# Question: Suppose that the demand D for a spare airplane part

Suppose that the demand D for a spare airplane part has an exponential distribution with mean 50, that is,

This airplane will be obsolete in 1 year, so all production of the spare part is to take place at present. The production costs now are $1,000 per item—that is, c = 1,000—but they become $10,000 per item if they must be supplied at later dates—that is, p = 10,000. The holding costs, charged on the excess after the end of the period, are $300 per item.

T (a) Determine the optimal number of spare parts to produce.

(b) Suppose that the manufacturer has 23 parts already in inventory (from a similar, but now obsolete airplane). Determine the optimal inventory policy.

(c) Suppose that p cannot be determined now, but the manufacturer wishes to order a quantity so that the probability of a shortage equals 0.1. How many units should be ordered?

(d) If the manufacturer were following an optimal policy that resulted in ordering the quantity found in part (c), what is the implied value of p?

This airplane will be obsolete in 1 year, so all production of the spare part is to take place at present. The production costs now are $1,000 per item—that is, c = 1,000—but they become $10,000 per item if they must be supplied at later dates—that is, p = 10,000. The holding costs, charged on the excess after the end of the period, are $300 per item.

T (a) Determine the optimal number of spare parts to produce.

(b) Suppose that the manufacturer has 23 parts already in inventory (from a similar, but now obsolete airplane). Determine the optimal inventory policy.

(c) Suppose that p cannot be determined now, but the manufacturer wishes to order a quantity so that the probability of a shortage equals 0.1. How many units should be ordered?

(d) If the manufacturer were following an optimal policy that resulted in ordering the quantity found in part (c), what is the implied value of p?

**View Solution:**## Answer to relevant Questions

Reconsider Prob. 18.6-1 involving Henry Edsel’s car dealership. The current model year is almost over, but the Tritons are selling so well that the current inventory will be depleted before the end-of-year demand can be ...Speedy Wheels is a wholesale distributor of bicycles. Its Inventory Manager, Ricky Sapolo, is currently reviewing the inventory policy for one popular model that is selling at the rate of 500 per month. The administrative ...Reconsider Prob. 19.2-2. (a) Formulate a linear programming model for finding an optimal policy. During any period, a potential customer arrives at a certain facility with probability 1 2. If there are already two people at the facility (including the one being served), the potential customer leaves the facility ...Obtaining uniform random numbers as instructed at the beginning of the Problems section, use the acceptance-rejection method to generate three random observations from the probability density functionPost your question