1181 words - 5 pages

Goal Programming

By

Dr. Mojgan Afshari

Goal Programming (GP)

Goal programming involves solving problems

containing not one specific objective function, but rather a collection of goals that we would like to achieve. Firms usually have more than one goal. For example, maximizing total profit, maximizing market share, maintaining full employment, providing quality ecological management It is not possible for LP to have multiple goals

Goal Programming (GP)

Most LP problems have hard constraints that

cannot be violated...

There are 1,566 labor hours available. There is $850,00 available for projects.

In

some cases, restrictive ...view middle of the document...

hard

5: The expansion should cost approximately $1,000,000.

Defining the Goal Constraints

Small Rooms

X1 d d 5

1

1

Medium Rooms

X 2 d d 10

2

2

Large Rooms

X 3 d d 15

3

3

Defining the Goal Constraints

Total Expansion

400X1 750X 2 1,050X 3 d d 25,000

Total Cost

4

4

18000X1 33000X 2 45.150X 3 d d 1,000,000

where

5

5

d ,d 0

i

i

GP Objective Functions

There are numerous objective functions we

could formulate for a GP problem. Minimize the sum of the deviations:

MIN

•

d

i

i

d i

Problem: The deviations measure different things, so what does this objective represent?

GP Objective Functions (cont’d)

Weights can be used in the previous objectives to allow the decision maker indicate desirable vs. undesirable deviations the relative importance of various goals

Minimize the weighted sum of deviations wi d i wi d i MIN

i

Or Minimize the weighted sum of % deviations

MIN

1 wi d i wi d i t i i

Defining the Objective

Assume It is undesirable to underachieve any of the first

three room goals It is undesirable to overachieve or underachieve the 25,000 sq ft expansion goal It is undesirable to overachieve the $1,000,000 total cost goal In this case , we want to minimize the weighted percentage deviation for our problem

w5 w1 w w 3 w w 4 4 MIN : d1 2 d 2 d3 d d d5 4 4 5 10 15 25,000 25,000 1,000,000

Initially, we will assume all the above weights equal 1 and all other weights are 0.

Implementing the Model

w5 w1 w w 3 w w 4 4 MIN : d1 2 d 2 d3 d4 d4 d5 5 10 15 25,000 25,000 1,000,000

Subject to:

X1 d d 5

X 2 d d 10

2 2

1

1

Small Rooms Medium Rooms Large Rooms

4 4

X 3 d d 15

3

3

400X1 750X 2 1,050X 3 d d 25,000

18000X1 33000X 2 45.150X 3 d 5 d 5 1,000,000

d ,d 0

i

i

Xi ≥ 0 Xi must be integers

Solving the Model

14

Comments About GP

GP involves making trade-offs among the various

goals until the most satisfying solution is found.

GP

objective function values should not be compared because the weights are changed in each iteration. Compare the solutions! soft constraint to a hard constraint.

An arbitrarily large weight will effectively change a

Hard constraints can be place on deviational

variables.

...

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