MGT303-2 Quantitative Analysis : Essay Fountain

Question:

Task

RAKZ is considering the purchase of two types of industrial robots. The Robot 1 (alternative 1) is a large robot capable of performing a variety of tasks, including welding and painting. The Robot 2 (alternative 2) is a smaller and slower robot, but it has all the capabilities of Robot 1. The robots will be used to perform a variety of repair operations on large industrial equipment. Of course, RAKZ can always do nothing and not buy any robots (alternative 3). The market for the repair operation could be either Growing or Declining. RAKZ has constructed a payoff matrix showing the expected returns of each alternative and the probability of a favorable or unfavorable market. The data are presented:

 

 

Alternatives

State of Nature (Market Statute)

Growing

Declining

Alternative 1

5,000

– 40,000

Alternative 2

30,000

– 2 0,000

Alternative 3

0

0

Probability

0.6

0.4

Provide your advises (best solutions) to the decision maker through using the QM software using the following criteria:

First:

  1. Expected Monitory Value
  2. Equally likely (Laplace),Maximax and Maximin,
  3. Criterion of Realism (Hurwicz), where Hurwicz coefficient  =0.70,
  4. Minimax regret decision and
  5. Discuss your decisions (a) to (d)

Second:

RAKZ is considering the possibility of conducting a survey on the market potential for industrial equipment repair using robots. The cost of the survey is $5,000.  

Use QM software to:

  1. Develop the Decision Tree for RAKZ decision analysis
  2. Compute the Expected Monetary Value (EMV) as criterion on which you make your decisions.
  3. Discuss your decisions by exploring your ideas and thoughts regarding the use of the Decision Tree technique.
 

Answer:

Decision Analysis

First:

  1. Expected Monetary Value

The Expected Monitory Value (EMV) for alternative 1, 2, and 3 are -13,000, 10,000 and 0 respectively.

  1. Equally likely (Laplace),Maximax and Maximin

The maximum pay-off under a Laplace is 5000.

The maximax from the pay-off table is 30,000.

The maximin from the pay-off table is 0.

  1. Criterion of Realism (Hurwicz), where Hurwicz coefficient =0.70

The maximum of the criterion of Realism (Hurwicz) with a coefficient where  =0.70 is 15000.

  1. Minimax regret decision

The minimax regret decision is 20000, hence the decision to opt for alternative 2.

  1. Discuss your decisions (a) to (d)

The best decision on the basis of the expected monitory value ((EMV) is the one with the highest expected value. Thus, the best decision is to go with alternative 2 since it has the greatest expected value of 10,000 among the three. Hence, when the decision situation happens a large number of times then the average payoff that will result will be 10,000.

Under the equally likely (Laplace) criteria, weights that re are of equal nature are assigned assuming the state of nature are likely to occur equally. A 0.5 probability (50%) is assumed. The maximum of the result obtained is 5000. Hence, the decision is to proceed with alternative 2.

The maximax criterion selects the decision which results in the maximum of the maximum pay-off. Under the maximax, the decision is to select the maximum payoffs under the growing market conditions. Thus, the maximum payoff of the three is 30,000. The decision is to pick the alternative 2 under a very optimistic future with no regards to the potential loss of 20,000.

Under the maximin criterion, the choice is to select the alternative which reflects the maximum of the minimum payoffs. The decision is made in assumption that the minimum payoff occurs of which the maximum is chosen. Thus, the maximin payoff of the three is 0. The decision is to pick the alternative 0 of doing nothing and not buying any robots. The decision for alternative 3 is rather conservative since the alternatives put into consideration only included the worst outcomes which could occur.

The Hurwicz criterion states that the election of the alternative decision is based on the maximum weighted value which was a determined to be 15000. Hence, the decision under the Hurwicz is to opt for alternative 2.

Under the minimax regret criterion, the maximum regret is determined for each decision and the minimum of the corresponding regret values is selected. Hence, the decision is to opt for alternative 2. Thus, if RAKZ opted for alternative 1 and 3, the resultant regret would be 40000 and 3000 respectively. However, when choosing alternative 2, then the regret would be 20000.

From the six pay-off decision options, alternative 2 has clearly stood out. The pay-off for proceeding with alternative 2 were always better than the pay-offs of the other two alternatives, that is, alternative 1 and alternative 3. Hence, RAKZ should proceed with purchasing Robot 2 (alternative 2). It can be also noted that the use of the several decision criteria did not result in a mix of decisions unlike in other cases.

Second:

  1. Develop the Decision Tree for RAKZ decision analysis
  2. Compute the Expected Monetary Value (EMV) as criterion on which you make your decisions

The Expected Monetary Value (EMV) is -13000 for alterntive 1, 10,000 for alternative 2 and 0 for alternative 3.

  1. Discuss your decisions by exploring your ideas and thoughts regarding the use of the Decision Tree technique.

Under the decision tree, we choose the node with the highest expected payoff as we move to node 1 (Taylor III, 2013). The branch corresponding with the highest payoff of 10,000 is from node 1 to node 3. The branch represent the purchase of Robot 2 (alternative 2), which is similar to the earlier results of the expected value criterion.

The decision tree can only be used in making one decision (when there are no sequences of decisions) in which the decision will continuously yield the same and anticipated payoff as the expected value criterion (Dey, 2012). Hence, in decision situations, the decision tree is not as effective. Nevertheless, when a series or sequence of decisions are to be made, then the decision tree is very useful.

 

References

Dey, P.K. Project risk management using multiple criteria decision-making technique and decision tree analysis: a case study of Indian oil refinery. Production Planning & Control. 2012 Dec 1;23(12):903-21.

Taylor III, B. Introduction To Management Science; Management Science, 2013.

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