A Two Stage EOQ Model for Deteriorating Products Incorporating Quantity & Freight Discounts, Under Fuzzy Environment

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 202)


As the industrial environment becomes more competitive, supply chain management (SCM) has become essential. Especially in the case of deteriorating products, demand is an imprecise parameter and leads to uncertainty in other parameters like holding cost and total cost. The objective of the current study is to manage procurement & distribution coordination, who faces many barriers because of the imprecise behaviour of the parameters discussed above while calculating economic order quantity (EOQ), which moves from one source to an intermediate stoppage (Stage I) and further to final destination (Stage II) incorporating quantity and freight discounts at the time of transporting goods in stage I and using truckload (TL) and less than truckload (LTL) policy in stage II. Finding solutions for such class of coordination is highly complex. To reduce the complexity and to find the optimal solution, differential evolution approach is used. The model is validated with the help of a case problem.


Supply chain management Fuzzy optimization Quantity & freight discounts Truck load & less than truck load Differential evolution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Roy, A. Kar, S., Maiti, M.: A deteriorating multi-item inventory model with fuzzy costs and resources based on two different defuzzification techniques. Applied Mathematical Modelling. 32, 208-223 (2008).Google Scholar
  2. Minner, S.: Multiple-supplier inventory models in SCM: A review. International Journal of Production Economics. 81/82, 265-279 (2003).Google Scholar
  3. Ranjan, B., Susmita, B.: A review of the causes of bullwhip effect in a supply chain. The International Journal of Advanced Manufacturing Technology. 54, 1245-1261(2011).Google Scholar
  4. Alamri, A. A., Balkhi, Z. T.: The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioraion rates. International Journal of Production Economics. 107, 125-138 (2007).Google Scholar
  5. Hsu, P. H., Wee, H. M., Teng, H. M.: Preservation technology investment for deteriorating inventory. International Journal of Production Economics. 124, 388-394 (2010).Google Scholar
  6. Misra, R.B.: Optimum production lot-size model for a system with deteriorating inventory. Int. J. Prod. Res. 13, 495–505 (1975).Google Scholar
  7. Goyal, S.K., Gunasekaran, A.: An integrated production inventory marketing model for deteriorating item. Comput. Ind. Eng. 28, 755–762 (1995).Google Scholar
  8. Benkherouf, L.A.: Deterministic order level inventory model for deteriorating items with two storage facilities. Int. J. Prod. Economics. 48, 167–175 (1997).Google Scholar
  9. Giri, B.C., Chaudhuri, K. S.: Deterministic models of perishable inventory with stock dependent demand rate and non-linear holding cost. Euro. J. Oper. Res. 19, 1267–1274 (1998).Google Scholar
  10. Goyel, S.K., Giri, B.C.: Recent trends in modeling of deteriorating inventory. Euro. J. Oper. Res. 134, 1–16 (2001).Google Scholar
  11. Tu, H.H.J., Lo, M.C., & Yang, M.F.: A two-echelon inventory model for fuzzy demand with mutual beneficial pricing approach in a supply chain. African Journal of Business Management. 5(14), 5500-5508 (2011).Google Scholar
  12. Xu, R., Zhai, X.: Optimal models for single-period supply chain problems with fuzzy demand. Information Sciences. 178(17), 3374–3381 (2008).Google Scholar
  13. Price, K.V., Storn, R.M.: Differential Evolution-A simple and efficient adaptive scheme for global optimization over continuous space (Tech. Rep. No. TR-95-012). ICSI. Available via the Internet: (1995).Google Scholar
  14. Price, K.V.: An introduction to Differential Evolution. In: Corne, D., Marco, D. & Glover, F. (Eds.), New Ideas in Optimization. London, UK: McGraw-Hill. 78-108 (1999).Google Scholar
  15. Zimmermann, H.J.: Description and optimization of fuzzy systems. International Journal of General Systems. 2, 209–215 (1976).Google Scholar

Copyright information

© Springer India 2013

Authors and Affiliations

  1. 1.Department of Operational ResearchFaculty of Mathematical Sciences, University of DelhiDelhiIndia
  2. 2.Fortune Institite of International BusinessNew DelhiIndia

Personalised recommendations