1. Goal Programming Linear program has multiple objectives, often conflicting in nature Target values or goals can be set for each objective identified Not all goals can be simultaneously obtained, resulting in a problem that would otherwise be considered infeasible

2. Investment Portfolio Example An investment service company has $50,000 to use in developing a portfolio for a client that is restricted to 2 stocks shown on next slide The company has two goals –Obtain at least 9% return –Limit investment in Key Oil to at most 60% of the total investment ($30,000)

3. Stock Data Price/ShareEstimated Annual Return AGA Products$506% Key Oil$10010%

4. Satisficing Solutions Instead of optimizing the model to determine the best solution for one objective, the model is satisficed: several objectives are simultaneously maximized to obtain minimal satisfactory levels.

5. GP Constraint Types System or hard constraints: Constraints for which no flexibility in standards or basic requirements exist (e.g. capital available, limited capacity) Goal or soft constraints: Constraints for which targets or goals at various levels would be acceptable (e.g. required return or acceptable risk)

6. Deviation Variables D i + = amount by which goal i exceeds specified target value D i - = amount by which goal i falls short of specified target value Goal Constraints have format: Actual value - D i + + D i - = Target Value

7. Solution Techniques Absolute Priorities: Goals are ranked in priority. Several models are solved, requiring one goal be satisfied at a time, in the order of its importance. Weighted Variables: Preferences for deviations from goals are expressed by specifying a weight for the respective deviation variable and including this weighted variable in the objective function that is to be minimized. The model is run just once.

8. GP Objective Functions Minimize sum of relevant deviations –Problem with different units ($ -vs- pounds) –Implicit trade-offs between goals hard to assess Minimize sum of percentage deviations –(1/target)*deviation=percent deviation –Won’t work when target is 0 –Implicit trade-offs between goals hard to assess Minimize sum of weighted percentage deviations –Pick w i for each percentage deviation and use iterative procedure to refine weights

9. Summary of Goal Programming 1. Identify the decision variables 2. Identify hard constraints 3. State goals along with their target values 4. Create constraints using the decision variables that would achieve the goals exactly 5. Transform soft constraints into goal constraints by including deviational variables 6. Determine which deviational variables are undesirable 7. Formulate an objective that penalizes undesirable deviations 8. Identify appropriate weights for objective 9. Optimize the problem 10. Inspect the solution, not the objective! If unacceptable, return to step 8.