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Goal Programming

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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...

hard

constraints

are

too

 You have a maximum price in mind when buying a car

(this is your “goal” or target price).  If you can’t buy the car for this price you’ll likely find a way to spend more.
 We use soft constraints to represent such goals

or targets we’d like to achieve.

A Goal Programming Example: Myrtle Beach Hotel Expansion
 Davis McKeown wants to expand the convention

center at his hotel in Myrtle Beach, SC.  The types of conference rooms being considered are:
Size (sq ft) Unit Cost

Small
Medium Large


400
750 1,050

$18,000
$33,000 $45,150



Davis would like to add 5 small, 10 medium and 15 large conference rooms. He also wants the total expansion to be 25,000 square feet and to limit the cost to $1,000,000.

Defining the Decision Variables
X1 = number of small rooms to add

X2 = number of medium rooms to add
X3 = number of large rooms to add

Defining the Goals
 Goal 1: The expansion should include approximately 5  Goal  Goal

 Goal
 Goal

small conference rooms. 2: The expansion should include approximately 10 medium conference rooms. 3: The expansion should include approximately 15 large conference rooms. 4:

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