Beth Dale is the Director of Development for a nonprofit organization that depends

largely on charitable gifts for its operations. Beth needs to assign four different staff

people to make trips to call on four possible donors. Only one staff person can call

on each donor and each staff person can make only one call. Beth estimates the probability

of each staff person successfully obtaining the donation from each potential

giver as follows:

Donor

Staff 1 2 3 4

Sam 0.95 0.91 0.90 0.88

Billie 0.92 0.95 0.95 0.82

Sally 0.95 0.93 0.93 0.85

Fred 0.94 0.87 0.92 0.86

a. Formulate an NLP model to determine the assignment of staff persons to donors

that maximizes the probability of receiving all donations.

b. Implement your model in a spreadsheet and solve it. What is the optimal solution?

c. Suppose it is estimated that the donations possible from donors 1, 2, 3, and 4 are

for $1 million, $2 million, $0.5 million, and $0.75 million, respectively. How

should Beth assign her staff if she wants to maximize the expected value of the

donations received?

d. All staffers will have the least luck soliciting funds from donor number 4, so no

one really wants to be assigned to this donor. Indeed, each staffer will regret not

being assigned to the donor with whom they have the highest probability of success.

Suppose we define the amount of this regret for each staffer by their maximum

probability of success minus the probability of success for their actual

assignment. What assignment of staffers to donors will minimize the maximum

regret suffered by any staffer?