Question

Lawson’s Department Store faces a buying decision for a seasonal product for which demand can be high or low. The purchaser for Lawson’s can order 1, 2, or 3 lots of the product before the season begins but cannot reorder later. Profit projections (in thousands of dollars) are shown.

	State of Nature
Decision Alternative	High Demand (S1)	Low Demand (S2)
Order 1 lot, D1	60	50
Order 2 lots, D2	80	30
Order 3 lots, D3	100	10
P(Sj)	0.4	0.6

1. Find the optimal decision using the expected value approach.
2. Use the expected loss opportunity method to find the Expected Value of Perfect Information.
3. Conduct a graphical sensitivity analysis identifying the decisions for the different P(S1).
4. For the optimal solution, given the current probabilities of the state of nature, what would be the range of optimality (that is the range of values for its payoff where that decision alternative will still remain optimal) for its payoffs compared to the closest Expected Value.

Answer 1

SOLUTION;-

GIVEN DATA;-

A)

Expected Value of D1 = 60*0.4 + 50*0.6 = 54

Expected Value of D2 = 80*0.4 + 30*0.6 = 50

Expected Value of D3 = 100*0.4 + 10*0.6 = 46

Expected Value of D1 is the highest, therefore it is the optimal decision.

B) EVPI = Expected Loss opportunity of optimal decision = 16

C) Graphical sensitivity analysis is as follows

D) Current optimal decision is D1.

Current optimal decision (D1) will remain optimal, as longas its Expected Value is greater than or equal to 50.

Note that 50 is the EV of the next best decision after the optimal decision

. So when EV of current optimal decision goes below 50, then it ceases to be optimal.