# Operations research

1 January 2017

When we are attempting to make a business decision, the decision criteria should always be to minimize cost. Answer Selected Answer: False Question 2 EVSI can never exceed EVPI Answer Selected Answer: True Question 3 You are currently paying \$12 per hour for labor, and labor costs are included in the calculation of the objective function coefficients of a maximization problem. The shadow price for labor printed on the sensitivity analysis report is \$8. It would be economically beneficial to you if you could secure extra labor for \$15 per hour. Answer Selected Answer: True

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If project 1 is performed then project 2 will not be performed. This can be modeled by the constraint X1 – X2 ? 1, where X1 and X2 are binary variables. Answer Selected Answer: False Question 5 Monte Carlo simulations are deterministic. Answer Selected Answer: False Question 6 In constructing a utility curve, Answer Selected Answer: b. the certainty of a certain amount is compared with the willingness to gamble that amount on a larger amount. Question 7 Banner Tools produces two styles of steel hammers with wooden handles.

The first sells for \$6 and consists of . pounds of steel; the second sells for \$15 and consists of 1 pound of steel. Since steel costs the firm \$4 per pound and the handle, labor, and packaging costs amount to \$1 for either hammer, the profits coefficients are \$6 – . 5(\$4) – \$1 = \$3 for the smaller hammer and \$15 – 1(\$4) – \$1 = \$10 for the larger hammer. Thus the objective function for this model is MAX 3X1 + 10X2. Given that the shadow price for steel is \$2, which of the following statements is correct?

Nike may build a factory at Millville (Y1) or it may not. It may also build a regional warehouse at the same site (W1). But Nike will not build a warehouse without also building a factory. So, its choices are: (1) neither factory nor warehouse; (2) factory only; or (3) factory and warehouse. The appropriate linear constraint to express this is: Answer Selected Answer: d. Y1 – W1 ? 0 Question 9 In sensitivity analysis, a zero shadow price for a resource ordinarily means that Answer Selected Answer: a. the resource has not been used up Question 10

Which of the following would not generally be listed as a reason for the popularity of simulation as a managerial tool? Answer Selected Answer: a. Ability to provide optimal solutions Question 11 The campus bookstore wishes to determine how many units of a discontinued computer it should purchase for an upcoming sale. The computers cost \$800 each and the bookstore believes it can sell them for \$1100 each. At that price the bookstore estimates that the demand will be between one and four units. Any computers unsold at the end of the sale will be marked down in price by 50% and will quickly sell out.

If the bookstore does not have enough computers in stock to satisfy all the demand, it estimates that it will incur a goodwill loss of \$100 for each unsatisfied customer. Determine the optimal decision. What is the expected payoff for the optimal? Answer Selected Answer: c. 462. 5 Question 12 A company faces possible industrial action by workers during the final rounds of wage negotiation with a workers’ union. The union is currently demanding pay increases and benefits worth \$2m: substantially more than the industry standard.

Ping, the company’s CEO is confident that the union will actually accept a lower amount but is not sure how to proceed. Ping has identified two possible offers that he could make to the union. Package A is \$1m in pay increases and benefits (around the industry standard) and Package B is \$700,000 in pay increases and benefits. Ping reasons “If we offer package A I think there’s a fair chance, say 40%, that the union will accept it straight away. If they don’t they will come back with their own proposal, let’s call it package Y, probably around \$1. 5m. We could just accept that.

If we rejected package Y then I think we’ve got a potential problem. The union might accept our first offer of \$1m but it’s likely that they would see that as a defeat and so they might call a strike. I think there’s about a 75% chance of a strike. But because the strike is being called when we’ve got a \$1m offer on the table, which is about what the rest of the industry is paying, I don’t think it would last more than a week and I think in the end we would probably agree to around a \$1. 2m package. ” Any strike will cost the company \$150,000 per week over and above the cost of the package.

Ping’s second alternative is to begin by offering package B. He estimates there is a 20% chance of the union accepting that offer immediately. There is also about a 10% chance that the union would be insulted by package B because it is substantially below what the industry is paying and immediately call a strike. In that case the strike would most likely last 3 weeks and a final agreement would be reached on a package worth about \$1. 1m.

Thirdly, the union might come back with their own proposal, package Y. Now the company has three possible responses if the union proposes package Y. (1) They can accept package Y. 2) They can reject it, in which case at this point the union would have about a 90% chance of calling a strike that would last 4 weeks and end in an agreement on a \$1. 1m package or the union would have a 10% chance of accepting package B. (3) Or the company could increase their offer to package A. Because increasing the offer would be seen in this situation as a gesture of goodwill on the part of the company, the union would most likely accept package A (with 70% probability) although there would still be 30% chance of a 1 week strike that ended in an agreement on a \$1. 25m package.

Note that all amounts of money are in present value dollars and measure the full cost of each option both immediately and in the future). Draw a decision tree. What is the optimal for the most immediate decision? Answer Selected Answer: b. Offer B Question 13 Extel Industries produces integrated circuit components for use in the next generation of automobiles. In particular, it can make the AT50 unit that can control the air temperature in the car, the V35 unit that monitors vibration and makes adjustments accordingly, and the GM30 that regulates the engine so that the car provides maximum efficiency.

The unit profits on these units are \$84, \$112, and \$126, respectively. Each of these units uses different quantities of three computer chips (as shown below), which Extel purchases from a Taiwanese distributor. C101 H122 P043 AT50 1 1 1 V35 1 1 2 GM30 1 2 1 Each week Extel receives 350 C101’s, 300 H122’s, and 400 P043’s.

The purchase price for these chips represents a sunk cost to Extel. Solve this using linear optimization. Which units will Extel produce? Answer Selected Answer: b. AT50 and V35 Question 14 The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

The management indicated that if machine 4 is used, machine 1 will not be used since only a limited number of employees are capable of operating machines 1 and 4. Machine Fixed cost to set up Variable cost per hose Capacity production run 1 750 1. 25 6000 2 500 1. 0 7500 3 1000 1. 00 4000 4 300 2. 00 5000 Solve this using integer optimization. Given the information above which machines should be used? Answer Selected Answer: b. 1 and 3 Sunday, May 6, 2012 8:43:14 AM HST OK

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