Non-Preemptive GP Model

In non-preemptive GP, the buyer sets goals to achieve for each objective and preference in achieving those goals are expressed as numerical weights. The buyer has the following four goals  

The weights INy W2, W3, and W4 are obtained from Phase 1. The criteria weights used in the model are, cost (0.343), quality (0.338), lead time (0.246) and VaR risk (0.073). The non-preemptive GP model can be formulated as follows  

Subject to the constraints (7.27 through 7.32) and (7.34 through 7.38). Because of the use of numerical weights, the objectives have to be scaled properly. However, only a single objective optimization problem had to be solved here. 

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The weights Wy Wz, and W3 can be obtained using the methods discussed in Section 6.3. The non-preemptive GP model can be formulated as... 

Zi, Z2, 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. 

In both preemptive and non-preemptive GP models, the DM has to specify fhe targets or goals for each objective. In addition, in the preemptive GP models, the DM specifies a preemptive priority ranking on the goal achievements. In the non-preemptive case, the DM has to specify relative weights for goal achievements. 

Under the non-preemptive GP model, the DM specifies relative weights on the goal achievements, say Wj and W2. Then the objective function becomes... 

In non-preemptive GP, weights Wj and W2 are 0.75 and 0.25 for price and quality, respectively. The target values used are the same as in preemptive GP. The solution of the non-preemptive GP model is shown in Table 9.6. Non-preemptive GP requires scaling the target values are used as scaling constants. 

Preemptive GP ranks the objective fimctions with respect to the ordered preferences of the DMs and minimizes the deviations from the target values associated with each objective in the ranked order. Several different techniques can be used to derive preemptive priorities. One convenient way is to use discrete alternative multi-criteria decision-making methods such as rating, Borda count, pairwise comparison, or the analytic hierarchy process (AHP) method (see Ravindran et al. [2010] for an application). These methods also provide a numerical strength-of-preference value that can be used in non-preemptive GP models. The preemptive GP model formulation, assuming that the preference ordering of the objectives is Zy Zy Zy Zy as follows ... 

Same target values are used in the Tchebycheff GP model also. Objectives are scaled as in the non-preemptive GP. Using the Tchebycheff method, the optimal solution obtained is illustrated in Table 7.27. The same three suppliers S8, Sll, and S19 are chosen and only the price goal is achieved. 

Constraints (Equations 9.6 through 9.13) and (Equations 9.21 through 9.24) stated earlier will also be included in this model. The disadvantages of this method are (i) the scaling of goals is necessary (as required in non-preemptive GP) and (ii) outliers are given more importance and could lead to poor solutions. 

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. 

This section discusses the solution techniques for solving the proposed multicriteria optimization model. To solve the multiple and conflicting objectives model, we use preemptive goal programming (P-GP), non-preemptive goal programming (NP-GP), and the interactive method. 

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