A Comprehensive Study on Economic Production Quantity with Ramp-Type Demand and Constant Deterioration Under Fuzzy Environment

Kausik Das () and Sahidul Islam ()
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Kausik Das: University of Kalyani
Sahidul Islam: University of Kalyani

SN Operations Research Forum, 2024, vol. 5, issue 2, 1-21

Abstract: Abstract In this paper, we have discussed a deterministic inventory model with constant demand rate and finite production rate. The demand function has been considered a ramp-type demand which is basically a Heaviside function. For advertisement of product, the marketing cost has also been considered in this model. Due to uncertainty in various cost parameters, we have taken some of them as pentagonal fuzzy number. We defuzzify the total average cost by graded mean integration technique. This research presents a comprehensive investigation into the Economic Production Quantity (EPQ) model in the context of ramp-type demand and constant deterioration, within a fuzzy environment. In traditional inventory management, the EPQ model is widely utilized to determine the optimal production quantity that minimizes total inventory costs. However, real-world scenarios often involve uncertain and imprecise factors, necessitating the incorporation of fuzzy set theory to handle ambiguity. This study addresses this gap by integrating fuzzy logic into the EPQ framework, considering both ramp-type demand patterns and constant deterioration rates. A mathematical model is developed to optimize the production quantity, taking into account fuzzy demand and deterioration rates. The proposed model is then solved using appropriate optimization techniques known as graded mean integration (GMI) method to obtain the total inventory costs. Two numerical examples have been considered to illustrate the results, and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the total average cost and cycle length along with the optimal value have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same. The optimum value of total average cost shows us the validity of our EPQ model. The findings highlight the significance of considering fuzziness in inventory decision-making processes, particularly in environments characterized by uncertain demand patterns and deteriorating inventory items. This research contributes to the existing literature by offering insights into the application of fuzzy logic in EPQ models, thereby enhancing decision-making capabilities in inventory management under uncertain conditions.

Keywords: Deterministic EPQ model; Ramp-type demand; Finite production rate; Pentagonal fuzzy number; Graded mean integration (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s43069-024-00328-6

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