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Goal Programming Essay

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

...view middle of the document...

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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