Page 127 - DMTH404_STATISTICS

Unit 8: Expected Value with Perfect Information (EVPI)

Since the EOL of buying Type I Souvenir is minimum, the optimal decision is to buy Type Notes
I Souvenir.
(iii) Cost of uncertainty = EOL of optimal action = Rs. 340

Example 20:
The following is the information concerning a product X :

(i) Per unit profit is Rs 3.
(ii) Salvage loss per unit is Rs 2.
(iii) Demand recorded over 300 days is as under:

Units demanded : 5 6 7 8 9
of
No . days : 30 60 90 75 45
Find: (i) EMV of optimal order.
(ii) Expected profit presuming certainty of demand.

Solution.
(i) The given data can be rewritten in terms of relative frequencies, as shown below :

Units demanded : 5 6 7 8 9
No . days : 0.1 0.2 0.3 0.25 0.15
of
From the above probability distribution, it is obvious that the optimum order would lie
between and including 5 to 9.

Let A denote the number of units ordered and D denote the number of units demanded per
day.

If D ³ A , profit per day = 3A, and if D < A, profit per day = 3D - 2(A - D) = 5D - 2A.
Thus, the profit matrix can be written as

Units Demanded 5 6 7 8 9
Probability ®
0.10 0.20 0.30 0.25 0.15 EMV
)
Action (units ordered ¯
5 15 15 15 15 15 15.00
6 13 18 18 18 18 17.50
7 11 16 21 21 21 19.00
8 9 14 19 24 24 19.00
9 7 12 17 22 27 17.75

From the above table, we note that the maximum EMV = 19.00, which corresponds to the
order of 7 or 8 units. Since the order of the 8th unit adds nothing to the EMV, i.e., marginal
EMV is zero, therefore, order of 8 units per day is optimal.
(ii) Expected profit under certainty

= (5 0.10 6 0.20 7 0.30 8 0.25 9 0.15´ + ´ + ´ + ´ + ´ ) 3´ = Rs 21.45

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