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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 657465, 12 pages
Research Article

Modeling and Optimization of Stochastic Joint Replenishment and Delivery Scheduling Problem with Uncertain Costs

1School of Management, Huazhong University of Science and Technology, Wuhan 430074, China
2School of Information Management, Central China University, Wuhan 430079, China

Received 26 March 2013; Accepted 16 July 2013

Academic Editor: Mustapha Ait Rami

Copyright © 2013 Lin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The stochastic joint replenishment and delivery scheduling (JRD) problem is a key issue in supply chain management and is a major concern for companies. So far, all of the work on stochastic JRDs is under explicit environment. However, the decision makers often have to face vague operational conditions. We develop a practical JRD model with stochastic demand under fuzzy backlogging cost, fuzzy minor ordering cost, and fuzzy inventory holding cost. The problem is to determine procedures for inventory management and vehicle routing simultaneously so that the warehouse may satisfy demand at a minimum long-run average cost. Subsequently, the fuzzy total cost is defuzzified by the graded mean integration representation and centroid approaches to rank fuzzy numbers. To find optimal coordinated decisions, a modified adaptive differential evolution algorithm (MADE) is utilized to find the minimum long-run average total cost. Results of numerical examples indicate that the proposed JRD model can be used to simulate fuzzy environment efficiently, and the MADE outperforms genetic algorithm with a lower total cost and higher convergence rate. The proposed methods can be applied to many industries and can help obtaining optimal decisions under uncertain environment.