Question

A college student, Stan Ford, recently took a course in operations research. He now enjoys

applying what he learned to optimize his personal decisions. He is analyzing one such decision

currently, namely, how much money (if any) to take out of his savings account to buy $100

traveler’s checks before leaving on a short vacation trip to Europe next summer.

Stan already has used the money he had in his checking ac- count to buy traveler’s checks

worth $1,200, but this may not be enough. In fact, he has estimated the probability distribution of

what he will need as shown in the following table:

Amount

needed ($) 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700

Probability 0.05 0.10 0.15 0.25 0.20 0.10 0.10 0.05

If he turns out to have less than he needs, then he will have to leave Europe 1 day early for every

$100 short. Because he places a value of $150 on each day in Europe, each day lost would thereby

rep- resent a net loss of $50 to him. However, every $100 traveler’s check costs an extra $1.

Furthermore, each such check left over at the end of the trip (which would be redeposited in the

savings ac- count) represents a loss of $2 in interest that could have been earned in the savings

account during the trip, so he does not want to purchase too many.

(a) Describe how this problem can be interpreted to be an inventory problem with uncertain

demand for a perishable product. Also identify the unit cost of under ordering and the unit

cost of over ordering.

(b) Use the stochastic single-period model for perishable products and the table of probabilities

to make Stan’s decision.

(c) Draw a graph of the CDF of demand​

Answer 1

Answer:

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