Transcript Types of IP Models - Loyola Marymount University

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

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)
Stock Data
Price/Share
Estimated
Annual Return
AGA Products
$50
6%
Key Oil
$100
10%
Satisficing Solutions

Instead of optimizing the model to
determine the best solution for one
objective, the model is satisficed:
several objectives are simultaneously
maximized to obtain minimal satisfactory
levels.
GP Constraint Types

System or hard constraints:
Constraints for which no flexibility in standards or
basic requirements exist (e.g. capital available,
limited capacity)

Goal or soft constraints:
• Constraints for which targets or goals at various
levels would be acceptable (e.g. required return
or acceptable risk)
Deviation Variables
Di+ = amount by which goal i exceeds
specified target value
 Di- = amount by which goal i falls short
of specified target value
 Goal Constraints have format:

Actual value - Di+ + Di- = Target Value
Solution Techniques

Absolute Priorities: Goals are ranked in
priority. Several models are solved, requiring
one goal be satisfied at a time, in the order of
its importance.
 Weighted Variables: Preferences for
deviations from goals are expressed by
specifying a weight for the respective
deviation variable and including this weighted
variable in the objective function that is to be
minimized. The model is run just once.
GP Objective Functions

Minimize sum of relevant deviations
– Problem with different units ($ -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 wi for each percentage deviation and use
iterative procedure to refine weights
Summary of Goal Programming
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Identify the decision variables
Identify hard constraints
State goals along with their target values
Create constraints using the decision variables that
would achieve the goals exactly
Transform soft constraints into goal constraints by
including deviational variables
Determine which deviational variables are undesirable
Formulate an objective that penalizes undesirable
deviations
Identify appropriate weights for objective
Optimize the problem
Inspect the solution, not the objective! If
unacceptable, return to step 8.