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Exam 5: Advanced Linear Programming Applications

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Question 21

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The overall goal of portfolio models is to create a portfolio that provides the best balance between

A) short-term and long-term investments.
B) gains and losses.
C) risk and return.
D) liquidity and stability.

E) All of the above
F) A) and B)

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Question 22

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Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%. Formulate the appropriate linear program. $\text { Annual Returns (Flanning Scenarios) }$ $\begin{array}{c|rrrr}\text { Mutual Fund } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } & \text { Year 4 }\\\hline \text { International Stock } & 22.37 & 26.73 & 6.46 & -3.19 \\\text { Large-Cap Blend } & 14.88 & 18.61 & 10.52 & 5.25 \\\text { Mid-Cap Blend } & 19.45 & 18.04 & 5.91 & -1.94 \\\text { Small-Cap Blend } & 13.79 & 11.33 & -2.07 & 6.85 \\\text { Intermediate Bond } & 7.29 & 8.05 & 9.18 & 3.92\end{array}$

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Question 23

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DEA does not necessarily identify the operating units that are relatively efficient.

If the inputs of the composite unit in DEA are greater than the inputs for an individual unit, then the composite is more efficient.

Modern revenue management systems maximize revenue potential for an organization by helping to manage

Revenue management methodology was originally developed for

Consider a two-person, zero-sum game where the payoffs listed below are the winnings for Player A. Identify the pure strategy solution. What is the value of the game? $\begin{array} { c | c c c } & & { \text { Player B Strategies } } \\\text { Player A Strategies } & b _ { 1 }& b _ { 2 } & b _ { 3 } \\\hline a _ { 1 } & 5 & 5 & 4 \\a _ { 2 } & 1 & 6 & 2 \\a _ { 3 } & 7 & 2 & 3\end{array}$

The output shows the solution to a DEA model where facilities in Seaview (S), Farmington (F), Lewiston (L), and San Domingo (D) are compared. The inputs, in order, are number of machines, size of work force, and goodness of location. The outputs, in order, are production, quality rating, and on-time completion percentage. The model examines the efficiency of Lewiston. MIN 0S+0F+0L+0D+1E S.T. 1) 1S+1F+1L+1D=1 2) 5S+22F+36L+15D-36E<0 3) 400S+1500F+3150L+1060D-3150E<0 4) 24S+13F+32L+17D-32E<0 5) 800S+2900F+1860L+1700D+0E>1860 6) 95S+92F+83L+94D+0E>83 7) 83S+85F+90L+91D+0E>90 OPTIMAL SOLUTION Objective Function Value = 0.510 $\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { S } & 0.000 & 0.385 \\\text { F } & 0.167 & 0.000 \\\text { L } & 0.000 & 0.490 \\\text { D } & 0.833 & 0.000 \\\text { E } & 0.510 & 0.000\end{array}$ $\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 1.365 \\2 & 2.208 & 0.000 \\3 & 474.479 & 0.000 \\4 & 0.000 & 0.031 \\5 & 40.000 & 0.000 \\6 & 10.667 & 0.000 \\7 & 0.000 & - 0.021\end{array}$ a.Is the Lewiston plant efficient? Why or why not? If not, which plants should it emulate in order to improve? b.How much more production does the composite facility provide than the Lewiston site? c.What is the quality rating for the composite facility?

Consider the following two-person, zero-sum game. Payoffs are the winnings for Company X. Formulate the linear program that determines the optimal mixed strategy for Company X. $\begin{array} { c | c c c } && { \text { Company Y Strategies } } \\\text { Company X Strategies } & y _ { 1 } & y _ { 2 } & y _ { 3 } \\\hline x _ { 1 } & 4 & 3 & 9 \\x _ { 2 } & 2 & 5 & 1 \\x _ { 3 } & 6 & 1 & 7\end{array}$

Explain the differences between the LP formulations for a conservative portfolio and moderate-risk portfolio.

Shown below is the solution to the linear program for finding Player A's optimal mixed strategy in a two-person, zero-sum game. $\text { OBJECTIVE FUNCTION VALUE }=3.500$ $\begin{array}{ccc}\text { VARIABLE } & \text { VALUE } & \text { REDUCED COSTS } \\\text { PA1 } & 0.050 & 0.000 \\\text { PA2 } & 0.600 & 0.000 \\\text { PA3 } & 0350 & 0.000 \\\text { GAINA } & 3.500 & 0.000\end{array}$ $\begin{array}{ccc}\text { CONSTRAINT } & \text { SLACK/SURPLUS } & \text { DUAL PRICES } \\\hline 1 & 0.000 & -0.500 \\2 & 0.000 & -0.500 \\3 & 0.000 & 0.000 \\4 & 0.000 & 3.500\end{array}$ a.What is Player A's optimal mixed strategy? b.What is Player B's optimal mixed strategy? c.What is Player A's expected gain? d.What is Player B's expected loss?

List several types of organizations with multiple operating units where data envelopment analysis might be applied and give examples of possible inputs and outputs for each organization.

A linear programming application used to measure the relative efficiency of operating units with the same goals and objectives is

The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.

Revenue management methodology was originally developed for the banking industry.