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

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Different Representation of Linear System of Equations

Linear Equations: Augmented matrix:

Compact form: A x = b

A= x = b =

IE 416, Chap 2:1, July 98

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

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 anda 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

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

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 hr 40 Train $21 $9 $10 1 hr 1 hr no limit______________________________________________

no max 80 max 100 limit

X1 = number of soldiers / weekX2 = number of trains / week

IE 416, Chap 3:1, July 98

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

Graphical solution of Giapetto Inc.Page 58 of textbook