Exam 10: Multi-Criteria Models

There are two distinct ways in which goal programming problems may be formulated and solved.

Goal constraints are referred to as "soft" constraints because

As the number of items (decision alternatives) increases, random index value used in consistency calculations increases.

In the Analytical Hierarchy Process, consistency of a decision maker is perfect if the consistency index is at least 0 .

In Analytical hierarchy process (AHP), all other things remaining the same, consistency ratio will

Using a scoring model, evaluate the following retirement options. Joe Greyhair is deciding between three cities to spend his golden (maybe silver) years in retirement. The factors used by Joe are cost of living, availability of medical care, physical security, and quality of life. He would like to rate them on a 5-point scale, with 5 as most important to 1 as least important. His expected level of satisfaction for any criterion/ city combination is to be rated on a 9-point scale, 9 being extremely favorable to 1 being extremely unfavorable. (Note that high and low may not convey the right meaning: for example cost of living being high will result in a high score, since the other factors like physical security being high may be desirable, resulting in addition of wrong types of scores. Note also that desirability in each scale goes as a higher number.) The scores for the factors under consideration are given in Table 13, and the scores obtained by the three cities under consideration, namely, Toledo, Ohio, New Greyland, Mexico, and Madras, India, are given below in Table 14. The weighted score for each city is given in Table 15.

In the Analytical Hierarchy Process, for the pairwise comparisons of attribute preferences of the decision maker to be completely consistent, where A-B is 3 and B-C is 2, A-C should be

In goal programming problems with unweighted priority, we solve one linear program to simultaneously optimize all goals.

Consistency ratio below 0.10 will affect the results of the Analytical Hierarchy Process.

If we have several objectives with different priorities, and we want to decide the quantities for each decision variable, we should use

Scoring models and the Analytical Hierarchy Process (AHP) differ in the form of the final answer in that AHP presents how much for each decision variable, whereas the scoring model gives which alternative is the best.

In goal programming models, suppose we have solved the linear program corresponding to the first priority by minimizing $10 \mathrm{u}_{1}$ . If the optimal objective function value is 0 , then the linear program corresponding to the second priority will have

The weighted goal programming model has many similarities with the linear programming model.

Solve the following decision problem using the Analytical Hierarchy Process. Joe Greyhair is planning his relocation after retirement. He is currently working in Toledo, Ohio, which is one of the contending retirement cities. The other two competing locations are New Greyland, Mexico-a special region created by Mexican Government to attract American retirees-and Madras (now known as Chennai), India, where Joe has spent sometime before. There are three important criteria for Joe: cost of living on an annualized basis, availability of medical care, and overall quality of life. Cost of living is $\$ 50,000$ in Toledo, $30,000 in New Greyland, and $20,000 in Madras. For availability of medical care, the cities rank (from best to worst): Toledo, New Greyland, and Madras. For the overall quality of life, they rank (from best to worst): Madras, followed by New Greyland, and, a close third, Toledo. Preference scale for pairwise comparisons is given in the Table 1.

In the Analytical Hierarchy Process, if the problem had 4 criteria, then it would have pairwise criteria pair comparisons.

In scoring models, score range (possible score values) for each factor is usually the same.

In XYZ Inc. the goal for labor utilization is 500 hours per month, and the firm is making two products $\mathrm{X}_{1}$ and $\mathrm{X}_{2}$ , which denote the units of these products produced per month. $\mathrm{X}_{1}$ requires 3 hours per unit for labor, and $\mathrm{X}_{2}$ requires 5 hours per unit for labor. The corresponding goal programming constraint would be

In the Analytical Hierarchy Process, the graphical representation of hierarchies diagram has a number of decision alternatives in the second level (that is, if we had 5 choices from which we want to choose one, there will be five entries in the second level).

In goal programming models

In the Analytical Hierarchy Process, the decision maker's subjective judgment is included in the evaluation process and hence the same problem solved by two different decision makers may yield completely different results.