Determining Economic Order Quantity (EOQ) with Increase in a Known Price under Uncertainty through Parametric Non-Linear Programming Approach

Document Type : Research Paper

Authors

1 industrial engineering, kharazmi university, shiraz, iran

2 Department of Industrial Engineering, Faculty of Engineering. Kharazmi University, Tehran, Iran

Abstract

Constant unit procurement cost is one of the main assumptions in the classic inventory control policies. In the realistic world and practice, suppliers sometimes face increase in the price of a known item. In this paper, an inventory model for items with a known one-time-only price increase under fuzzy environment is presented by employing trapezoidal fuzzy numbers to find the optimal solution. We developed three different policies on the basis of methods such as α-cuts, for defuzzification of internal parameters before solving the model, and Vujosevic, for difuzzification of the external parameters after solving it. In the first policy, we integrated α-cuts method and Parametric Non-Linear Programming ( ) problems to attain the Membership Functions ( ) of external variables in the primary model for achieving the optimal solution. These variables were reached by internal parameters through two-phase maximum/minimum non-linear programming problems and the external variables were approximate fuzzy numbers. Under the other two policies, we used defuzzification techniques of Centroid of Gravity ( ), Signed Distance ( ), and the Maximum Degree of Membership ( ) to attain crisp numbers. The optimal order policies by the three methods were compared and numerical computations showed that the efficiency of the first method (i.e., the presented one) was considerably better than that of the other two methods. In fact, the first method selected the optimal and attractive strategies by allocating membership functions to different α-cuts and provided the Decision Maker ( ) with great information to decide and select the best strategies. The methods were validated by a numerical example. The main aim of this model was determining the special ordering range and net costs saving quantity (involving ordering, holding, and purchasing costs). The time of ordering for positive net costs saving was calculated.

Keywords

References

Arcelus, F., J, Shah, N., H., & Srinivasan, G. (2001). Retailer’s response to special sales: price discount vs. trade credit. Omega, 29(5), 417-428.
Arcelus, F., J., Shah, N., H., & Srinivasan, G. (2003). Retailer’s pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives. International Journal of Production Economics, 81, 153-162.
Baykasoğlu, A., Subulan, K., & Karaslan, F., S. (2016). A new fuzzy linear assignment method for multi-attribute decision making with an application to spare parts inventory classification. Applied Soft Computing, 42, 1-17.
Bharani, B. (2018). Fuzzy Economic Production Quantity Model for a Sustainable System via Geometric programming. Journal of Global Research in Mathematical Archives (JGRMA), 5(6), 26-33.
Brown, R., G. (1982). Advanced Service Parts Inventory Control. Materials Management Systems. Inc. Norwich VT.
Brown, R. G. (1967). Decision Rules for Inventory Management. Aurora: Holt Rinehart & Winston.
Cárdenas-Barrón, L., E., Smith, N., R., & Goyal, S., K. (2010a). Optimal order size to take advantage of a one-time discount offer with allowed backorders. Applied Mathematical Modelling, 34(6), 1642-1652.
Cárdenas-Barrón, L., E., Smith, N., R., & Goyal, S., K. (2010b). Optimal order size to take advantage of a one-time discount offer with allowed backorders. Applied Mathematical Modelling, 34(6), 1642-1652.
Chanda, U., Kumar, A., & Kumar Das, J. (2018). Fuzzy EOQ model of a high technology product under trial-repeat purchase demand criterion. International Journal of Modelling and Simulation, 38(3), 168-179.
Chen, S., P. (2005). Parametric nonlinear programming approach to fuzzy queues with bulk service. European Journal of Operational Research, 163(2), 434-444.
Chen, S., P. (2007). Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method. European Journal of Operational Research, 177(1), 445-457.
Das, B., C., Das, B., & Mondal, S., K. (2015). An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Applied Soft Computing, 28, 453-465.
De, S., K., & Mahata, G., C. (2017). Decision of a fuzzy inventory with fuzzy backorder model under cloudy fuzzy demand rate. International Journal of Applied and Computational Mathematics, 3(3), 2593-2609.
De, S., K., & Sana, S., S. (2013). Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index. Economic Modelling, 31, 351-358.
De, S., K., & Sana, S., S. (2014). A multi-periods production–inventory model with capacity constraints for multi-manufacturers–a global optimality in intuitionistic fuzzy environment. Applied Mathematics and Computation, 242, 825-841.
Dey, O. (2017). A fuzzy random integrated inventory model with imperfect production under optimal vendor investment. Operational Research, 1-15.
Garai, T., Chakraborty, D., & Roy, T., K. (2019). Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment. Annals of Data Science, 6(1), 61-81.
Ghosh, A., K. (2003). On some inventory models involving shortages under an announced price increase. International Journal of Systems Science, 34(2), 129-137.
Hsu, W., K., & Yu, H., F. (2011). An EOQ model with imperfective quality items under an announced price increase. Journal of the Chinese Institute of Industrial Engineers, 28(1), 34-44.
Hu, J., S., Xu, R., Q., & Guo, C., Y. (2011). Fuzzy economic production quantity models for items with imperfect quality. International Journal of Information and Management Sciences, 43-58.
Huang, H., I., Lin, C., H., & Ke, J., C. (2006). Parametric nonlinear programming approach for a repairable system with switching failure and fuzzy parameters. Applied Mathematics and Computation, 183(1), 508-517.
Jana, D., K., Das, B., & Maiti, M. (2014). Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment. Applied Soft Computing, 21, 12-27.
Kazemi, N., Shekarian, E., Cárdenas-Barrón, L., E., & Olugu, E., U. (2015). Incorporating human learning into a fuzzy EOQ inventory model with backorders. Computers & Industrial Engineering, 87, 540-542.
Kumar, R., S. (2018). Modelling a type-2 fuzzy inventory system considering items with imperfect quality and shortage backlogging. Sādhanā, 43(10), 163.
Lev, B., & Soyster, A., L. (1979). An inventory model with finite horizon and price changes. Journal of the Operational Research Society, 30(1), 43-53.
Lev, B., Weiss, H., J., & Soyster, A., L. (1981). Optimal ordering policies when anticipating parameter changes in EOQ systems. Naval Research Logistics Quarterly, 28(2), 267-279.
Liu, J., & Zheng, H. (2012). Fuzzy economic order quantity model with imperfect items, shortages and inspection errors. Systems Engineering Procedia, 4(2011), 282-289.
Mahata, G., C., & Goswami, A. (2013). Fuzzy inventory models for items with imperfect quality and shortage backordering under crisp and fuzzy decision variables. Computers & Industrial Engineering, 64(1), 190-199.
Mojaveri, H., S., & Moghimi, V. (2017). Determination of Economic Order Quantity in a fuzzy EOQ Model using of GMIR Deffuzification. Indonesian Journal of Science and Technology, 2(1), 76-80.
Naddor, E. (1966). Inventory systems. New York: Wiley.
Patro, R., Nayak, M., M., & Acharya, M. (2019). An EOQ model for fuzzy defective rate with allowable proportionate discount. OPSEARCH, 1-25.
Qin, X., S., Huang, G., H., Zeng, G., M., Chakma, A., & Huang, Y., F. (2007). An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty. European Journal of Operational Research, 180(3), 1331-1357.
Rani, S., Ali, R., & Agarwal, A. (2019). Fuzzy inventory model for deteriorating items in a green supply chain with carbon concerned demand. OPSEARCH, 56(1), 91-122.
Sadeghi, J., Mousavi, S., M., & Niaki, S., T., A. (2016). Optimizing an inventory model with fuzzy demand, backordering, and discount using a hybrid imperialist competitive algorithm. Applied Mathematical Modelling, 40(15-16), 7318-7335.
Sadeghi, J., Niaki, S., T., A., Malekian, M., R., & Wang, Y. (2018). A Lagrangian relaxation for a fuzzy random EPQ problem with shortages and redundancy allocation: two tuned meta-heuristics. International Journal of Fuzzy Systems, 20(2), 515-533.
Samal, N., K., & Pratihar, D., K. (2014). Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering. Computers & Industrial Engineering, 78, 148-162.
Saranya, R., & Varadarajan, R. (2018). A fuzzy inventory model with acceptable shortage using graded mean integration value method. Journal of Physics: Conference Series, 1000, 12009.
Sarker, B., R., & Al Kindi, M. (2006). Optimal ordering policies in response to a discount offer. International Journal of Production Economics, 100(2), 195-211.
Shaikh, A., A., Bhunia, A., K., Cárdenas-Barrón, L., E., Sahoo, L., & Tiwari, S. (2018). A Fuzzy Inventory Model for a Deteriorating Item with Variable Demand, Permissible Delay in Payments and Partial Backlogging with Shortage Follows Inventory (SFI) Policy. International Journal of Fuzzy Systems, 20(5), 1606-1623.
Taheri-Tolgari, J., Mohammadi, M., Naderi, B., Arshadi-Khamseh, A., & Mirzazadeh, A. (2018). An inventory model with imperfect item, inspection errors, preventive maintenance and partial backlogging in uncertainty environment. Journal of Industrial & Management Optimization, 275-285.
Taleizadeh, A., A., & Pentico, D., W. (2013). An economic order quantity model with a known price increase and partial backordering. European Journal of Operational Research, 228(3), 516-525.
Taleizadeh, A., A., Zarei, H., R., & Sarker, B., R. (2017). An optimal control of inventory under probablistic replenishment intervals and known price increase. European Journal of Operational Research, 257(3), 777-791.
Tersine, R., J. (1994). Principles of Inventory and Materials Management. (4th ed.). New Jersey: PTR Prentice Hall.
Tersine, R., J. (1996). Economic replenishment strategies for announced price increases. European Journal of Operational Research, 92(2), 266-280.
Vujošević, M., Petrović, D., & Petrović, R. (1996). EOQ formula when inventory cost is fuzzy. International Journal of Production Economics, 45(1-3), 499-504.
Wang, R., S., & Wang, L., M. (2010). Maximum cut in fuzzy nature: Models and algorithms. Journal of Computational and Applied Mathematics, 234(1), 240-252.
Yanasse, H., H. (1990). EOQ systems: the case of an increase in purchase cost. Journal of the Operational Research Society, 41(7), 633-637.
Zimmermann, H., J. (2011). Fuzzy set theory—and its applications. Springer Science & Business Media.
 
Journal of Quality Engineering and Production Optimization
Volume 4, Issue 1
June 2019
Pages 197-219

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