Supplemental Problem You are faced with the following decisi

Supplemental Problem

You are faced with the following decision to choose the best proposal from a group of 5 bids. The proposals are for a system to scan incoming containers as the arrive at the hospital shipping and receiving dock. Two key attributes have been identified by the proposal evaluation team as influencing the decision: (1) the cost of buying and implementing the scanner system ($Millions); and (2) the time required to scan a typical shipment (seconds).

The five contractors have submitted the information in Table 1.

Table 1. Proposal Data for Scanning Systems

Proposal

Cost ($M)

Scan Time (sec)

A

1.4

20

B

0.6

80

C

1.8

5

D

0.4

120

E

1.0

40

After discussion with the team, no one can agree on whether cost or scan time is most important so the tradeoff scaling constants for these attributes are set at k1=0.5 and k2=0.5. The team also agrees they are risk neutral with respect to the attributes.

Q1: Derive the utility functions for these attributes.

Q2: Using the additive multiattribute decision model, compute the expected utility of each proposal. Which is the best choice?

Q3: After some consideration and debate with an agency advisory group, the team must change the tradeoff scaling constants to k1=0.5 and k2=0.8. This will require that the expected utilities be recalculated using the multiplicative multiattribute decision model. To do this you must compute the master scaling constant, K. Find the master scaling constant value to eight decimal places.

Q4: Using the information from Q3, re-compute the expected utilities of the proposals. Which is the best choice?

Q5: Why are they different? (Don

Solution

The utility functions along with scaling constants weighted is given above.

b) As both factors together minimum for C.

C is the best choice.

c) k1 =0.5 k2 =0.8. New table is given below:

AS B shows minimum now, B is the best choice.