MedStar Health is expanding into Virginia. The firm must select one location whe
ID: 464630 • Letter: M
Question
MedStar Health is expanding into Virginia. The firm must select one location where it can build a clinic to serve patients. The following table lists the expected profits for clinics in three locations and the expected probabilities of the two possible situations: high numbers of patients utilizing the clinic or low numbers of patients utilizing the clinic. Location High (0.75) Low (0.25) Alexandria $1,500,000 $600,000 Woodbridge $950,000 $900,000 Leesburg $1,200,000 $200,000 Find the best decision using the following: a. Develop a payo table for this situation. b. Find the following: 1. Maximax 2. Maximin 3. Equal likelihood 4. Minimax regret c. Create a sensitivity graph comparing the dierent alternatives as the probability of numbers of patient’s changes.
Explanation / Answer
Payoff table:
From the question
Maximax:The maximax looks at the best that could happen under each action and then chooses the action with the largest value. They assume that they will get the most possible and then they take the action with the best best case scenario. The maximum of the maximums or the "best of the best"
Therfore, Decision should be Alexandria because it has profit ($1500000) which is maximum of all other options
Maximin: The maximin person looks at the worst that could happen under each action and then choose the action with the largest payoff. They assume that the worst that can happen will, and then they take the action with the best worst case scenario. The maximum of the minimums or the "best of the worst".
Therfore, Decision should be Woodbridge because it has profit($900000) which is maximum of all other 's minimum profit value.
Equal likelihood: It weights each state of nature equally, thus assuming that the states of nature are equally likely to occur. Since there are two states of nature in our example, we assign a weight of 0.50 to each one. Next, we multiply these weights by each payoff for each decision and select the alternative with the maximum of these weighted values.
Alexandria : 0.5*1500000 +0.5*600000=1050000
Woodbridge: 0.5*950000+0.5*900000=925000
Leesburg: 0.5*1200000+0.5*200000=700000
Maximum of above is for alexandria. thus this best option
Minimax regret: This appproach is neither purely optimistic nor purely conservative.
Rij= absolute value(Vj-Vij)
Rij = the regret associated with decision alternative
Vj= the payoff value corresponding to best decision (largest value in colum of payoff table)
Vij= the pay off corresponding to decision
Select the decision alternative with minimum of the maximum regret value.Using the concept,Both alexandria or leesburg have equal value thus both can be selected
Author's note: please be specific to the part that need to be answered
Location High (0.75) Low(0.25) Alexandria $1,500,000 $600,000 Woodbridge $950,000 $900,000 Leesburg $1,200,000 $200,000