Introduction to Operations ResearchSummer 2013

MSC 521

P5: Life-of-Type Production at Ellen’s Electronics

Life-of-type production occurs when a single production run must be made now for inventory sparesfor a part in order to meet all future demands for that part over the life of the system. This usually occurs when a manufacturer is about to shut down a production line and no additional spare parts will be produced. The Electronic Parts Division (EPD) of Ellen’s Electronicsis about to shut down its production line of the AC-220V-A2advanced navigation system used on-board ten of the Boeing 787 Dreamliners.[1] The airlines have not indicated a desire to purchase any of these spare navigation systems. Therefore Ellen must decide how many to produce in anticipation of future sales to the airline industry.

The demand for these navigation systemscould range from zero to 10 with 10 being the number of 787’s that have the AC-220V-A2 installed. It costs $70,000 to produce each navigation system. The selling price to the airline is $85,000. Any system not sold to the airline has a salvage value of $8,000. For each unfilled demand, Ellenbelieves the loss of goodwill to the airline industry will cost them $15,000 in future business.

Using decision theory, determine how many each navigation systems should be produced to maximize profits. Base your responses on each of the following criteria:

1. Criterion of Pessimism

2. Criterion of Optimism

3. Hurwicz criterion with 50 percent optimism

4. Minimax regret

5. Laplacecriterion

6. Expected value criterion (EMV). The time to failure requiring replacement of a single navigation system has been estimated to have an exponential distribution with a mean of 24,917 operating (flying) hours.The probability of a failure over the 30,000[2] hour life of the system is given by .Therefore the number of demands (failures) can be modeled as a binomial distribution (the prior) with n = 10 and p =0.70.

7. Find the Expected Value of Perfect Information (EVPI)

8. Posterior analysis: Because of the large economic consequences of this decision, Ellen has conducted accelerated reliability life testing of thenavigational systems. The results of the reliability test predicted 3failures among the 10 navigational systems. Historical data has shown the following likelihood probabilities when 3 failures are predicted:

Demands / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
likelihood / 0.03 / 0.12 / 0.23 / 0.27 / 0.2 / 0.1 / 0.04 / 0.01 / 0.001 / 0 / 0

Determine the resulting posterior distribution, and select the best alternate using the expected value criterion.

9. Being a creative and holistic individual, you decide to compute the average of the Hurwicz and EMV criteria (i.e. values found in 3 and 6). The maximum of these average values is your alternative of choice under this criterion.

10. Collect you consulting fee – 10 percent of the expected profit in question 6.

The AC-220V-A2

The Boeing 787

Solution Page – submit your solution on-line via the appropriate Webpage

Enter your values in 1,000 of dollars.

Question / Optimal number to manufacture / Value of criterion
1.
2.
3.
4.
5.
6.
7. / EVPI =
8.
9.
10. / Consulting fee =

[1]The Boeing 787 Dreamliner is a long-range, mid-size wide-body, twin-engine jet airliner developed by Boeing Commercial Airplanes. Its variants seat 210 to 290 passengers. Boeing states that it is the company's most fuel-efficient airliner and the world's first major airliner to use composite materials as the primary material in the construction of its airframe

[2] Each aircraft will fly approximately 3000 hours a year with a 10 year engine life.