International Journal of Fuzzy Systems

, Volume 18, Issue 6, pp 1141–1161 | Cite as

A Fuzzy Reverse Logistics Inventory System Integrating Economic Order/Production Quantity Models

  • Ehsan Shekarian
  • Ezutah Udoncy Olugu
  • Salwa Hanim Abdul-RashidEmail author
  • Eleonora Bottani


This paper develops a reverse inventory model where the recoverable manufacturing process is affected by the learning theory. We propose the inclusion of the fuzzy demand rate of the serviceable products and the fuzzy collection rate of the recoverable products from customers in the total cost function of the model. Two popular defuzzification methods, namely the signed distance technique, a ranking method for fuzzy numbers, and the graded mean integration representation method are employed to find the estimate of the total cost function per unit time in the fuzzy sense. We provide a comprehensive numerical example to illustrate and compare the results obtained by the two mentioned defuzzification methods. This is one of the only few attempts in the related literature comparing the performance of these methods with the effect of the fuzziness of both of the demand and the collection rate in the presence of the learning simultaneously. The results indicate that deciding on which method could be used depends on the target strategy that could focus on the total cost, ordering lot size, or recovery lot size.


Fuzzy set theory Signed distance Graded mean integration representation Reverse logistics Inventory management Economic order/production quantity 



The first author wishes to express his gratitude to University of Malaya for funding his research (Grant No. RP018b-13aet).


  1. 1.
    Tibben-Lembke, R.S., Rogers, D.S.: Going Backwards: Reverse Logistics Trends and Practices. University of Nevada, Reno Center for Logistics Management. (1998)Google Scholar
  2. 2.
    Fleischmann, M., Bloemhof-Ruwaard, J.M., Dekker, R., van der Laan, E., van Nunen, J.A.E.E., Van Wassenhove, L.N.: Quantitative models for reverse logistics: a review. Eur. J. Oper. Res. 103(1), 1–17 (1997)zbMATHCrossRefGoogle Scholar
  3. 3.
    Rubio, S., Chamorro, A., Miranda, F.J.: Characteristics of the research on reverse logistics (1995–2005). Int. J. Prod. Res. 46(4), 1099–1120 (2007)zbMATHCrossRefGoogle Scholar
  4. 4.
    Junior, M.L., Filho, M.G.: Production planning and control for remanufacturing: literature review and analysis. Prod. Plan. Control. 23(6), 419–435 (2011)CrossRefGoogle Scholar
  5. 5.
    Guide Jr, V.D.R.: Production planning and control for remanufacturing: industry practice and research needs. J. Oper Manag. 18(4), 467–483 (2000)CrossRefGoogle Scholar
  6. 6.
    Prahinski, C., Kocabasoglu, C.: Empirical research opportunities in reverse supply chains. Omega-Int. J. Manag. S 34(6), 519–532 (2006)CrossRefGoogle Scholar
  7. 7.
    Sasikumar, P., Kannan, G.: Issues in reverse supply chains, part I: end-of-life product recovery and inventory management–an overview. Int. J. Sustain. Eng. 1(3), 154–172 (2008)CrossRefGoogle Scholar
  8. 8.
    Pokharel, S., Mutha, A.: Perspectives in reverse logistics: a review. Resour. Conserv. Recy. 53(4), 175–182 (2009)CrossRefGoogle Scholar
  9. 9.
    Guide Jr, V.D.R., Van Wassenhove, L.N.: The evolution of closed-loop supply chain research. Oper. Res. 57(1), 10–18 (2009)zbMATHCrossRefGoogle Scholar
  10. 10.
    Akçalı, E., Çetinkaya, S.: Quantitative models for inventory and production planning in closed-loop supply chains. Int. J. Prod. Res. 49(8), 2373–2407 (2010)CrossRefGoogle Scholar
  11. 11.
    Hazen, B.T.: Strategic reverse logistics disposition decisions: from theory to practice. Int. J. Logist. Syst. Manag. 10(3), 275–292 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Souza, G.C.: Closed-loop supply chains: a critical review, and future research. Decis. Sci. 44(1), 7–38 (2013)CrossRefGoogle Scholar
  13. 13.
    Sheriff, K.M., Gunasekaran, A., Nachiappan, S.: Reverse logistics network design: a review on strategic perspective. Int. J. Logist. Syst. Manag. 12(2), 171–194 (2012)CrossRefGoogle Scholar
  14. 14.
    Seuring, S.: A review of modeling approaches for sustainable supply chain management. Decis. Support Syst. 54(4), 1513–1520 (2013)CrossRefGoogle Scholar
  15. 15.
    Steeneck, D.W., Sarin, S.C.: Pricing and production planning for reverse supply chain: a review. Int. J. Prod. Res. 51(23–24), 6972–6989 (2013)CrossRefGoogle Scholar
  16. 16.
    Chan, F.T., Chan, H.K.: A survey on reverse logistics system of mobile phone industry in Hong Kong. Manage. Decis. 46(5), 702–708 (2008)CrossRefGoogle Scholar
  17. 17.
    Govindan, K., Soleimani, H., Kannan, D.: Reverse logistics and closed-loop supply chain: a comprehensive review to explore the future. Eur. J. Oper. Res. 240(3), 603–626 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Schrady, D.A.: A deterministic inventory model for reparable items. Nav. Res. Logist. Q 14(3), 391–398 (1967)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8(3), 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Wright, T.P.: Factors affecting the cost of airplanes. J. Aeronaut. Sci. (Institute of the Aeronautical Sciences) 3(4), 122–128 (1936)CrossRefGoogle Scholar
  21. 21.
    Jaber, M.Y., El Saadany, A.M.A.: An economic production and remanufacturing model with learning effects. Int. J. Prod. Econ. 131(1), 115–127 (2011)CrossRefGoogle Scholar
  22. 22.
    Tsai, D.-M.: Optimal ordering and production policy for a recoverable item inventory system with learning effect. Int. J. Syst. Sci. 43(2), 349–367 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Ilgin, M.A., Gupta, S.M.: Environmentally conscious manufacturing and product recovery (ECMPRO): a review of the state of the art. J. Environ. Manag. 91(3), 563–591 (2010)CrossRefGoogle Scholar
  24. 24.
    Bushuev, M.A., Guiffrida, A., Jaber, M.Y., Khan, M., Sarkis, J., Sarkis, J.: A review of inventory lot sizing review papers. Manag. Res. Rev. 38(3), 283–298 (2015)CrossRefGoogle Scholar
  25. 25.
    Nahmias, S., Rivera, H.: A deterministic model for a repairable item inventory system with a finite repair rate. Int. J. Prod. Res. 17(3), 215–221 (1979)CrossRefGoogle Scholar
  26. 26.
    Mabini, M.C., Pintelon, L.M., Gelders, L.F.: EOQ type formulations for controlling repairable inventories. Int. J. Prod. Econ. 28(1), 21–33 (1992)CrossRefGoogle Scholar
  27. 27.
    Richter, K.: The EOQ repair and waste disposal model with variable setup numbers. Eur. J. Oper. Res. 95(2), 313–324 (1996)zbMATHCrossRefGoogle Scholar
  28. 28.
    Richter, K.: The extended EOQ repair and waste disposal model. Int. J. Prod. Econ. 45(1–3), 443–447 (1996)CrossRefGoogle Scholar
  29. 29.
    Richter, K.: Pure and mixed strategies for the EOQ repair and waste disposal problem. OR. Spektrum. 19(2), 123–129 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Richter, K., Dobos, I.: Analysis of the EOQ repair and waste disposal problem with integer setup numbers. Int. J. Prod. Econ. 59(1–3), 463–467 (1999)CrossRefGoogle Scholar
  31. 31.
    Teunter, R.H.: Economic ordering quantities for recoverable item inventory systems. Nav. Res. Log. 48(6), 484–495 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Koh, S.-G., Hwang, H., Sohn, K.-I., Ko, C.-S.: An optimal ordering and recovery policy for reusable items. Comput. Ind. Eng. 43(1–2), 59–73 (2002)CrossRefGoogle Scholar
  33. 33.
    Teunter, R.H.: Economic order quantities for stochastic discounted cost inventory systems with remanufacturing. Int. J. Logist. 5(2), 161–175 (2002)CrossRefGoogle Scholar
  34. 34.
    Teunter, R.: Lot-sizing for inventory systems with product recovery. Comput. Ind. Eng. 46(3), 431–441 (2004)CrossRefGoogle Scholar
  35. 35.
    Inderfurth, K., Lindner, G., Rachaniotis, N.: Lot sizing in a production system with rework and product deterioration. Int. J. Prod. Res. 43(7), 1355–1374 (2005)zbMATHCrossRefGoogle Scholar
  36. 36.
    Dobos, I., Richter, K.: A production/recycling model with stationary demand and return rates. Cent. Eur. J. Oper. Res. 11, 35–46 (2003)MathSciNetzbMATHGoogle Scholar
  37. 37.
    Dobos, I., Richter, K.: A production/recycling model with quality consideration. Int. J. Prod. Econ. 104(2), 571–579 (2006)CrossRefGoogle Scholar
  38. 38.
    Konstantaras, I., Papachristos, S.: Lot-sizing for a single-product recovery system with backordering. Int. J. Prod. Res. 44(10), 2031–2045 (2006)zbMATHCrossRefGoogle Scholar
  39. 39.
    Jaber, M.Y., Rosen, M.A.: The economic order quantity repair and waste disposal model with entropy cost. Eur. J. Oper. Res. 188(1), 109–120 (2008)zbMATHCrossRefGoogle Scholar
  40. 40.
    Oh, Y., Hwang, H.: Deterministic inventory model for recycling system. J. Intell. Manuf. 17(4), 423–428 (2006)CrossRefGoogle Scholar
  41. 41.
    Konstantaras, I., Papachristos, S.: Optimal policy and holding cost stability regions in a periodic review inventory system with manufacturing and remanufacturing options. Eur. J. Oper. Res. 178(2), 433–448 (2007)zbMATHCrossRefGoogle Scholar
  42. 42.
    Konstantaras, I., Papachristos, S.: A note on: developing an exact solution for an inventory system with product recovery. Int. J. Prod. Econ. 111(2), 707–712 (2008)CrossRefGoogle Scholar
  43. 43.
    Konstantaras, I., Papachristos, S.: Note on: an optimal ordering and recovery policy for reusable items. Comput. Ind. Eng. 55(3), 729–734 (2008)CrossRefGoogle Scholar
  44. 44.
    Jaber, M.Y., El Saadany, A.M.A.: The production, remanufacture and waste disposal model with lost sales. Int. J. Prod. Econ. 120(1), 115–124 (2009)CrossRefGoogle Scholar
  45. 45.
    Konstantaras, I., Skouri, K.: Lot sizing for a single product recovery system with variable setup numbers. Eur. J. Oper. Res. 203(2), 326–335 (2010)zbMATHCrossRefGoogle Scholar
  46. 46.
    El Saadany, A.M.A., Jaber, M.Y.: A production/remanufacturing inventory model with price and quality dependant return rate. Comput. Ind. Eng. 58(3), 352–362 (2010)CrossRefGoogle Scholar
  47. 47.
    Konstantaras, I., Skouri, K., Jaber, M.Y.: Lot sizing for a recoverable product with inspection and sorting. Comput. Ind. Eng. 58(3), 452–462 (2010)CrossRefGoogle Scholar
  48. 48.
    Alinovi, A., Bottani, E., Montanari, R.: Reverse Logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies. Int. J. Prod. Res. 50(5), 1243–1264 (2012)CrossRefGoogle Scholar
  49. 49.
    El Saadany, A.M.A., Jaber, M.Y.: A production/remanufacture model with returns’ subassemblies managed differently. Int. J. Prod. Econ. 133(1), 119–126 (2011)CrossRefGoogle Scholar
  50. 50.
    Alamri, A.A.: Theory and methodology on the global optimal solution to a general reverse logistics inventory model for deteriorating items and time-varying rates. Comput. Ind. Eng. 60(2), 236–247 (2011)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Hasanov, P., Jaber, M.Y., Zolfaghari, S.: Production, remanufacturing and waste disposal models for the cases of pure and partial backordering. Appl. Math. Model. 36(11), 5249–5261 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    Widyadana, G.A., Wee, H.M.: An economic production quantity model for deteriorating items with multiple production setups and rework. Int. J. Prod. Econ. 138(1), 62–67 (2012)CrossRefGoogle Scholar
  53. 53.
    Jaber, M.Y., Zanoni, S., Zavanella, L.E.: A consignment stock coordination scheme for the production, remanufacturing and waste disposal problem. Int. J. Prod. Res. 52(1), 50–65 (2014)CrossRefGoogle Scholar
  54. 54.
    Matar, N., Jaber, M.Y., Searcy, C.: A reverse logistics inventory model for plastic bottles. Int. J. Logist. Manag. 25(2), 315–333 (2014)CrossRefGoogle Scholar
  55. 55.
    Nonaka, T., Fujii, N.: An EOQ model for reuse and recycling considering the balance of supply and demand. International journal of automation technology. 9(3), 303–311 (2015)CrossRefGoogle Scholar
  56. 56.
    Dobos, I., Richter, K.: An extended production/recycling model with stationary demand and return rates. Int. J. Prod. Econ. 90(3), 311–323 (2004)CrossRefGoogle Scholar
  57. 57.
    Zouadi, T., Yalaoui, A., Reghioui, M., El Kadiri, K.E.: Lot-sizing for production planning in a recovery system with returns. Rairo-Oper. Res. 49(1), 123–142 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  58. 58.
    Singh, S.R., Rathore, H.: Two-warehouse reverse logistic inventory model for deteriorating item under learning effect. In: Das, K.N., Deep, K., Pant, M., Bansal, J.C., Nagar, A. (eds.) Proceedings of Fourth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol. 335, pp. 45–57. Springer India (2015)Google Scholar
  59. 59.
    Singh, S.R., Rathore, H.: Reverse logistic model for deteriorating items with non-instantaneous deterioration and learning effect. In: Mandal, J.K., Satapathy, S.C., Kumar Sanyal, M., Sarkar, P.P., Mukhopadhyay, A. (eds.) Information Systems Design and Intelligent Applications, vol. 339. Advances in Intelligent Systems and Computing, pp. 435-445. Springer India, (2015)Google Scholar
  60. 60.
    Lee, H.-M., Yao, J.-S.: Economic order quantity in fuzzy sense for inventory without backorder model. Fuzzy. Set. Syst. 105(1), 13–31 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  61. 61.
    Hsieh, C.H.: Optimization of fuzzy production inventory models. Inform Sci. 146(1), 29–40 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  62. 62.
    Chang, H.-C.: An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput. Oper. Res. 31(12), 2079–2092 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  63. 63.
    Ouyang, L.-Y., Yao, J.-S.: A minimax distribution free procedure for mixed inventory model involving variable lead time with fuzzy demand. Comput. Oper. Res. 29(5), 471–487 (2002)zbMATHCrossRefGoogle Scholar
  64. 64.
    Chang, H.-C., Yao, J.-S., Ouyang, L.-Y.: Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand. Eur. J. Oper. Res. 169(1), 65–80 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  65. 65.
    Vijayan, T., Kumaran, M.: Inventory models with a mixture of backorders and lost sales under fuzzy cost. Eur. J. Oper. Res. 189(1), 105–119 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    Guiffrida, A.: Fuzzy inventory models. In: Jaber, M.Y. (ed.) Inventory Management: Non-Classical Views, pp. 173–198. CRC Press, Boca Raton (2009)CrossRefGoogle Scholar
  67. 67.
    Björk, K.-M.: An analytical solution to a fuzzy economic order quantity problem. Int. J. Approx. Reason. 50(3), 485–493 (2009)zbMATHCrossRefGoogle Scholar
  68. 68.
    Björk, K.-M.: A multi-item fuzzy economic production quantity problem with a finite production rate. Int. J. Prod. Econ. 135(2), 702–707 (2012)Google Scholar
  69. 69.
    Shekarian, E., Jaber, M.Y., Kazemi, N., Ehsani, E.: A fuzzified version of the economic production quantity (EPQ) model with backorders and rework for a single–stage system. Eur. J. Ind. Eng. 8(3), 291–324 (2014)CrossRefGoogle Scholar
  70. 70.
    Shekarian, E., Glock, C.H., Amiri, S.M.P., Schwindl, K.: Optimal manufacturing lot size for a single-stage production system with rework in a fuzzy environment. J. Intell. Fuzzy. Syst. 27(6), 3067–3080 (2014)MathSciNetGoogle Scholar
  71. 71.
    Guchhait, P., Maiti, M.K., Maiti, M.: Inventory policy of a deteriorating item with variable demand under trade credit period. Comput. Ind. Eng. 76, 75–88 (2014)zbMATHCrossRefGoogle Scholar
  72. 72.
    Sharifi, E., Shabani, S., Sobhanallahi, M.A., Mirzazadeh, A.: A fuzzy economic order quantity model for items with imperfect quality and partial backordered shortage under screening errors. Int. J. Appl. Decis. Sci. 8(1), 109–126 (2015)Google Scholar
  73. 73.
    Pal, S., Mahapatra, G.S., Samanta, G.P.: A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness. Econ. Model. 46, 334–345 (2015)CrossRefGoogle Scholar
  74. 74.
    Kumar, R.S., Goswami, A.: EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment. Int. J. Syst. Sci. 46(8), 1486–1497 (2015)zbMATHGoogle Scholar
  75. 75.
    Guchhait, P., Maiti, M.K., Maiti, M.: An EOQ model of deteriorating item in imprecise environment with dynamic deterioration and credit linked demand. Appl. Math. Model. (2015). doi: 10.1016/j.apm.2015.02.003 MathSciNetzbMATHGoogle Scholar
  76. 76.
    Sarkar, B., Mahapatra, A.S.: Periodic review fuzzy inventory model with variable lead time and fuzzy demand. Int. Trans. Oper. Res. (2015). doi: 10.1111/itor.12177 Google Scholar
  77. 77.
    Yadav, D., Singh, S., Kumari, R.: Retailer’s optimal policy under inflation in fuzzy environment with trade credit. Int. J. Syst. Sci. 46(4), 754–762 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  78. 78.
    Mahata, G.C.: A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments. J. Intell. Manuf. 11, 1–15 (2014)Google Scholar
  79. 79.
    Kazemi, N., Olugu, E.U., Salwa Hanim, A.-R., Ghazilla, R.A.B.R.: Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters. J. Intell. Fuzzy. Syst 28(5), 2377–2389 (2015)MathSciNetCrossRefGoogle Scholar
  80. 80.
    Kazemi, N., Shekarian, E., Cárdenas-Barrón, L.E., Olugu, E.U.: Incorporating human learning into a fuzzy EOQ inventory model with backorders. Comput. Ind. Eng. 87, 540–542 (2015)CrossRefGoogle Scholar
  81. 81.
    Jaber, M.Y., Guiffrida, A.L.: Learning curves for processes generating defects requiring reworks. Eur. J. Oper. Res. 159(3), 663–672 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  82. 82.
    Kauffman, A., Gupta, M.M.: Introduction To Fuzzy Arithmetic: Theory and Application. VanNostrand Reinhold, New York (1991)Google Scholar
  83. 83.
    Zimmermann, H.-J.: Fuzzy Set Theory—and Its Applications. Springer Science & Business Media, New York (2001)CrossRefGoogle Scholar
  84. 84.
    Chen, S.H., Chang, S.M.: Optimization of fuzzy production inventory model with unrepairable defective products. Int. J. Prod. Econ. 113(2), 887–894 (2008)CrossRefGoogle Scholar
  85. 85.
    Yao, J.-S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy. Set. Syst. 116(2), 275–288 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  86. 86.
    Chen, S.H., Hsieh, C.H.: Graded mean integration representation of generalized fuzzy number. J. Chin. Fuzzy Syst. 5(2), 1–7 (1999)Google Scholar
  87. 87.
    Huang, T.T.: Fuzzy multilevel lot-sizing problem based on signed distance and centroid. Int. J. Fuzzy Syst. 13(2), 98–110 (2011)MathSciNetGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ehsan Shekarian
    • 1
  • Ezutah Udoncy Olugu
    • 1
  • Salwa Hanim Abdul-Rashid
    • 1
    Email author
  • Eleonora Bottani
    • 2
  1. 1.Centre for Product Design and Manufacturing, Department of Mechanical Engineering, Faculty of EngineeringUniversity of MalayaKuala LumpurMalaysia
  2. 2.Department of Industrial EngineeringUniversity of ParmaParmaItaly

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