14 HAL computer must determine which of seven research and development (R&D;) pr

Question

14 HAL computer must determine which of seven research and development (R&D;) projects to undertake. For each project four quantities are of interest: 40 90 18 19 .60 .65 200 440 a the net present value (NPV in millions of dollars) of the project b the annual growth rate in sales generated by the Goal 3 The average growth rate of all projects chosen project c the probability that the project will succeed d the cost (in millions of dollars) of the project The relevant information is given in Table 69. HAL has For the following sets of priorities, use preemptive (integer) should be at least 15%. Goal 4 The total cost of all chosen projects should be at most $1 billion set the following four goals: goal programming to determine which projects should be selected. Goal 1 The total NPV of all chosen projects should be at least $200 million. Priority Set 1 24>>3 Goal 2 The average probability of success for all projects Priority Set 2 34>>>2 chosen should be at least.75

Explanation / Answer

Steps to solve the preemptive goal problem

The priority is 2>4>1>3

The goals in the order of importance are:

2>4>1>3

Start with the objective of achieving the first goal (or coming as close as

possible):

– Minimize (Under Goal 2)

•

Then, if for example goal 1 is achieved (i.e., Under Goal 1 = 0), then

– Minimize (Under Goal 4)

subject to

(Under Goal 1) = 0

1. Introduce new changing cells, Amount Over and Amount Under, that will measure how much the current solution is over or under each goal.

•The Amount Over and Amount Under changing cells are forced to maintain the correct value with the following constraints:

Level Achieved – Amount Over + Amount Under = Goal

•Start with the objective of achieving the first goal (or coming as close as possible):

– Minimize

(Probablity/Under Goal 2)

• Continue with the next goal, but constrain the previous goals to not get any worse:

– Minimize (cost/Under Goal 4)

subject to

NPA/Under Goal 1 = (amount achieved in previous step)

• Repeat the previous step for all succeeding goals.

Project NPV AGR Probalbity Cost 1 40 20 0.75 220 2 30 16 0.7 140 3 60 12 0.75 280 4 45 8 0.9 240 5 55 18 0.65 300 6 40 18 0.6 200 7 90 19 0.65 440

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