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Operational Analysis

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Option Analysis: Using The Method Of Even Swaps

by Dr. W.J. Hurley and Dr. W.S. Andrews

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An important problem for defence planners is assessing the trade-off among decision factors (criteria)1 for competing systems. Among the operations research tools available for such analyses, Multi-Criteria Decision Analysis (MCDA) is perhaps the most useful.

In the case where a staff officer uses a MCDA technique, say in an Options Analysis, he usually has to sell the argument to senior decision-makers. Depending on the complexity of the MCDA tool used, this can be a very difficult task – especially if superiors are unfamiliar with the specific tool being used. The staff officer ends up with two problems. First, he must convince his superiors that the technique he is using is appropriate. Then, assuming he can do this, he must argue his preferred alternative within the structure of this technique. If his technique is complex, the first of these problems is difficult. The officer must make a decision regarding how much to reveal about his ‘Black Box’. This almost always boils down to a state of affairs where the officer invokes academic cant, the superior does not fully understand the ‘Black Box’, and the decision is made largely on the basis of faith and the reputation of the staff officer.

In this note we present a simple MCDA technique termed the Method of Even Swaps.2 This method arrives at a preferred alternative through a series of simple comparisons and judgments. It has the characteristic that most intelligent decision-makers can easily understand it. Moreover, it lays bare the critical assumptions that lead to a preferred alternative.

To illustrate the method, we use a simple example involving the selection of an Unmanned Aerial Surveillance and Target Acquisition System (UASTAS). A typical UASTAS system comprises ground stations and unmanned airframes. Airframes are programmed to fly over forward areas of the battlefield. They have extremely sophisticated on-board sensor systems which transmit almost-real-time information (including video) from their field of view back to a ground station. The problem is to choose the preferred option given assessments of each system on a number of important factors.

An Example

Suppose you are a staff officer assigned to the UASTAS project described above. You are responsible for an Options Analysis to determine which of four compliant off-the-shelf systems is best. These are labelled A, B, C and D. After consultation with fellow staffers, you arrive at the following set of assessment criteria:

  • Range: the effective range of an airframe measured in kilometres.

  • Field of View: an aggregate measure of the range of sensors measured in square kilometres.

  • Response Time: the time in minutes to mission-plan and launch a back-up airframe in the event in-flight reprogramming is not possible.

  • Survivability: the probability an airframe completes a mission in a defined hostile environment. (It was estimated with error by Land Operational Research Staff).

  • Cost: the sum of the Procurement Cost and the discounted future costs of Operation, Personnel and Maintenance, measured in present-year dollars.

This is a fairly small set of criteria by DND Option Analysis standards. But since our purpose is simply to demonstrate how the technique works, we make no claim that these criteria are complete or consistent.

These criteria and options give rise to the following Consequences Table:

Consequences Table

 

System A

System B

System C

System D

Range

56

60

60

55

Field Of View

1.00

1.18

1.15

1.15

Response

62

60

50

70

Survivability

0.85

0.90

0.90

0.92

Cost

52

49

42

55

Table 1

Each system is measured on each criterion. In the absence of objective data for a criterion, the decision-maker could simply rank-order the systems. That is, a ‘1’ would be assigned to the system which is best on that criterion, a ‘2’ to the second best system, and so on.

With this Consequences Table in hand, the systems are then rank-ordered on each assessment criterion:

Consequences Table (Rank-Order)

 

System A

System B

System C

System D

Range

3

1

1

4

Field Of View

4

1

2

2

Response

3

2

1

2

Survivability

4

2

2

1

Cost

3

2

1

4

Rank Sum

17

8

7

15

Table 2

For instance, consider each system on the Range criterion. Systems B and C have the highest range and consequently each is assigned the rank 1. System C has the next highest range followed by System D. Therefore we assign a rank of 3 to System A and 4 to System D.

The bottom row of this rank-order consequences table is the sum of the column rank-orders. Clearly we would like to look at systems with low rank-order sums. In this case, Systems B and C have low rank-sums; Systems A and D have high rank-sums.

We begin pruning the Consequences Table by looking for dominated alternatives. Consider Systems A and B. Note that B has a lower rank-order for every assessment criterion. Hence A is said to be dominated by B and we can exclude System A from further consideration.

Now we examine System B and System D. System B is at least as good as System D for every assessment criterion except Survivability. Given that Survivability is measured with error and the two measures are close anyway (.90 for System B and .92 for System D), the decision is made that System B is preferred to System D. We say that System D is nearly dominated by System B and System D is eliminated.

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The reduced Consequences Table is as follows:

Consequences Table

 

System B

System C

Range

60

60

Field Of View

1.18

1.15

Response

60

50

Survivability

0.90

0.90

Cost

49

42

Table 3

Note that these two systems have identical measures on Range and Survivability. We can now eliminate these criteria to reduce the Consequences Table to:

Consequences Table

 

System B

System C

Field Of View

1.18

1.15

Response Time

60

50

Cost

49

42

Table 4

Now we are in a position to do an even swap. Consider System C and ask what we are prepared to pay in dollars (Cost) to get the Field of View up to 1.18 square kilometres. Suppose we are prepared to pay an additional $2 million.3 Then, the revised Consequences Table is:

Consequences Table

 

System B

System C

Field Of View

1.18

1.15+.03

Response Time

60

50

Cost

49

42+2

Table 5

and now we can eliminate the Field of View criterion giving:

Consequences Table

 

System B

System C

Response Time

60

50

Cost

49

44

Table 6

Now the decision is clear. System C has a lower Response Time and a lower Cost. Hence System C is preferred to System B, and therefore System C is the preferred option.

Note that we have arrived at the conclusion that System C is best with only one assumption: as long as we are prepared to pay something less than $7 million for a 2.6 percent increase in System C’s Field of View, System C is the best alternative.

Some General Points

Suppose we define a decision path to be a sequence of dominance and even swap decisions that lead to the specification of a preferred alternative. It should be clear that, for any Consequences Table, there are a variety of paths that result in a preferred option.

It should also be noted that we could ask a decision-maker to specify some trade-offs a priori. For instance we could ask the decision-maker how much he is prepared to pay to get a 10 percent increase in Field of View, how much he is prepared to pay to get a 10 percent decrease in Response Time, and so on for the other two criteria. Assuming linearity of preferences, this would enable us to collapse the Consequences Table in a single step. However, as the example above demonstrates, this is not required. In that example, we required the decision-maker only to specify a single trade-off.

In this regard, there is a common misconception about how this method works. Some have suggested that the method is faulty because it implicitly assigns equal weights to the criteria. Of course, this is not the case. While it is true that the Method of Even Swaps does not require us to assign relative values to all criteria (as we have to do in just about every other multi-criteria system), it is hardly the case that we implicitly assess these as equally weighted.

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Summary

It is worth pointing out that the Method of Even Swaps has its origin in the rather famous advice that Benjamin Franklin offered Joseph Priestly:

... To get over this, my way is to divide half a sheet of paper by a line into two columns; writing over the one ‘Pro’, and over the other ‘Con’. Then, during three or four days’ consideration, I put down under the different heads short hints of the different motives that at different times occur to me, for or against the measure.

When I have thus got them all together in one view, I endeavor to estimate their respective weights; and where I find two ones on each side that seem equal, I strike them both out. If I find a reason pro equal to two reasons con, equal to some three reasons pro, I strike out the five....

Hammond, Keeney and Raiffa have extended Franklin’s logic in a very creative way to the case where there are more than two alternatives.4

In some cases, it may well be that the Method of Even Swaps is not appropriate. In fact, Guitouni and Martel argue that it is unlikely one MCDA technique will ever prove superior for all decisions.5 This position is certainly consistent with the large number of multi-criteria models available. While it may be true that other MCDA approaches offer better discrimination among options at the cost of complexity in some cases, our view is that the Method of Even Swaps is especially useful when a preferred option must be ‘sold’ to senior decision-makers.

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Dr. W.J. Hurley is a professor in the Department of Business Administration and Dr. W.S. Andrews is a professor in the Department of Chemistry and Chemical Engineering at the Royal Military College of Canada.

Notes

  1. In the operations research literature, ‘criteria’ refers to characteristics which are important to the decision-maker. For instance, if we were considering tanks, the size of the gun would be a criterion. Within DND, the word ‘factor’ is used in the same sense. We use the two interchangeably throughout this paper.
  2. See John S. Hammond, Ralph L. Keeney and Howard Raiffa, “Even Swaps: A Rational Method for Making Trade-Offs,” Harvard Business Review, March-April 1998, pp. 137-149 and John S. Hammond, Ralph L. Keeney and Howard Raiffa, Smart Choices: A Practical Guide to Making Better Decisions, Harvard Business School Press, Boston, 1999.
  3. The method does not require that we do an even swap with dollars. We could have used the Field of View and Response Time criteria. However, given our experience with this methodology, decision-makers find it easier to make swaps with the Cost criterion.
  4. Hammond et al, Op. Cit.
  5. Adel Guitouni and Jean-Marc Martel, “Tentative Guidelines to Help Choosing an Appropriate MCDA Method,” European Journal of Operations Research 109, 1998, pp. 501-521.

The authors would like to thank Lieutenant-Colonel (ret’d) Mike McKeown for background information and Captain Laim McGarry for very helpful comments.

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