The Effect of Volume Discounts in the Economic Order Quantity Model Using Fuzzy Approach
Subject Areas :
Industrial Management
Gholamreza Amini Khiabani
1
,
Karim Hamdi
2
1 - MSc. Faculty of Economic and management, Islamic Azad University, Science and Research Branch, Tehran, Iran
2 - Associate Prof., Faculty of Economic and management, Islamic Azad University, Science and Research Branch, Tehran, Iran
Received: 2015-12-22
Accepted : 2016-07-18
Published : 2016-09-04
Keywords:
Abstract :
Production Programming and Inventory Control are known as most important topics in manufacturing companies subordinated the uncertainty and risk. This uncertainty increases the system costs while economic order quantity (EOQ) gives direct benefit to the organization. In this research, a new inventory control model will be devised due to the volume discount and under fuzzy approach. To calculate the optimal parameters, we used pre-solving de-fuzzification for all entrance parameters and pro-solving de-fuzzification for all output parameters based on torques method in parameters certainty. Meanwhile, converting de-fuzzification models to classical models and replacing de-fuzzy digits finally led to calculate the suggestive parameters. To better illustrate the model sensitivity, we used a case study. The result showed this heuristic approach would analytically examine the model and determine optimal parameters quantity for each level and each optimal level could be selected depends on the organization policies.
References:
Björk, , M. (2008). The Economic Production Quantity Problem with a Finite Production Rate and Fuzzy Cycle Time. Proceedings of the 41st Hawaii International Conference on System Sciences.
Björk, K. M. (2009). An Analytical Solution to a Fuzzy Economic Order Quantity Problem. International Journal of Approximate Reasoning, 50(3), 485–493.
Chen, Sh. H., & Chang, SH. M. (2008). Optimization of Fuzzy Production Inventory Model with Unrepairable Defective Products. International Journal Production Economics, 113(2), 887–894.
Der, Chen, L., & Jing, Shing, Y. (2000). Fuzzy Economic Production for Production Inventory. Fuzzy Sets and Systems, 111(3), 465،495.
Haaj, Shirmohammadi, A. (2005). Principles of Production and Inventory Planning and Control. Arkan Publishing.
Hu, J., Xu, R, & Guo, C. (2011). Fuzzy Economic Production Quantity Models for Items with Imperfect Quality. International Journal of Information and Management Sciences, 22(1), 43- 58.
Huey،Ming, L., & Jing, Shing, Y. (1998). Economic Production Quantity for Fuzzy Demand Quantity and Fuzzy Production Quantity. European Journal of Operational Research, 109(1), 203-211.
Jau،Chuan, K., Hsin،I, H. & Chuen, Horng, L. (2006). Parametric Programming Approach for Batch Arrival Queues with Vacation Policies and Fuzzy Parameters. Applied Mathematics and Computation, 180(1), 217–232.
Jau، Chuan, K., & Chuen, Horng, L. (2005). Fuzzy Analysis of Queuing Systems with an Unreliable Server: A Nonlinear Programming Approach. Applied Mathematics and Computation, 175(1), 330–346.
Jershan, C., Jing، Shing, Y. and Huey، Ming, L. (2005). Fuzzy Inventory Defuzzification by Singned Distance method.” Journal of Information Science and Engineering, 21(1), 673،694.
11.Jing،Shing, Y., & Jershan, C. (2003). Inventory without Backorder with Fuzzy Total Cost and Fuzzy Storing Cost Defuzzified by Centroid and Signed Distance. European Journal of Operational Research, 148(2), 401–409.
Jolai, F., Gheisariha, E. and Nojavan, F. (2011). Inventory Control of Perishable Items in a Tw, Echelon Supply Chain. Journal of Industrial Engineering, University of Tehran, Special Issue, 69, 77.
Lee, H. M., & Yao, J. S. (1999). Economic Order Quantity in Fuzzy Sense for Inventory without Backorder Model. Fuzzy Sets and Systems, 105(1), 13، 31.
Mohabbatdar, S. and Esmaeili, M. (2011). Optimal Selling Price, Marketing Expenditure and Order Quantity with Backordering. Journal of Industrial Engineering, University of Tehran, Special Issue, 103-112.
15.Negi, D. S. & Lee, E. S. (1992). Analysis and Simulation of Fuzzy Queue. Fuzzy Sets and Systems, 46(3), 321– 330.
16.Razmi, J., Seifoory, M. & Pishvaee, M. S. (2011). A Fuzzy Multi،Attribute Decision Making Model for Selecting the Best Supply Chain Strategy: Lean, Agile or Leagile. Journal of Industrial Engineering, University of Tehran, Special Issue, 127،142.
17.San, Chyi, C. (1999). Fuzzy Production Inventory for Fuzzy Product Quantity with Triangular Fuzzy Number. Fuzzy Sets and Systems, 107(1), 37-57.
Shiang،Tai, L. (2008). Fuzzy Profit Measures for a Fuzzy Economic Order Quantity Model. Applied Mathematical Modelling, 32(10), 2076–2086.
19. Shih, Pin, C. (2004). Parametric Nonlinear Programming for Analyzing Fuzzy Queues with Finite Capacity. European Journal of Operational Research, 157(2), 429–438.
20. Shi, Pin, C. (2007). Solving Fuzzy Queuing Decision Problems via a Parametric Mixed Integer Nonlinear Programming Method. European Journal of Operational Research, 177(1), 445–457.
21. Shih, Pin, C. (2005). Parametric Nonlinear Programming Approach to Fuzzy Queues with Bulk Service. European Journal of Operational Research, 163(2), 434–444.
Shishebori, D., & Hejazi, S. R. (2009). Application of Fuzzy AHP Technique to Selection the Most Efficient Method of Improving of Productivity. Journal of Industrial Engineering, University of Tehran, 43(1), 5-66.
Taheri،Tolgari, J., Mirzazadeh, A. & Jolai, F. (2012). An Inventory Model for Imperfect Items under Inflationary Conditions with Considering Inspection Errors. Computers and Mathematics with Applications, 63(6), 1007–1019.
Vujosevic, M., Petrovic, D. & Petrovic, R. (1996). EOQ Formula when Inventory Cost is Fuzzy. International Journal of Production Economics, 45(1،3), 499-504.
Yang, G., K. (2011). Discussion of Arithmetic Defuzzifications for Fuzzy Production Inventory Models. African Journal of Business Management, 5(6), 233-2344.
Yao, J. s., & Lee, H. M. (1996). Fuzzy Inventory with Backorder for Fuzzy Order Quantity. Information Sciences, 93(3-4), 283- 319.
Yao, J. s., & Lee, H. M. (1999). Fuzzy Inventory with or without Backorder for Fuzzy Order Quantity with Trapezoid Fuzzy Number. Fuzzy Sets and Systems, 105(3), 311- 337.
Yao, J. S., Chang, S. C. & Su, J. S. (2000). Fuzzy Inventory without Backorder for Fuzzy Order Quantity and Fuzzy Total Demand Quantity. Computer and Operation Research, 27(10), 935-962.
Zadeh, L. A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1(1), 28-31
Zimmermann, H. J. (2001). Fuzzy Set Theory and its Applications. 4th ed., Kluwer Academic, Boston
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Björk, , M. (2008). The Economic Production Quantity Problem with a Finite Production Rate and Fuzzy Cycle Time. Proceedings of the 41st Hawaii International Conference on System Sciences.
Björk, K. M. (2009). An Analytical Solution to a Fuzzy Economic Order Quantity Problem. International Journal of Approximate Reasoning, 50(3), 485–493.
Chen, Sh. H., & Chang, SH. M. (2008). Optimization of Fuzzy Production Inventory Model with Unrepairable Defective Products. International Journal Production Economics, 113(2), 887–894.
Der, Chen, L., & Jing, Shing, Y. (2000). Fuzzy Economic Production for Production Inventory. Fuzzy Sets and Systems, 111(3), 465،495.
Haaj, Shirmohammadi, A. (2005). Principles of Production and Inventory Planning and Control. Arkan Publishing.
Hu, J., Xu, R, & Guo, C. (2011). Fuzzy Economic Production Quantity Models for Items with Imperfect Quality. International Journal of Information and Management Sciences, 22(1), 43- 58.
Huey،Ming, L., & Jing, Shing, Y. (1998). Economic Production Quantity for Fuzzy Demand Quantity and Fuzzy Production Quantity. European Journal of Operational Research, 109(1), 203-211.
Jau،Chuan, K., Hsin،I, H. & Chuen, Horng, L. (2006). Parametric Programming Approach for Batch Arrival Queues with Vacation Policies and Fuzzy Parameters. Applied Mathematics and Computation, 180(1), 217–232.
Jau، Chuan, K., & Chuen, Horng, L. (2005). Fuzzy Analysis of Queuing Systems with an Unreliable Server: A Nonlinear Programming Approach. Applied Mathematics and Computation, 175(1), 330–346.
Jershan, C., Jing، Shing, Y. and Huey، Ming, L. (2005). Fuzzy Inventory Defuzzification by Singned Distance method.” Journal of Information Science and Engineering, 21(1), 673،694.
11.Jing،Shing, Y., & Jershan, C. (2003). Inventory without Backorder with Fuzzy Total Cost and Fuzzy Storing Cost Defuzzified by Centroid and Signed Distance. European Journal of Operational Research, 148(2), 401–409.
Jolai, F., Gheisariha, E. and Nojavan, F. (2011). Inventory Control of Perishable Items in a Tw, Echelon Supply Chain. Journal of Industrial Engineering, University of Tehran, Special Issue, 69, 77.
Lee, H. M., & Yao, J. S. (1999). Economic Order Quantity in Fuzzy Sense for Inventory without Backorder Model. Fuzzy Sets and Systems, 105(1), 13، 31.
Mohabbatdar, S. and Esmaeili, M. (2011). Optimal Selling Price, Marketing Expenditure and Order Quantity with Backordering. Journal of Industrial Engineering, University of Tehran, Special Issue, 103-112.
15.Negi, D. S. & Lee, E. S. (1992). Analysis and Simulation of Fuzzy Queue. Fuzzy Sets and Systems, 46(3), 321– 330.
16.Razmi, J., Seifoory, M. & Pishvaee, M. S. (2011). A Fuzzy Multi،Attribute Decision Making Model for Selecting the Best Supply Chain Strategy: Lean, Agile or Leagile. Journal of Industrial Engineering, University of Tehran, Special Issue, 127،142.
17.San, Chyi, C. (1999). Fuzzy Production Inventory for Fuzzy Product Quantity with Triangular Fuzzy Number. Fuzzy Sets and Systems, 107(1), 37-57.
Shiang،Tai, L. (2008). Fuzzy Profit Measures for a Fuzzy Economic Order Quantity Model. Applied Mathematical Modelling, 32(10), 2076–2086.
19. Shih, Pin, C. (2004). Parametric Nonlinear Programming for Analyzing Fuzzy Queues with Finite Capacity. European Journal of Operational Research, 157(2), 429–438.
20. Shi, Pin, C. (2007). Solving Fuzzy Queuing Decision Problems via a Parametric Mixed Integer Nonlinear Programming Method. European Journal of Operational Research, 177(1), 445–457.
21. Shih, Pin, C. (2005). Parametric Nonlinear Programming Approach to Fuzzy Queues with Bulk Service. European Journal of Operational Research, 163(2), 434–444.
Shishebori, D., & Hejazi, S. R. (2009). Application of Fuzzy AHP Technique to Selection the Most Efficient Method of Improving of Productivity. Journal of Industrial Engineering, University of Tehran, 43(1), 5-66.
Taheri،Tolgari, J., Mirzazadeh, A. & Jolai, F. (2012). An Inventory Model for Imperfect Items under Inflationary Conditions with Considering Inspection Errors. Computers and Mathematics with Applications, 63(6), 1007–1019.
Vujosevic, M., Petrovic, D. & Petrovic, R. (1996). EOQ Formula when Inventory Cost is Fuzzy. International Journal of Production Economics, 45(1،3), 499-504.
Yang, G., K. (2011). Discussion of Arithmetic Defuzzifications for Fuzzy Production Inventory Models. African Journal of Business Management, 5(6), 233-2344.
Yao, J. s., & Lee, H. M. (1996). Fuzzy Inventory with Backorder for Fuzzy Order Quantity. Information Sciences, 93(3-4), 283- 319.
Yao, J. s., & Lee, H. M. (1999). Fuzzy Inventory with or without Backorder for Fuzzy Order Quantity with Trapezoid Fuzzy Number. Fuzzy Sets and Systems, 105(3), 311- 337.
Yao, J. S., Chang, S. C. & Su, J. S. (2000). Fuzzy Inventory without Backorder for Fuzzy Order Quantity and Fuzzy Total Demand Quantity. Computer and Operation Research, 27(10), 935-962.
Zadeh, L. A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1(1), 28-31
Zimmermann, H. J. (2001). Fuzzy Set Theory and its Applications. 4th ed., Kluwer Academic, Boston
