A three rates of EOQ/EPQ Model for Instantaneous Deteriorating Items Involving Fuzzy Parameter Under Shortages
Swagatika Sahoo1, Milu Acharya2, Mitali Madhusmita Nayak3
1Swagatika Sahoo, Department of Mathematics, Institute of Technical Education and Research, Siksha „O‟ Anusandhan University, Bhubaneswar Odisha, India.
2Milu Acharya, Department of Mathematics, Institute of Technical Education and Research, Siksha „O‟ Anusandhan University, Bhubaneswar Odisha, India.
3Mitali Madhusmita Nayak, Department of Mathematics, Institute of Technical Education and Research, Siksha „O‟ Anusandhan University, Bhubaneswar Odisha, India.
Manuscript received on 20 June 2019 | Revised Manuscript received on 27 June 2019 | Manuscript Published on 22 June 2019 | PP: 405-418 | Volume-8 Issue-8S2 June 2019 | Retrieval Number: H10750688S219/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper emphasizes on developing both crisp and fuzzy (Economic ordered quantity (EOQ)/Economic production quantity(EPQ)) single commodity models with a three rates of production inventory for deteriorating items in which the demand rate is a function of both advertisement and selling price. The objective of the crisp model is to determine the optimum values of advertising cost, cycle time and selling price with the aim of maximizing the total profit. Again, in the fuzzy inventory model, fuzziness is introduced for the price rate, Triangular fuzzy number is considered to represent the fuzziness of the price rate and the total profit function is defuzzified by using the signed distance method. We develop some useful theorems for each type of models to establish the formulas for advertising cost, selling price, replenishment schedule and optimal order quantity and algorithm is designed to find the optimum solutions of both the model. Numerical examples are provided for both the models and sensitivity analyses are conducted to know the effect of changes made the values of different parameters.
Keywords: Defuzzification, Production Inventory Model, Price and Advertising Cost, Shortages, Triangular fuzzy Number.
Scope of the Article: Fuzzy Logics