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In the present study, an inventory model with parabolic holding cost, quadratic demand rate, partial backlogging over a time horizon for weibull rate of deteriorating item is proposed. We have supposed the demand rate to be a quadratic function of time. Since the outbreak of pandemic COVID- 19 problem disturbed the political, social, economic, and financial structure of the whole world and both the demand and supply chain management have been affected badly therefore, parabolic holding cost is far better to be taken in account. We explore the inventory system to incorporate three parameters .i.e. purchase cost , backordering cost and cycle time which have been fuzzified using pentagonal fuzzy numbers to obtain total inventory cost. Graded mean integration method and Signed distance method are used to de-fuzzify the total cost. The main aim of the paper is to minimize the total cost per unit time in fuzzy environment. Sensitivity analysis of the optimal solution and its effects have been discussed.
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