Developing a Multi-Product Economic Production Quantity Model To Fuzzy Sense Using of Signed Distance Method


  • Mohammad Khodashenas Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Valiasr street, Tehran
  • Hamidreza Salmani Mojaveri Department of Management and Economic, Science and Research Branch, Islamic Azad University, Shahrak e gharb, Tehran
  • Fatemeh Mohammadnezhad Chari Department of Industrial Engineering, Payam e Noor University, 15 Khordad street, Sari



Defuzzification, signed distance, fuzzy set, multi-product economic production quan¬ti¬ty, inventory


Today, inventory management issue has become a concern for a lot of organizations and it is the most necessary issues for organizations by production and inventory plan implementing. Among inventory models, models based on economic production quantity are of the most practical models. Each of the economic production quantity is based on set of para­me­ters that are estimated by experts and decision makers. Since uncertainty exists in real world, it is difficult for experts to estimate parameters, accurately. Therefore, in such situation, using economic production quantity under non-integer conditions would be more appropriate than the crisp conditions and also under such conditions organizations have to determine their cumu­la­tive production in their supply chain in fuzzy sense. In this paper, a multi-product economic production quantity (EPQ) model, under fuzzy conditions, has been fuzzified and optimized by using signed distance method in order to minimize all costs. a numerical example and sensitivity analysis have also provided to illustrate the practical use of the proposed method.


Bayindir, Z. P., Birbil, S. I., and Frenk, J. B. G., A Deterministic Inventory Production Model with General Inventory Cost Rate Function and Piecewise Linear Concave Production Costs, European Journal of Operational Research, 179(1), 2007, pp. 114-123.

Bit, A. K., Biswal, M. P., and Alam, S. S., (1992), Fuzzy Programming Approach to Multi-criteria Decision Making Transformation Problem, Fuzzy Sets and Systems, 50, 1992, pp. 135-142.

Björk, K. M., An Analitical Solution to a Fuzzy Economic Order Quantity Problem, Interna¬tional Journal of Approximate Reasoning, 50, 2009, pp.458-493.

Brandimarte P., and Zotteri, G., Introduction to Distribution Logistics, First ed., John Wiley & Sons, New Jersey, USA, 2007.

Bowersox, D. J, Closs, D. J., and Cooper, M. B., Supply Chain Logistics Management, Second ed., MC Graw. Hill, New York, USA, 2007.

Buzacott, J. A., The Structure of Manufacturing Systems: Insights on the Impact of Variability, International Journal of Flexible Manufacturing Systems,11(2), 1999, pp. 702-707.

Chang, S. C., Fuzzy Production Inventory for Fuzzy Product Quantity with Triangular Fuzzy Number, Fuzzy Sets and Systems, 107, 1999, pp. 37-57.

Chang, H-C., An Application of Fuzzy Sets Theory to the EOQ Model with Imperfect Qua¬lity Items, Computers and Operations Research, 31, 2004, pp.2079–2092.

Chen, K. K, Y-S. P.Chiu and Ting, C-K., Pro¬ducer’s Replenishment Policy for an EPQ Model with Rework and Machine Failure Taking Place in Backorder Reloading Time, WSEAS Transac¬tion on Mathematic, 9, 2010, pp.223-233.

Chiu, S.W., Production Run Time Problem with Machine Breakdowns under AR Control Policy and Rework, Journal of Scientific and Industrial Research, 66, 2007, pp.979-988.

Flapper S. D. P., Fransoo, J. C., Broekmeulen, R. A. C. M., and Inderfurth, K., Planning and Control of Rework in the Process Industries: A Review, Production Planning and Control,13(1), 2002, pp. 26-34.

Guiffrida, A. L., Fuzzy Inventory Models, in: M. Y. Jaber (Ed.), Inventory Management: Non-classical Views, CRC Press, FL, Boca Raton, pp. 173-190, 2009, (chapter 8).

Halim, K.A., Giri, B. C., and Chaudhuri, K. S., Fuzzy EPQ Model for an Imperfect Production System, International Journal of System Science, 40(1), 2009, pp. 45-52.

Hou, K. L., An EPQ Model with Setup Costs and Process Quality as Function of Capital Expen¬diture, Applied Mathematical Modeling, 31(1), 2007, pp. 10-17.

Hsieh, C. H., Optimization of Fuzzy Production Inventory Models, Information Science, 146, 2002, pp.29-40.

Jinsong Ho, Ruqian Xu, and Caiyun Guo, Fuzzy Economic Production Quantity Models for Items with Imperfect Quality, International Journal of Information and Management Sciences,22, 2011, pp. 43-58.

Kacpryzk, J., and Stanieski, P., Long Term Inven¬tor Policy-making through Fuzzy Decision Making Models, Fuzzy Sets and Systems, 8(2), 1982, pp. 117-132.

Lee, H. M., and Yao, J. S., Economic Production Quantity for Fuzzy Demand Quan¬tity and Fuzzy Production Quantity, European Journal of Operational Research, 109, 1998, pp.203-211.

Lin, D. C., and Yao, J. S., Fuzzy Economic Production for Production Inventory, Fuzzy Set and Systems, 111, 2000, pp.465-495.

Park, K. S., Fuzzy Set Theoretic Interpretation of Economic Order Quantity, IEEE Transactions on Systems, Man, and Cybernetics, SMC-17, 1987, pp. 1082-1084.

Shan Huo Chen, Chien-Chung, Wang and Shu Man Chang, Fuzzy Economic Production Quan¬tity Model for Items with Imperfect Quality, International Journal of Innovative Computing, Information and Control, 3(1), 2007, pp. 85-95, Feburary 2007.

Sommer, G., Fuzzy Inventory Scheduling, in: Lasker, G, ed. Applied Systems and Cybernetics, New York: Pergamon Press, pp.3052-3060, 1981.

Taleizadeh, A. A, Wee, H.M., and Sadjadi, S. J., Multi-product Production Quantity Model with Repair Failure and Partial Back¬ordering, Jour¬nal of Computers and Engineering, 59, 2010, pp. 45-54.

Taleizadeh, A. A., Harmony Search Algorithms for Inventory Management Problems, African Journal of Business Management, 6(36), 2012, pp. 9864-9873, 12 September, 2012, avail¬able online at AJBM.

Uthayakumar, R., and Valliathal, M., Fuzzy Economic Production Quantity Model for Wei¬bull Deteriorating Items with Ramp Type of Demand, International Journal of Strategic Deci¬sion Sciences (IJSDS), Gandhigram Rural University, India,Chikkaiah Naicker College, India, 2011. Source title: http://www.igi-global. com/article/fuzzy-economic-production-quantity-model/58318.

Widyadana, G. A. and Wee, H. M., Economic Production Quantity (EPQ) Deteriorating Inven¬to¬ry Model with Machine Breakdown and Stochas¬tic Repair Time, Proceeding of the IEEE IEEM, 2009.


How to Cite

Khodashenas, M., Mojaveri, H. S., & Chari, F. M. (2013). Developing a Multi-Product Economic Production Quantity Model To Fuzzy Sense Using of Signed Distance Method. Jurnal Teknik Industri, 15(1), 39-44.