Hudson Corporation is considering three options for managing its data processing
ID: 3294062 • Letter: H
Question
Hudson Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows:
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Demand Staffing Options High Medium Low Own staff 700 600 500 Outside vendor 900 650 400 Combination 700 600 300Explanation / Answer
Part (a)
Let pij = pay-off for the ith strategy Si (staffing decision) under jth-State-of-nature Dj (demand).
Then, expected cost (EMV) for Si = [j = 1,3]{pij x P(Dj)}, I = 1, 2, 3.
Excel calculations of the above is given below:
Demand (Dj)
Staffing Options (Si)
High
Medium
Low
Own staff
700
600
500
Outside vendor
900
650
400
Combination
700
600
300
Total
P(Dj)
0.5
0.2
0.3
1
EMV(S1)
350
120
150
620
EMV(S2)
450
130
120
700
EMV(S3)
350
120
90
560
Since EMV(S3) is minimum, optimum strategy is to go for ‘combination’. ANSWER 1
And the corresponding expected cost is $ 560000 ANSWER 2
Part (b)
For the optimum strategy under Part (a), variance of the cost = {E(S3)2}– {E(S3)}2
Standard deviation of S3 = sqrtV(S3).
Excel calculations of the above is given below:
E(S3)^2
245000
72000
27000
344000
V(S3)
30400
SD(S3)
174.35596
So, Standard deviation of S3 = $174356.
Assuming the pay-off (cost) follow Normal distribution,
Probability of the cost exceeding $625,000 = P[Z > {(625000 - 560000)/174356}], where Z ~ N(0, 1).
= P(Z > 0.3728) = 0.3537 [using Excel Function] ANSWER
Demand (Dj)
Staffing Options (Si)
High
Medium
Low
Own staff
700
600
500
Outside vendor
900
650
400
Combination
700
600
300
Total
P(Dj)
0.5
0.2
0.3
1
EMV(S1)
350
120
150
620
EMV(S2)
450
130
120
700
EMV(S3)
350
120
90
560
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