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The application of mathematics and the scientific

The application of mathematics and the scientific method to military operations was called operations research. Today, the term operations research (or, often, management science) means a scientific approach to decision making, .… under conditions

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The application of mathematics and the scientific

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  1. The application of mathematics and the scientific method to military operations was called operations research. Today, the term operations research (or, often, management science) means a scientific approach to decision making, .… under conditions requiring the allocation of scarce resources. IE 416, Chap 1:1, July 98

  2. Different Representation of Linear System of Equations Linear Equations: Augmented matrix: Compact form: A x = b x = b = A= IE 416, Chap 2:1, July 98

  3. Page 20: Gauss-Jordan Method: Elementary Row Operation, ero Type 1 ero: (Row i)' = C (Row i) Type 2 ero: (Row i)' = C (Row j) + (Row i) Type 3 ero: (Row i)' = (Row j) (Row j)' = (Row i) IE 416, Chap 2:3, July 98

  4. Page 18: A solution to a linear system of m equations in n unknowns is a set of values for the unknowns that satisfies each of the system's m equations. For any linear system, a variable that appears with a coefficient of 1 in a single equation and a coefficient of 0 in all other equations is called a basic variable (BV). Any variable that is not a basic variable is called a nonbasic variable (NBV). IE 416, Chap 2:2, July 98

  5. Linear Programming Terms(Chap. 3) * Summarize the problem as a matrix * Formulate the problem: decision variable, objective function (OF), OF coefficient, constraint (ST), technological coefficient, right hand side (RHS), sign restriction, unrestricted in sign (URS), assumptions (divisibility, certainty, … ) * Solve the problem: feasible region (based on constraints, bounded, unbounded, no f.r.), graphical solution, iso-profit (cost) line, optimal solution (extreme point, no solution, one solution, multi- solution), binding constraint, nonbinding constraint, infeasible LP, unbounded LP IE 416, Chap 3, May 99

  6. Summary of Giapetto Inc. (Page 49) Toy Sell Costs Hours of labor/toy Demand price Raw Labor Carpenter Finish per week ______________________________________________ Soldier $27 $10 $14 1 hr 2 hr40 Train $21 $9 $10 1 hr 1 hr no limit ______________________________________________ no max 80 max 100 limit X1 = number of soldiers / week X2 = number of trains / week IE 416, Chap 3:1, July 98

  7. Formulation of Giapetto Problem: O.F. Max Z = 3 X1 + 2 X2 S.T. 2X1 + X2 100 Finish X1 + X2 80 Carpenter X1  40 Soldier X1 , X2 0 Sign IE 416, Chap 3:2, July 98

  8. Graphical solution of Giapetto Inc. Page 58 of textbook

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