tions. Your assignment needs to be submitted on or before September 14, 2023.

Q1. CASE 7S-2 Airport Security

Shortly after the tragic events of September 11, 2001, the United States Congress enacted emergency legislation to give the Department of Transportation primary responsibility for providing security at over 400 major U.S. airports. The Transportation Security Administration was then created within the Department of Transportation to carry out this responsibility.

A leading OR consultant in the airline industry, Adeline Jonasson, has been hired by the Transportation Security Administration to head up a task force on airport security. The specific charge to the task force is to investigate what advanced security technology should be developed and used at airport checkpoints to maximize the effectiveness with which passengers can be screened within budget constraints.

Even prior to 2001, airline passengers had become familiar with the two basic types of systems used to check each passenger at a security checkpoint. One is a portal that can detect concealed weapons as the passenger walks through. The other is a screening system that scans the passengers carry-on luggage. Various proposals have been made for advanced security technology that would improve these two systems. Adelines task force now needs to make recommendations on which direction to go for the next generation of these systems.

The task force has been told that the functional requirement for the new portal system is that it must be able to detect even one ounce of explosives and hazardous liquids as well as metallic

1|Page

weapons being concealed by a passenger. The technology needed to do this includes quadrupole resonance (closely related to magnetic resonance technology used by the medical industry) and magnetic sensors. There are various ways to design the portal with this technology that would satisfactorily meet the functional requirement. However, the designs would differ greatly in the frequency with which false alarms would occur as well as in the purchase cost and maintenance cost for the portal. The frequency of false alarms is a key consideration since it substantially affects the efficiency with which the passengers can be processed. Even more importantly, a high frequency of false alarms greatly decreases the alertness of the security personnel for detecting the relatively rare terrorists who are actually concealing destructive devices.

The most basic version of the portal system that satisfactorily meets the functional requirement would have an estimated purchase price of $90,000 and, on the average, would incur an annual maintenance cost of $15,000. The drawback of this version is that it would generate a false alarm for approximately 10 percent of the passengers. This false alarm rate can be reduced by using more expensive versions of the system. Each additional $15,000 in the cost of the portal system would lower the false alarm rate 1 percent and also would increase the annual maintenance cost by $1,500. The most expensive version would cost $210,000, so it would have a false alarm rate of only 2 percent of the customers as well as an annual maintenance cost of $27,000.

Regarding the new screening system for carry-on luggage, the functional requirement is that it must clearly reveal suspicious objects as small as the smallest Swiss army knife. The technology needed to do this combines X-ray imaging, a thermal neutron scanner, and computer tomography imaging (which compares the density and other physical properties of any suspicious objects with known high-risk materials). It is estimated that the most basic version that satisfactorily meets this functional requirement would cost $60,000 plus an annual maintenance cost of $9,000. As with the most basic portal system, the drawback of this version is that it isnt sufficiently discriminating between suspicious objects that actually are destructive devices and those that are harmless. Thus, this version would generate false alarms for approximately 6 percent of the customers. In addition to wasting time and delaying passengers, such a high false alarm rate would make it very difficult for the screening operator to pay sufficient attention when the far more unusual true alarms occur. However, more expensive versions of the screening system would be considerably more discriminating. In particular, each additional $30,000 in the

2|Page

cost of the system would enable a reduction of 1 percent in the false alarm rate, while also increasing the annual maintenance cost by $1,200. Thus, the most expensive version, costing $150,000, would decrease the false alarm rate to 3 percent and incur an annual maintenance cost of $12,600.

The task force has been given two budgetary guidelines.

First Budgetary Guideline: Plan on a total expenditure of $250,000 for both the portal system and the screening system for carry-on luggage at each security checkpoint.

Second Budgetary Guideline: Plan on holding down the average total maintenance costs for the two systems at each security checkpoint to no more than $30,000. These budget guidelines prohibit using the most expensive versions of both the portal system and the screening system for carryon baggage. Therefore, the task force needs to determine which financially feasible combination of versions for the two systems will maximize the effectiveness with which passengers can be screened. Doing this requires first obtaining input from the top management of the Transportation Security Administration regarding what the measure of effectiveness should be and then what managements goals and priorities are for achieving substantial effectiveness and meeting the budgetary guidelines.

Fortunately, Adeline already has had extensive discussions with top management to obtain its guidance on these matters. These discussions led to the adoption of a clear policy that was approved all the way up to the Secretary of Transportation (who also informed the chairmen of the Congressional oversight committees of this action). The policy establishes the following order of priorities.

Priority 1: The functional requirement for each of the two new systems must be met. (This is satisfied by all the versions under consideration by the task force.)

Priority 2: The total false alarm rate for both systems should not exceed 0.1 per passenger.

Priority 3: Meet the first budgetary guideline.

Priority 4: Meet the second budgetary guideline.

3|Page

Now that it has obtained all the needed managerial input, the task force is ready to begin its analysis.

a. b.

c.

Identify the two decisions to be made, and define a decision variable for each one. Describe why this problem is a preemptive goal programming problem by giving quantitative expressions for each of the goals in terms of the decision variables defined in part (a).

Draw a single two-dimensional graph where the two axes correspond to the decision variables defined in part (a). Consider each of the goals in order of priority and use the quantitative expression obtained in part (b) for this goal to draw a plot on this graph that graphically displays the values of the decision variables that fully satisfy this goal. After completing this for all the goals, use this graph to determine the solution for this preemptive goal programming problem.

Q2. Suppose that a decision maker faced with four decision alternatives and four states of nature. S/he develops the following consequential table for cost:

Decision States of Nature

Alternative S1 S2 S3 S4

D1 14 9 10 5 D2 11 10 8 7 D3 9 10 10 11 D4 8 10 11 13

a.

b. c.

If the decision maker knows nothing about the probabilities of the four states of nature, what is the recommended decision using the optimistic, pessimistic, and minimax regret approaches?

Which approach do you prefer? Explain in brief

Assume that the payoff table provides profit rather than cost payoffs. What is the recommended decision using the optimistic, pessimistic, and minimax regret approaches?

4|Page

Q3. Two firms commercialize two products that they both compete for. Each firm currently has 50 % of the market share. As the two products have been recently improved, both firms are planning to launch an advertising campaign. If neither firm advertises, their market share remains the same. If one of them launches a more powerful advertising campaign, the other loses a proportional percentage of its customers. Market research indicates that it is feasible to reach 50 % of potential customers by TV, 30 % through the press and 20 % on the radio.

a.

b.

c.

Q4. Suppose St. Marys University is about to play AAU for tennis championship. The St, Marys team has two players (A and B), and the IAAU team has three players (X, Y, and Z). The following facts are known about the players relative abilities: X will always beat B; Y will always beat A; A will always beat Z. In any other match, each player has a 12 chance of winning. Before St. Mary plays AAU, the St. Marys coach must determine who will play first singles and who will play second singles. The AAU coach (after choosing which two players will play singles) must also determine who will play first singles and second singles. Assume that each coach wants to maximize the expected number of singles matches won by the team. Use game theory to determine optimal strategies for each coach and the value of the game to each team.

Q5. Consider a problem hierarchy with 4 criteria on which the three alternatives are to be judged. For pairwise comparison the first criteria will be compared against the remaining 3, the second criteria against the remaining 2, the third criteria against the remaining 1 as it is clearly indicated in the given below table.

Take the problem as if it were a zero-sum Game, develop the payoff matrix for this game

Indicate the most appropriate advertising strategy for both firms

Determine the game value

5|Page

Table: 1 Pairwise comparison Matrix for the criteria

Besides, the pairwise comparison matrices of each decision alternative (DA) i.e. B1, B2 and B3) with respect to each criterion are given in the table below:

Based on the above given information:

a. Develop normalized matrices and priority vectors accordingly

b. Which decision alternatives will be selected by you as a decision maker and why?

c. Is there an inconsistency problem? If yes why? If no why not?

6|Page

Q6. Suppose there is a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each channel. Answer the following questions and recommend an alternative design for the fast-food franchise:

a. b. c. d. e.

What is the probability that no cars are in the system? What is the average number of cars waiting for service? What is the average number of cars in the system? What is the average time a car waits for service?

What is the probability that an arriving car will have to wait for service?

Q7. A

concerning their income, wealth and sales taxes. On the average 48 persons arrive in an 8- hour day. Each tax adviser spends 15 minutes on the average on an arrival. If the arrivals are Poisson distributed and service times are according to exponential distribution find:

a. The average number of customers in the system,

b. Average number of customers waiting to be serviced,

c. Average time a customer spends in the system

d. The probability that a customer has to wait before he gets service, e. The expected number of idle tax advisers at any specified time.

The End!!!

tax-consulting firm has 3 counters in its office to receive people who have problems

7|Page