assignment smq
TRANSCRIPT
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1. Formulate a preemptive goal programming model for this situation.
Decision variables:
= amount that the company can bill on Partner for Job 1
= amount that the company can bill on Partner for Job 2
= amount that the company can bill on Partner for Job 3
= amount that the company can bill on Senior employee for Job 1 = amount that the company can bill on Senior employee for Job 2
= amount that the company can bill on Senior employee for Job 3
= amount that the company can bill on Junior employee for Job 2
= amount that the company can bill on Junior employee for Job 3
= the number of Partner should be hired
= the number of Senior employee should be hired
= the number of Junior employee should be hired
Goal constraints:
Goal 1: Monthly billing should exceed RM68,000
will minimize the underachievement variable
Goal 2: At most 1 partner should be hired
will minimize the overachievement variable
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Goal 3: At most 3 senior employees should be hired
will minimize the overachievement variable
Goal 4: At most 5 junior employees should be hired
will minimize the overachievement variable
Hard constraints:
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Therefore,
Minimize
Subject to:
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3. Solve Question 2 by using any LP package. (Example: LINDO, Spreadsheet)
We will rewrite the problem using , , , , , , and variables because it is easier
to type the problem in LINGO with that notation without getting confused with the + and signs.
Therefore the new problem is:
Min
subject to
To solve with LINGO, we must minimize one variable at a time in the objective function. So, we
will first minimize .
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We will write in LINGO the following problem:
Min
subject to
and press Solve.
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If Goal 1 is achieved, then . We will get the following printout:
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We will note the objective function is 0, and the values of
and .
To solve for the second goal, we add , to the constraints as follows and this time we are
minimizing
, the second variable in the objective function.
By putting , we are ensured that the first goal is met. By solving we will get a printout as
follows:
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If Goal 2 is achieved, then .
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We will note the objective function is 0, and the values of
and .
To solve for the third goal, we add , to the constraints as follows and this time we are
minimizing
, the third variable in the objective function.
By putting , we are ensured that the second goal is met. By solving we will get a printout
as follows:
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If Goal 3 is achieved, then .
We will note the objective function is 0, and the values of
and .
To solve for the fourth goal, we add , to the constraints as follows and this time we are
minimizing , the fourth variable in the objective function.
By putting , we are ensured that the third goal is met. By solving we will get a printout as
follows:
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If Goal 4 is achieved, then .
We will note the objective function is 0, and the values of
and .
The optimal solution is:
Therefore,
The number of employees should be hired by Halim&Lee
= 1 partner + 3 senior employees + 5 junior employees
= 9 employees