Cost optimization model for items having fuzzy demand and deterioration with two-warehouse facility under the trade credit financing

Boina Anil Kumar; S. K. Paikray; Hemen Dutta; Boina Anil Kumar; S. K. Paikray; Hemen Dutta

doi:10.3934/math.2020109

AIMS Mathematics

2020, Volume 5, Issue 2: 1603-1620. doi: 10.3934/math.2020109

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Cost optimization model for items having fuzzy demand and deterioration with two-warehouse facility under the trade credit financing

1.
Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India
2.
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India

Received: 28 September 2019 Accepted: 26 December 2019 Published: 05 February 2020
MSC : 90B05, 03E72

Most of the researchers developed their inventory models to forecast the optimal replenishment quantity and time in view of minimizing the total inventory cost by considering deterministic demand and the deterioration of the items. But, in real business these demands and deterioration are mostly fuzzy in nature due to many practical factors, such as increase or decrease in goodwill of the product, competition from the substitute products, scientific advancement in preserving facilities, change in environmental conditions and so on. So by following researcher's classical inventory model, retailer may order less or excess amount of items than the actual requirement. As a result, retailer may face loss in business or increase in cost. Moreover, in many cases, suppliers offer trade credit to increase their sales, and by availing the trade credit facility the retailer purchases a number of items more than the existing storage capacity (in own warehouse) in order to minimize the ordering cost and investment capital. To accommodate these excess amounts of items retailer may hire a warehouse on rent basis. In the light of these facts, we develop a cost optimization model for the inventory items having fuzzy demand and deterioration with two-warehouse facility under trade credit financing by considering triangular fuzzy numbers for the associated parameters. The Graded Mean Integration Representation defuzzification technique is used and numerical examples are provided to justify the validity of the proposed model. Finally, sensitivity analysis of major parameters has been incorporated to draw the managerial insight on optimal solution.
- inventory model,
- fuzzy demand and deterioration,
- trade credit offer,
- graded mean integration method
Citation: Boina Anil Kumar, S. K. Paikray, Hemen Dutta. Cost optimization model for items having fuzzy demand and deterioration with two-warehouse facility under the trade credit financing[J]. AIMS Mathematics, 2020, 5(2): 1603-1620. doi: 10.3934/math.2020109

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Abstract

Most of the researchers developed their inventory models to forecast the optimal replenishment quantity and time in view of minimizing the total inventory cost by considering deterministic demand and the deterioration of the items. But, in real business these demands and deterioration are mostly fuzzy in nature due to many practical factors, such as increase or decrease in goodwill of the product, competition from the substitute products, scientific advancement in preserving facilities, change in environmental conditions and so on. So by following researcher's classical inventory model, retailer may order less or excess amount of items than the actual requirement. As a result, retailer may face loss in business or increase in cost. Moreover, in many cases, suppliers offer trade credit to increase their sales, and by availing the trade credit facility the retailer purchases a number of items more than the existing storage capacity (in own warehouse) in order to minimize the ordering cost and investment capital. To accommodate these excess amounts of items retailer may hire a warehouse on rent basis. In the light of these facts, we develop a cost optimization model for the inventory items having fuzzy demand and deterioration with two-warehouse facility under trade credit financing by considering triangular fuzzy numbers for the associated parameters. The Graded Mean Integration Representation defuzzification technique is used and numerical examples are provided to justify the validity of the proposed model. Finally, sensitivity analysis of major parameters has been incorporated to draw the managerial insight on optimal solution.

References

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