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The panel modeled the strategy for HIV prevention as an LP problem. The

key question was: How should the budget for prevention ($412 million in 1999)

allocate funds across dozens of alternative prevention programs, with myriad

constraints, to maximize the number of HIV cases prevented? Prevention pro-

grams ranged from counseling at-risk populations to screening blood dona-

tions to preventing mother-to-child transmissions to funding needle exchanges

for intravenous drug users. The panel marshaled the available economic and

medical data to solve a variety of LP problems under different scenarios (from

pessimistic to optimistic). They found that an optimal resource policy could

prevent about 3,900 new HIV infections per year at the $412 million funding

level. Investigation of the relevant shadow prices showed that increasing fund-

ing would lead to greater HIV prevention but at a diminishing rate.

In contrast to the optimal plan, U.S. prevention policy at the time allocated

funds to different programs, regions, and targeted populations roughly in pro-

portion to reported AIDS cases and prevented only an estimated 3,000 infec-

tions. (Although spending more dollars where there are more AIDS cases

probably makes sense for treatment, it is not the best plan for maximum pre-

vention. Proportional allocation also embodied a perverse incentive: The allo-

cation tended to target additional funds to programs reporting the most AIDS

cases rather than to health programs that successfully prevented or reduced

cases.) Overall, the most cost-effective prevention programs (derived with the

LP approach) were able to increase prevention by some 30 percent compared

to current programs of the time. Kaplan also noted that if the allocation

included funds for needle-exchange programs (at the time, federal law pro-

hibited funding for such programs), annual preventions would increase to

some 5,300. To sum up, Kaplan credited the resource allocation model with

organizing the tough thinking needed to combat AIDS.

FORMULATION AND COMPUTER SOLUTION

FOR LARGER LP PROBLEMS

Skill in recognizing, formulating, and solving linear programming problems

comes with practice. This section presents four decision problems that repre-

sent a cross section of important management applications of linear program-

ming. Once you are comfortable with these applications, the other decision

problems you encounter will begin to look familiar, and their formulation and

solution will be almost automatic. In addition, you will be able to formulate

larger-scale problems and then solve them using standard computer programs.

The final two problems display the kinds of LP solutions such programs pro-

vide, with emphasis on interpreting the computer output.

PRODUCTION FOR MAXIMUM OUTPUT A manufacturing firm can produce

a good using three different production methods, each requiring different

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