of fuzzy events. In this paper, possibility, necessity, and credibility measures of exponential fuzzy number, and its expected value has been derived. A multi-item two-warehouse deterministic inventory model for deteriorating items with stock-dependent demand has been developed. For the proposed inventory model, the different costs and other parameters are considered in exponential fuzzy nature. Solution methodology of this model using expected value has been discussed. A numerical example is considered to illustrate the multi-item two-warehouse deterministic inventory model. Finally, few sensitivity analyses are presented under different rates of deterioration to check the validity of the proposed model.
Highlights
Speaking, uncertainty is usual to all real-life problems, for example fuzziness and randomness
Possibility theory was proposed by Zadeh [2] and developed by many researchers, e.g., Dubois and Prade [3], Klir [4], Yager [5] and others
The expected value of fuzzy variable using possibility theory was proposed by Hilpern [9], and application of expected value operator called expected value model was introduced by Liu and Liu [6]
Summary
Uncertainty is usual to all real-life problems, for example fuzziness and randomness. The classical economic order quantity (EOQ) inventory model developed in 1915 had the specific requirements of deterministic cost and lack of deterioration of the stock item. A multi-warehouse inventory model for multi-items with time-varying demand and shortage was developed by Zhou [32]. Nia et al [35] developed a multi-item EOQ model under shortage with fuzzy vendor managed. In spite of the abovementioned developments, following additions can be made in exponential fuzzy number, the formulation and solution of inventory models for deteriorating items under imprecise environments. Multi-item two-warehouse deterministic inventory model for deteriorating items with stock dependent demand. Mathematical Formulation Using the above assumptions and notations, a multi-item deterministic inventory model for deteriorating items with stoke-dependent demand has been developed. The multi-item fuzzy inventory model is given by
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