1. ماهي بحوث العمليات What is Operations Researches
الباب الأول CHAPTER 1
ماهي بحوث العمليات What is Operations Researches
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2. Making a search a bout the history and developing of
Assignment 1 :
Making a search a bout the history and developing of
“OPERATIONS RESEARCHES”
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3. النمذجة بالبرمجة الخطية MODELLING WITH LINEAR PROGRAMMING
الباب الثاني CHAPTER 2
النمذجة بالبرمجة الخطية MODELLING WITH LINEAR PROGRAMMING
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4. The LP model, as in any OR model has three pasic components: page 12
1- Decision variables that we seek to determine.
2- Objective (goal) that we need to optimize ( maximize or minimize).
3- Constrains that the solution must satisfy.
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5. Model page 14 Properties of the LP
1- Proportionality التناسبية
التجميع 2- Additivity.
التأكد التام 3- Certainly
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6. GRAPHICAL SOLUTION The graphical procedure includes two steps:
1- Determination of the feasible solution space.
Determination of the optimum solution from among all the bfeasible points in the solution space.
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7. The feasible solution space: page 17
The feasible solution space of the problem represents the area in the first quadrant in wich all the constrains are satisfied simultaneously. All points in or on the boundry of the area is feasible solution. All points outside this area are infeasible
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8. Corner point: page 18
An important characteristic of the optimum LP solution is that it is always associatedيتحقق with a corner point of the solution space ( where two lines intersect)نقطة تقاطع خطين
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9. Solution of a Mximization Model page 16 Example 2.2.1
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10. EXAMPLE
Determine the feasible solution space and the optimum solution of the following model.
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11. EXAMPLE Select the best answer:
The corner points of the following system
are :
A) (0,0) , (0,2), (2,0) and (2,2)
B) (0,0) , (0,2) and (2,0)
C ) (0,0) , (2,0) and (2,2)
D) (-2,0) , (2,0) and (2,2)
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12. Solution of a Minimization Model page 23 Example 2.2.2
( Diet Problem) Ozark Farms uses at least 800 Ib of special feed. the
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13. Assignment 2 :
Determine the feasible solution space and the optimum solution of the following model
Max Z
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14. Assignment 2 :
Determine the feasible solution space and the optimum solution of the following model
Min Z
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