Preemptive GP Model

In preemptive GP, priority is assigned for each incommensurable goal and weights to goals at the same priority. Goals at higher priority have to be 

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

Based on Phase 1 results, price is the most important goal followed by MtT goal on quality, lead time, and VaR in that order, dn and dX are the deviation variables representing how far the solution deviates from each goal. In general, goal values are to be provided by the DMs. To determine the optimal solution for a preemptive GP model, a sequence of optimization problems has to be solved. 

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In the non-preemptive GP model, the buyer sets goals to achieve for each objective and preferences in achieving those goals expressed as numerical weights. Here, the buyer has three goals as follows ... 

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 the preemptive GP model, price is given the highest priority, followed by MtT risk of quality, lead time and VaR risk respectively. This is consistent with the criteria rankings obtained from the company staff (Section 7.14.2). 

Target values for each of the objectives are set at 110% of the ideal value. For example, the ideal (minimum) value for price objective is 508,680 hence the target value for price is 559,548 and the goal is to minimize the deviation above the target value. Table 7.25 illustrates the optimal solution using the preemptive GP model. Suppliers S8, Sll, and S19 are selected and target values for objectives Zy Z2, and Z3 are achieved in the optimal solution. The optimal solution also provides the optimal order quantities for each product and supplier. 

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 preemptive GP model, if the DM indicates that/, is mucii more important than/2, then the objective function will be... 

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. 

To solve the proposed P-GP model, we assume that preemptive priority is available. For the NP-GP model, we use criteria weights from a simple rating... 

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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