Optimal policies for inventory model with shortages, time-varying holding and ordering costs in trapezoidal fuzzy environment

Main Article Content

Pavan Kumar
صندلی اداری

Abstract

This paper proposes the optimal policies for a fuzzy inventory model considering the holding cost and ordering cost as continuous functions of time. Shortages are allowed and partially backlogged. The demand rate is assumed in such to be linearly dependent on time during on-hand inventory, while during the shortage period, it remains constant. The inventory problem is formulated in crisp environment. Considering the demand rate, holding cost and ordering cost as trapezoidal fuzzy numbers, the proposed problem is transformed into fuzzy model. For this fuzzy model, the signed distance method of defuzzification is applied to determine the average total cost (ATC) in fuzzy environment. The objective is to optimize the ATC and the order quantity. One solved example is provided in order to show the applicability of the proposed model. The convexity of the cost function is verified with the help of 3D-graph.

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Author Biography

Pavan Kumar, VIT Bhopal University

Senior Asst Professor, Department of Mathematics

References

Abad, P. (1996). Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Management Science, 42, 1093–1104.

Abad, P. (2001). Optimal price and order-size for a reseller under partial backlogging. Computers and Operation Research, 28, 53–65.

Alamri, A., & Balkhi, Z. (2007). The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioration rates. International Journal of Production Economics, 107, 125–138.

Biswas, A. K., & Islam, S. (2019). A fuzzy EPQ model for non-instantaneous deteriorating items where production depends on demand which is proportional to population, selling price as well as advertisement. Independent Journal of Management & Production, 10( 5), 1679-1703.

Chang, H., & Dye, C. (1999). An EOQ model for deteriorating items with time varying demand and partial backlogging. Journal of the Operational Research Society, 50, 1176–1182.

Chung, K. J., & Ting, P. S. (1993). A heuristic for replenishment of deteriorating items with a linear trend in demand. Journal of the Operational Research Society, 44, 1235-1241.

Dave, U., &Patel, L. (1981). (T, si)-policy inventory model for deteriorating items with time proportional demand. Journal of the Operational Research Society, 32, 137–142.

Dutta, D., & Kumar, p. (2015a). A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost: An interval number approach. Croatian Operational Research Review, 6(2), 321-334. DOI:10.17535/crorr.2015.0025

Dutta, D., & Kumar, P. (2015b). Application of fuzzy goal programming approach to multi- objective linear fractional inventory model, International Journal of Systems Science, 46(12), 2269-2278.

Dye, C. (2007a). Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging. European Journal of Operational Research, 181, 668–678.

Dye, C. (2007b). Joint pricing and ordering for a deteriorating inventory with partial backlogging. Omega, 35(2), 184–189.

Goyal, S., & Giri, B. (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134, 1–16.

He, Y., Wang, S., & Lai, K. (2010). An optimal production-inventory model for deteriorating items with multiple-market demand. European Journal of Operational Research, 203(3), 593–600.

Ho, L-.H., Cheng, C-.L., Yang, M-.F., & Lo, M-.C. (2007). (Q, r) inventory model with backorder discount in fuzzy demand and fuzzy ordering cost. Journal of Information and Optimization Sciences, 28(4), 561-572.

Hung, K. (2011). An inventory model with generalized type demand, deterioration and backorder rates. European Journal of Operational Research, 208(3), 239–242.

Jalan, A., Giri, R., & Chaudhary, K. (1996). EOQ model for items with weibull distribution deterioration shortages and trended demand. International Journal of System Science, 27, 851–855.

Khalifa, H. A. E., Kumar, P., & Smarandache, F. (2020). On optimizing neutrosophic complex programming using lexicographic order. Neutrosophic Sets and Systems, 32, 330-343.

Kumar, P. (2019). An inventory planning problem for time-varying linear demand and parabolic holding cost with salvage value. Croatian Operational Research Review, 10(2), 187-199. DOI:10.17535/crorr.2019.0017

Kumar, P., & Keerthika, P. S. (2018). An inventory model with variable holding cost and partial backlogging under interval uncertainty: Global criteria method. International Journal of Mechanical Engineering & Technology, 9(11), 1567-1578.

Liao, J. (2008). An EOQ model with non instantaneous receipt and exponential deteriorating item under two-level trade credit. International Journal of Production Economics, 113, 852–861.

Mandal, B. (2010). An EOQ inventory model for Weibull distributed deteriorating items under ramp type demand and shortages. OPSEARCH, 47(2), 158–165.

Yang, M-.F., Tu, H-.J., & Wang, C-.M. (2007). Determining the single-vender and single-buyer inventory strategy with fuzzy setup cost and fuzzy ordering cost. Journal of Statistics and Management Systems, 10(4), 499-510.

Mishra, V. K., Singh, L. S. (2011). Deteriorating inventory model for time dependent demand and holding cost with partial backlogging. International Journal of Management Science and Engineering Management, 6(4), 267-271.

Rodrigues, P. C. C., Marins, F. A. S., & Souza, F. B. D. (2017). Application of a mathematical model for the minimization of costs in a micro-company of the graphic sector. Independent Journal of Management & Production, 8(5), 676-692.

Roy, A. (2008). An inventory model for deteriorating items with price dependent demand and time varying holding cost. Advanced Modeling and Optimization, 10, 25–37.

Shah, N., & Shukla, K. (2009). Deteriorating inventory model for waiting time partial backlogging. Applied Mathematical Sciences, 3, 421–428.

Skouri, K., Konstantaras, S., & Ganas, I. (2009). Inventory models with ramp type demand rate, partial backlogging and weibull deterioration rate. European Journal of Operational Research, 192, 79–92.

Teng, J., Ouyang, L., & Chen. L. (2007). A comparison between two pricing and lot-sizing models with partial backlogging and deteriorated items. International Journal of Production Economics, 105, 190–203.

Tripathi, R. P. (2011). Inventory model with time dependent demand rate under inflation when supplier credit linked to order quantity. International Journal of Business and Information Technology, 1(3), 174-183.

Wang, J., & Shu, Y. F. (2005). Fuzzy decision modelling for supply chain management. Fuzzy Sets and System, (150), 107–127.

Wu, O., & Cheng (2005). An inventory model for deteriorating items with exponential declining demand and partial backlogging. Yugoslav Journal of Operations Research, 15(2), 277–288.

Zadeh, L. A. (1965). Fuzzy sets, Information and Control, (8), 338-353.

Zimmermann, H. J. (1985). Application of fuzzy set theory to mathematical programming, Information Science, (36), 29-58.

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