Optimal replenishment policy for fuzzy inventory model with deteriorating items and allowable shortages under inflationary conditions
DOI:
https://doi.org/10.2298/YJOR150202002YKeywords:
inventory, deterioration, partial backlogging, inflation, triangular fuzzy number and signed distance methodAbstract
This study develops an inventory model to determine ordering policy for deteriorating items with constant demand rate under inflationary condition over a fixed planning horizon. Shortages are allowed and are partially backlogged. In today’s wobbling economy, especially for long term investment, the effects of inflation cannot be disregarded as uncertainty about future inflation may influence the ordering policy. Therefore, in this paper a fuzzy model is developed that fuzzify the inflation rate, discount rate, deterioration rate, and backlogging parameter by using triangular fuzzy numbers to represent the uncertainty. For Defuzzification, the well known signed distance method is employed to find the total profit over the planning horizon. The objective of the study is to derive the optimal number of cycles and their optimal length so to maximize the net present value of the total profit over a fixed planning horizon. The necessary and sufficient conditions for an optimal solution are characterized. An algorithm is proposed to find the optimal solution. Finally, the proposed model has been validated with numerical example. Sensitivity analysis has been performed to study the impact of various parameters on the optimal solution, and some important managerial implications are presented.References
Abad, P. L., “Optimal pricing and lot-sizing under condition of perishability and partial backlogging”, Management Science, 42 (1996) 1093-1104.
Ameli, M., Mirzazadeh, A., and Shirazi, M. A., “Economic order quantity model for items with imperfect items under fuzzy inflationary conditions”, Trends in Applied Sciences Research, 6 (3) (2011) 294-303.
Ameli, M., Mirzazadeh, A., and Shirazi, M. A., “Entropic economic order quantity model for items with imperfect quality considering constant rate of deterioration under fuzzy inflationary conditions”, International Journal of Industrial Engineering & Production Research, 24 (1) (2013) 91-99.
Bellman, R. E., and Zadeh, L. A., “Decision-making in a fuzzy environment”, Management Science, 17 (4) (1970) B141–B164.
Bierman, H., and Thomas, J., “Inventory decisions under inflationary conditions”, Decision Sciences, 8 (1977) 151-155.
Buzacott, J. A., “Economic order quantities with inflation”, Operational Research Quarterly, 26 (1975) 553-558.
Chung, K. J., Cárdenas-Barrón, L. E., “The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management”, Applied Mathematical Modelling, 37 (7) (2013) 4653-4660.
Dey, J. K., Mondal, S. K., and Maiti, M. M., “Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money”, European Journal of Operational Research, 185 (2008) 170-194.
De, S. K., and Goswami, A., “An EOQ model with fuzzy inflation rate and fuzzy deterioration rate when a delay in payment is permissible”, International Journal of Systems Science, 37 (5) (2006) 323–335.
Dye, C. Y., Ouyang, L. Y., and Hsieh, T. P., “Deterministic inventory model for deteriorating items with capacity constraint and time-proportional backlogging rate”, European Journal of Operational Research, 178 (3) (2007) 789–807.
Gen, M., Tsujimura, Y., and Zheng, D., “An application of fuzzy set theory to inventory control models”, Computers and Industrial Engineering, 33 (3-4) (1997) 553–556.
Halim, K. A., Giri, B. C., and Chaudhuri, K. S., “Fuzzy economic order quantity model for perishable items with stochastic demand, partial backlogging and fuzzy deterioration rate”, International Journal of Operational Research, 3 (1-2) (2008) 77–96.
Jaggi, C. K., Aggarwal, K. K., and Goel, S. K., “Optimal order policy for deteriorating items with inflation induced demand”, International Journal of Production Economics, 34 (2006) 151-155.
Kaufmann, A., and Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications, New York: Van Nostrand Reinhold, 1991.
Mahata, G. C., and Goswami, A., “A fuzzy replenishment policy for deteriorating items with ramp type demand rate under inflation”, International Journal of Operational Research, 5 (3) (2009) 328-348.
Maity, A. K., and Maiti, M., “A numerical approach to a multi-objective optimal inventory control problem for deteriorating multi-items under fuzzy inflation and discounting”, Computers and Mathematics with Applications, 55 (2008) 1794–1807.
Manna, P., Manna, S. K. and Giri, B. C., “An economic order quantity model with ramp type demand rate, constant deterioration rate and unit production cost”, Yugoslav Journal of Operations Research, 26 (3) (2016) 305-317.
Misra, R. B., “A note on optimal inventory management under inflation”, Naval Research Logistics Quarterly, 26 (1979) 161-165.
Misra, R. B., “A study of inflationary effects on inventory systems”, Logistic Spectrum, 9 (3) (1975) 260-268.
Pattnaik, M., “Optimality test in fuzzy inventory model for restricted budget and space: move forward to a non-linear programming approach”, Yugoslav Journal of Operations Research, 25 (3) (2015) 457-470.
Pu, P. M., and Liu, Y. M., “Fuzzy Topology1, neighborhood structure of a fuzzy point and Moore-Smith Convergence”, Journal of Mathematical Analysis and Application, 76 (1980) 571-599.
Roy, A., Maiti, M. K., Kar, S., and Maiti, M., “An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon”, Applied Mathematical Modelling, 33 (2009) 744–759.
Sarkar, B., Saren, S., Cárdenas-Barrón, L. E., “An inventory model with trade-credit policy and variable deterioration for fixed lifetime products”, Annals of Operations Research, 229 (1) (2015) 677–702.
Shah, N. H., Cárdenas-Barrón, L. E., “Retailer's decision for ordering and credit policies for deteriorating items when a supplier offers order-linked credit period or cash discount”, Applied Mathematics and Computation, 259 (2015) 569-578.
Shah, N. H., Patel, D. G., and Shah, D. B., “EPQ model for imperfect production processes with rework and random preventive machine time for deteriorating items and trended demand”, Yugoslav Journal of Operations Research, 25 (3) (2015) 421-439.
Valliathal, M., and Uthayakumar, R., “Fuzzy inventory model for retailer’s optimal replenishment policies under inflationary condition”, International Journal of Pure and Applied Sciences and Technology, 1 (1) (2010) 49-69.
Vujosevic, M., Petrovic, D., and Petrovic, R., “EOQ formula when inventory cost is fuzzy”, International Journal of Production Economics, 45 (1996) 499–504.
Vrat, P., and Padmanabhan, G., “An EOQ model for items with stock dependent consumption rate and exponential decay”, Engineering Costs and Production Economics, 19 (1990) 379-383.
Wee, H. M., and Law, S. T., “Economic production lot size for deteriorating items taking account of time value of money”, Computers and Operations Research, 26 (1999) 545-558.
Wee, H. M., and Law, S. T., “Replenishment and pricing policy for deteriorating items taking into account the time-value of money”, International Journal of Production Economics, 71 (2001) 213-220.
Widyadana, G. A., Cárdenas-Barrón, L. E., and Wee, H. M., “Economic order quantity model for deteriorating items and planned backorder level”, Mathematical and Computer Modelling, 54 (5-6) (2011) 1569-1575.
Wu, J., Ouyang, L. Y., Cárdenas-Barrón, L. E., Goyal, S. K., “Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing”, European Journal of Operational Research, 237 (3) (2014) 898-908.
Yang, H. L., Tern, J. T., and Chern, M. S., “An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages”, International Journal of Production Economics, 123 (2010) 8–19.
Yao, J. S., and Chiang, J., “Inventory without backorder with fuzzy total cost and fuzzy storing cost defuzzified by centroid and signed distance”, European Journal of Operational Research, 148 (2) (2003) 401–409.
Zadeh, L. A., “Fuzzy Sets”, Information and Control, 8 (3) (1965) 338–353.
Zimmerman, H. J., “Description and optimization of fuzzy systems”, International Journal of General Systems, 2 (1976) 209–215.
Downloads
Published
Issue
Section
License
Copyright (c) 2016 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
