ماهي بحوث العمليات What is Operations Researches الباب الأول CHAPTER 1 ماهي بحوث العمليات What is Operations Researches د. فاتن مؤمن

Making a search a bout the history and developing of Assignment 1 : Making a search a bout the history and developing of “OPERATIONS RESEARCHES” د. فاتن مؤمن

النمذجة بالبرمجة الخطية MODELLING WITH LINEAR PROGRAMMING الباب الثاني CHAPTER 2 النمذجة بالبرمجة الخطية MODELLING WITH LINEAR PROGRAMMING د. فاتن مؤمن

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. د. زكية الصيعري

Model page 14 Properties of the LP 1- Proportionality التناسبية التجميع 2- Additivity. التأكد التام 3- Certainly د. زكية الصيعري

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. د. فاتن مؤمن

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 د.زكية الصيعري

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 د. زكية الصيعري

Solution of a Mximization Model page 16 Example 2.2.1 د. زكية الصيعري

EXAMPLE Determine the feasible solution space and the optimum solution of the following model. د. زكية الصيعري

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) د. زكية الصيعري

Solution of a Minimization Model page 23 Example 2.2.2 ( Diet Problem) Ozark Farms uses at least 800 Ib of special feed. the د. زكية الصيعري

Assignment 2 : Determine the feasible solution space and the optimum solution of the following model Max Z د. زكية الصيعري

Assignment 2 : Determine the feasible solution space and the optimum solution of the following model Min Z د. زكية الصيعري