The following table lists the anticipated profits of four operations under three scenarios.

Options    Low Demand Medium Demand High Demand

A 110 160 180

B 100 130 160

C 145 110 185

D 140 120 155

 

For the situation given in the table above (same data as question #22), assume that the probabilities of the outcomes are known to be a 60% chance of low demand, 20% chance of medium demand, and 20% chance of high demand. Using the expected value criterion, which plan should be chosen?

 

By first checking for domination, the getting the expected value of an option by getting the sum of the products of the profit under a certain scenario with the probability of that scenario for all options that are not dominated, the plan that returns the highest expected value is plan C with an expected value of 146.

Step-by-step explanation

Since we are given a profit matrix, first we check for dominance, or if there is any strategy that returns a higher profit across all scenarios against another strategy.

Comparing A and B: we see that A returns a higher profit in each scnario against B (110 > 100 in the low demand scenario, 160 > 130 in the medium demand scenario, and 180 > 160 in the high demand scenario). We can say that A dominates B, meaning B will never be the optimal scenario.

Comparing A and C: A does not always return a higher profit in each scenario against C (160 > 110 for medium demand but 110 < 145 for low demand), and also, C does not always return a higher profit in each scenario against A (145 > 110 for low demand but 110 < 160 for medium demand). No domination.

Comparing A and D: A does not always return a higher profit in each scenario against D (160 > 120 for medium demand but 110 < 140 for low demand), and also, D does not always return a higher profit in each scenario against A (140 > 110 for low demand but 120 < 160 for medium demand). No domination.

No need to compare B with any other strategy because it has already been dominated.

Comparing C and D: C does not always return a higher profit in each scenario against D (145 > 140 for low demand scenario but 110 < 120 for medium demand scenario), and also, D does not always return a higher profit in each scenario against C (120 > 110 for medium demand scenario but 140 < 145 for low demand scenario). No domination.

The viable strategies remaining are A, C, and D:

Options Low Demand Medium Demand High Demand

A 110 160 180

C 145 110 185

D 140 120 155

In the expected value criterion, we get the expected value of a strategy by getting the sum of the products of the profit under a certain scenario with the probability of that scenario:

expected value = (profit under low demand)*(probability of low demand) + (profit under medium demand)*(probability of medium demand) + (profit under high demand)*(probability of high demand)

Then, since we are given profit values, we look for the highest expected value.

We are given the following as well:

probability of low demand = 60% = 0.60

probability of medium demand = 20% = 0.20

probability of high demand = 20% = 0.20

Option A:

expected value = (110)*(0.60) + (160)*(0.20) + (180)*(0.20) = 66 + 32 + 36 = 134

Option C:

expected value = (145)*(0.60) + (110)*(0.20) + (185)*(0.20) = 87 + 22 + 37 = 146

Option D:

expected value = (140)*(0.60) + (120)*(0.20) + (155)*(0.20) = 84 + 24 + 31 = 139

We see that among the expected values, the highest expected value is 146, which is the expected value of option C. Thus, plan C should be chosen.