W3_YN_Compensatory Model in MADM

W3_YN_Compensatory Model in MADM

Opportunity Statement

Throughout the week days, I spend time every day thinking about how to spend the coming weekend. After a long and stressful week at work, the weekend cannot come soon enough. In this post, I shall compare between the options for the best way to spend a weekend and choose the most optimal option.

Feasible Alternatives

Three alternatives on how to best spend my weekend are to be compared:

Option 1) Go on a road trip & hiking with friends.
Option 2) Spend the weekend at home with family.
Option 3) Spend time at the beach/park with family.

Outcomes of Feasible Alternatives

The alternatives will be compared using the compensatory model of the Multi-Attribute Decision Making Technique. The compensatory model includes two techniques; the Non-Dimensional Scaling Technique, and the Additive Weighting Technique. In this model, the relative importance of the attributes is taken into consideration by giving each of them a weight. The naming of the compensatory model comes from the fact that a weakness in an attribute of a product can be compensated by the strength of that product in another attribute in the model.

Acceptable Criteria

Three criteria will be used to compare between the alternatives:

1)      Cost: the average costs ($) spent in the weekend doing the relevant activity.

2)      Enjoyment: how refreshing and energizing the activity is.

3)      Family Time: how much time, in hours, I spend with my family doing the activity.

Analysis and Comparison of the Alternatives

Table 1 below details the value of all attributes for each of the alternatives.

Table 1: Data Summary

Attribute	Option 1	Option 2	Option 3
Cost ($)	80	15	40
Enjoyment	high	low	Medium
Family Time (hours)	2	8	7

We apply the first technique in the model, which is the non-dimensional scaling technique. In order to do so, the attributes must be converted and measured in a common measurement scale, which in our case is a dimensionless unit with a base of 1. The following two equations can be used, depending on whether the attribute is desirable or undesirable:

·         Desirable:

·        Undesirable:

The results of the technique are summarized in table 2 below:

Table 2: Non-Dimensional Scaling Technique Results

Attribute	Value	Formula	Dimensionless Value
Cost ($) (undesirable)	15	=(80-15)/(80-15)	1.00
	40	=(80-40)/(80-15)	0.62
	80	=(80-80)/(80-15)	0.00
Enjoyment (Relative Rank) (desirable)	high (3)	Relative Rank (3-1)/(3-1)	1.00
	low (1)	Relative Rank (1-1)/(3-1)	0.00
	medium (2)	Relative Rank (2-1)/(3-1)	0.50
Family Time (hours) (desirable)	8	=(8-2)/(8-2)	1.00
	7	=(7-2)/(8-2)	0.83
	2	=(2-2)/(8-2)	0.00

Because of the common scale, the value of all attributes related to each option can be added and then compared, which is shown in table 3 below.

Table 3: Non-Dimensional Scaling Technique Summary

Attribute	Option 1	Option 2	Option 3
Cost ($)	0.00	1.00	0.62
Enjoyment	1.00	0.00	0.50
Family Time (hours)	0.00	1.00	0.83
Total	1.00	2.00	1.95

According to this technique, option 2 is the most favorable. The non-dimensional technique, however, considers that all attributes are weighted equally, which is not necessarily true. In my case, I value family time more than I value enjoyment which I, in turn, value more than cost. To take into account, this technique is complemented by the Additive Weighting Technique. This technique gives more weight to the attributes that are of higher value to the person performing the comparison. The results of this technique is summarized in table 4 below. Note that “B” in the table is the relevant dimensionless value from table 3 above.

Table 4: Additive Weighting Technique Results

Attribute	Relative Rank	Normalized Weight (A)		Option 1		Option 2		Option 3
		Equation	A	B	A*B	B	A*B	B	A*B
Cost ($)	1	=Relative Rank / ∑Relative Ranks	0.167	0.000	0.000	1.000	0.167	0.620	0.103
Enjoyment	2		0.333	1.000	0.333	0.000	0.000	0.500	0.167
Family Time (hours)	3		0.500	0.000	0.000	1.000	0.500	0.830	0.415
Total	6	-	1.000	-	0.333	-	0.667	-	0.685

As per this technique, option 3 is the most favorable.

Preferred Alternative

According the first technique, option 2 is the most favorable. However, I value enjoyment and family time more than I value cost. The Additive Weighting Technique allowed me to give more weight to the attributes I value more. Using the second technique which builds upon the results of the non-dimensional scaling technique, it turns out that my true preferred option is option 3. So spending time with my family at the beach or the park yields a reasonable amount of enjoyment while spending less money and spending more time with my family.

Tracking and Reporting

I shall utilize the third option more often in my weekends. As I do so, I shall track the attributes I mentioned in this blog and notice any changes such as increasing costs or decreasing enjoyment. If major changes to the attributes occur, I shall seek other options that were not considered before such as going more often on long road trips with my family.

References

1)      GUILD OF PROJECT CONTROLS COMPENDIUM and REFERENCE (CaR) | Project Controls - planning, scheduling, cost management and forensic analysis (Planning Planet). (n.d.). Retrieved from http://www.planningplanet.com/guild/gpccar/managing-change-the-owners-perspective

2)    Decision Models: Compensatory and Noncompensatory. (n.d.). Retrieved from http://www.mycbbook.com/MYCBBook-Consumer-Decision-Judgment-Models.pdf

3)      Decision Making Considering Multiattributes. (2012). Retrieved from http://www.csun.edu/~ghe59995/MSE604/MSE604%20Ch.%2014%20-%20Decision%20Making%20Considering%20Multi-attributes.ppt