Problem $2$: The Joint Staff is evaluating several force structure alternatives using a combat simulation model. They are interested in the ability of the force to fight and win in a large scale combat operation. The measures that they have decided to use $($and that will be computed as output from the simulation model$)$ are Probability of Victory, Number of Casualties $($in number of people$),$ and Time to Mission Accomplishment $($in months$).$ Your task is to construct a value function and use it to evaluate the alternatives. For that purpose, the following information is given.

Parameters for Problem $2$:

Single dimensional value function for Probability of Victory is piecewise linear such that P$[$v$]=0$ has zero value, P$[$v$]=\mathrm{.}5$ has a value score of $\mathrm{.}25,$ and P$[$v$]=1$ has a value of $1.$ It is linear in between.

Single dimensional value function for Numbers of Casualties, which range from a low of $250$ to a high of $1500,$ is exponential with a midvalue at $500.$

The single dimensional value function for time to mission accomplishment ranges between $2$ months and $18$ months and is linear.

The analysts elicited the following alternatives from the decisions maker. The decision maker expressed indifference between these alternatives:

A B

Time to Mission Accomplishment:

$6$ months

$12$ months

Casualties:

$700$

$350$

C D

Casualties:

$1000$

$800$

Probability of Victory:

$\mathrm{.}95$

$\mathrm{.}80$

Compute the weights for the attributes. Write down the complete value function.

Problem $3$: Compute the weights associated with $4,5,$ and $6$ attributes in SMARTER, and compute the weights for $4$ attributes when attributes $2$ and $3$ are equal.

Problem $4$: Compute the weights associated with $4,5,$ and $6$ attributes in the Rank Reciprocal method, and compute the weights for $4$ attributes when attributes $2$ and $3$ are equal.

Problem $5$: Compute the weights associated with $4,5,$ and $6$ attributes in the Rank Sum method, and compute the weights for $4$ attributes when attributes $2$ and $3$ are equal.