Fuzzy GP Model

Fuzzy GP uses the ideal values as targets and minimizes the maximum weighted normalized distance from fhe ideal solution for each objective. An ideal solution is the vector of best values of each objective obtained by optimizing each objective independently, ignoring other objectives. In this application, ideal solutions were obtained by minimizing price, lead time, MtT and VaR type risks independently. If M equals the maximum deviation from fhe ideal solufion, then the fuzzy GP model is as follows  

Constraints (7.27 through 7.32) stated earlier will also be included in this model. 

Z3 and Z4 in the aforementioned formulation represent individual minima, that is, the ideal values for fhe respective objectives. Weight values Wi, W2, W3, and W4 are the same that are used in the non-preemptive GP model. The advantage of fuzzy GP is fhaf no target values have to be specified by the DM and there are no deviational variables. 

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For additional readings on the variants of fuzzy GP models, the reader is referred to Ignizio and Cavalier (1994), Tiwari et al. (1986), Tiwari et al. (1987), Mohammed (1997), and Hu et al. (2007). An excellent source of reference for goal programming methods and applications is the textbook by Schniederjans (1995). 

In the fuzzy GP model, ideal values (Table 7.24) are used as targets for the four objectives. The optimal solution obtained using fuzzy GP is shown in Table 7.28. 

In this section, we propose a weighted fuzzy goal programming (GP) model to solve the bi-criteria problem. In fuzzy GP, ideal values can be used as targets for the objectives (Masud and Ravindran 2008 Subramanian et al. 2013). In the proposed model, we minimize the sum of the weighted satisfaction degrees of the objectives. The proposed weighted fuzzy GP model is as follows ... 

If M equals the maximum deviation from the ideal solution, then the fuzzy GP model is as follows ... 

Constraints (6.28 through 6.37) stated earlier will also be included in this model, except that the target for Equations 6.28 through 6.30 are set to their respective ideal values. In this model Xi, and 3 are scaling constants to be set by the user. A common practice is to set the values X2, equal to the respective ideal values. The advantage of Fuzzy GP is that no target values have to be specified by the DM. 

This chapter presents a disruption risk quantification method and a multiobjective supplier selection model to generate mitigation plans against disruption risks. The proposed risk quantification method considers risk as a function of two components—impact and occurrence. Impact is modeled using GEVD distributions, and occurrence is assumed to be Poisson-distributed. The disruption risk quantification method calculates the estimated value of the loss due to disruptive events at a supplier, which is then used in a multi-objective optimization model. The model minimizes cost, lead time, and risk and then maximizes quality and determines the optimal supplier and order allocation for multiple products. The model is solved using four different GP solution techniques—preemptive, non-preemptive, min-max, and fuzzy GP Optimal solutions are displayed using the VPA, and the performance of the solution techniques is discussed. We observe that, for the data set we have tested, preemptive GP, non-preemptive GP, and min-max GP achieve three out of four objectives. 

Li YF, Xia GP, Yang YX et al (2005) Global supply chain tactical planning model based on fuzzy stochastic expected value programming. Syst Eng Theory Pract 8 1-9... 

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