W8_Stella_ Using Multiattribute Decision to choose a hospital for my Nanny

W8_Stella_ Using Multiattribute Decision to choose a hospital for my Nanny

January4, 2013

 

1. Problem Definition and Recognition

In continuation of my last reporting which my Nanny was knocked down by a motorbike. The plan to move her to a best hospital became a decision problem because she had a deep cut in the leg and a severe fracture on her right arm.

This week I will be applying two compensatory models to explain how the decision was taken. The factors that were considered before making the final decision on the choice of hospital are listed below.

i.              The quality of the hospital’s services

ii.             Cost

iii.            Distance (considering traffic and my office location)

iv.           Confidence (assurance based on my previous experience and other people’s opinion)

v.            Environment (the cleanliness of the environment)

Tab. 1 Summary information for choice of hospital

Alternatives
Attributes	Relative Rank	Private Hospital A	General Hospital B	Military Hospital
Quality	7	fair	good	Excellent
cost (estimated in NGN)	5	500,000	120,000	130,000
Distance (m)	3	10	80	40
confidence	4	weak	fair	strong
Duration (estimated)	2	3months	2months	1month
Environment	1	Excellent	fair	good

 

In this decision making, two of the compensatory model were applied, the Nondimensional scaling and the additive weighting.

 The non dimensional scaling requires all the attributes values to be converted to nondimesional form.

The procedure for converting the original data is explained in the formula below

Rating = (worst outcome – outcome being made dimensionless)/ (worst outcome –best outcome): this is used for large values e.g. cost

Rating = (outcome being made dimensionless – worst outcome)/ (best outcome –worst outcome): this is the relationship for converting original data to their dimensionless rating. The’ highest nondimensional value’ after the summation is the ‘best choice’.

The additive weighting makes use of nondimensional attributes and the results of the ranking to produce a partial contribution of the overall score for a particular alternative. It is determined in two steps;

i.              assign a relative weight to each attributes according to its ordinal ranking

ii.             normalize the relative ranking by dividing each ranking number by the sum of the rankings.

2. Feasible Alternatives.

From the applications of Additive weighting, nondimensional scaling and nondimensionless data in Tabs.2, 3 & 4 the feasible alternatives are General hospital and the Military hospital. Particularly Tab.3 and Tab.4 showed that the best choice/winner is military hospital because it has the highest additive weight and nondimensional values.

Tab.2

Nondimensional scaling
Attribute	Value / Relative rank	Dimensionless value
Quality	fair                        1	0
	good                      2	0.5
	excellent               3	0.67
Cost	120000	1
	130000	0.97
	500000	0
Distance	10	1
	40	0.57
	80	0
Confidence	weak                      1	0
	fair                         2	0.5
	strong                    3	0.67
Duration (months)	1	0
	2	0.5
	3	0.67
Environment	fair                         1	0
	good                       2	0.5
	excellent                3	0.67

Tab.3

Non Dimensionless Data
Attributes	Private Hospital A	General Hospital B	Military Hospital
Quality	0	0.5	0.67
cost (estimated )	0	1	0.97
Distance	1	0.57	0
confidence	0	0.5	0.67
Duration (estimated)	0	0.5	0.67
Environment	0	0.5	0.67
Total	1	3.57	3.65
			Best Alternative

 

Tab.4

Additive Weighting
Attributes	step 1 Relative Rank	Step 2      Normalized weight (A)	(B)	Private Hospital (A) *(B)	(B)	General Hospital (A) *(B)	(B)	Military Hospital (A) *(B)
Quality	7	0.318182	0	0	0.5	0.159091	0.67	0.213182
Cost	5	0.227273	0	0	1	0.227273	0.97	0.220455
Distance	3	0.136364	1	0.136364	0.57	0.077727	0	0
Confidence	4	0.181818	0	0	0.5	0.090909	0.67	0.121818
Duration	2	0.090909	0	0	0.5	0.045455	0.67	0.060909
Environment	1	0.045455	0	0	0.5	0.022727	0.67	0.030455
Total	22	1	1	0.136364	3.57	0.623182	3.65	0.646818
								winner

3.    Develop the outcomes for each alternative

Tab. 3 explained critically that General hospital has a closer or nearer option to the best choice looking at their total values 3.57 for General hospital and 3.65 for Military hospital. Nevertheless Military Hospital has the highest value thereby making it the best alternative.

Similarly, Tab.4 which explains the additive technique shows that the military Hospital is also the best alternative because it has the highest additive weight.

4.    Selection of Criteria

      Two compensatory models were used as detailed in Tabs. 2 & 4to get to the best choice.

     Looking closely at the two total values of General Hospital and Military hospital (from the two techniques), you would observe that the values are too close. Nevertheless the best choice was the Military hospital because it has the highest values.

    

5.    Analysis and comparison of the alternatives

Looking at the two compensatory models used, the results are virtually the same, based on this I can say that there is no much difference between the additive weighting technique and the nondimensional scaling.

 

In addition, if (maybe) quality was not considered in this selection, then General hospital would have been the best option.

 Similarly if cost was our ulterior criteria, then General hospital would have still been the best alternative.

 

6.    Select the preferred alternative

From the nondimensionless data in Tab.1 and Tab.4 “Military Hospital” has the highest values , so it was the best choice for this decision.

 

     7. Performance Monitoring & Post Evaluation of Result

 

The application of Additive weighting and or  Nondimensionless model are  really good performance monitoring tool in that they give right choice considering all the attributes all the same time.

Specifically Additive weighting is probably the best because it includes both the performance ratings and the importance weights of each attributes when evaluating the alternatives.

8. References:

i. Sullivan W., Wicks E., Koelling P., (2012) .Chapter 14 Decision making Considering Multiattributes (pp577 – 590) Engineering Economy (15^th Edition).England: Pearson Education Limited.

 
ii. Fred A., (2000) Multiattribute Decision-Making: Use of Three Scoring Methods to Compare the Performance of Imaging Techniques for Breast Cancer Detection, Retrieved from: repository.upenn.edu/cgi/viewcontent.cgi?article=1121...Share

 

iii.Giammalvo, P.D (2012, October 22). Integrated portfolio (asset), program (operations) and project management methodology course (An AACE methodology course). Day 1 (pp 92-96) LONADEK Lagos, Nigeria.

 

iv. Hauser J., Ding M., Gaskin P., (2009). Non-compensatory (and Compensatory) Models of

Consideration-Set Decisions; Proceedings of the Sawtooth Software Conference: Delray Beach FL. Retrieved from: www.researchgate.net/...compensatory...compensatory)_model...Share