The application of mathematics and the scientific

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 11, 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 21, 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 23, 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 22, 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
hr 40 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 31, 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 32, July 98
8
Graphical solution of Giapetto Inc. Page 58 of
textbook