Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory

A Study on the Fuzzy Joint Replenishment Models and Algorithms

Author FuQingLiang
Tutor WangLin
School Huazhong University of Science and Technology
Course Management Science and Engineering
Keywords Joint replenishment joint replenishment and delivery scheduling fuzzy defuzzification dependent chance programming differential evolution
CLC O224
Type Master's thesis
Year 2011
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The joint replenishment problem (JRP) has received considerable attention and all ofwork on the JRPs is under explicit environment. In fact, the decision makers often have toface vague operational conditions. In this thesis, we propose a JRP model and jointreplenishment and delivery scheduling (JRD) model under fuzzy environment. Commonly,there are two methods dealing with fuzziness. The first one is defuzzification. The secondone is constructing a dependent-chance programming (DCP) model which can provide amaximum credibility of an event that the total cost in the planning periods does not exceed acertain budget level. The main contents are as follows.Firstly, in order to explain the advantages and differences of two methods, continuousreview (Q, r) model are considered under fuzzy demands. Then, two approaches are appliedto the model and compared. Some advices about inventory cash flow management are given.Secondly, a JRP model with fuzzy minor replenishment cost and fuzzy inventory holding costis developed. Subsequently, the technique of traditional fuzzy simulation (FS) approach anddifferential evolution (DE) algorithm are integrated to design a hybrid intelligent algorithm(FSDE-I) to solve the proposed DCP model. Moreover, another intelligent algorithm(FSDE-II) is designed using an improved FS approach to estimate the credibility in a highlyrobust and precise way. Thirdly, a fuzzy JRD model of the one-warehouse, n-retailer systemwith fuzzy warehouse’s minor ordering cost and fuzzy inventory holding cost is proposed.Moreover, fuzzy parameters are assumed without exact membership functions. Subsequently,the fuzzy total cost is defuzzified by the signed distance method. To find an optimal solution,a DE algorithm is designed. Further, numerical examples illustrated the proposed model andalgorithm.

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