Samenvatting Operations Research
Linear programming
Ho : Introduction
*
types of modus :
·
physical/iconic models :
easy to comprehend
analog model harder to comprehend
·
:
·
symbolic mods hardest to comprehend :
* moder building proces :
1 formulation of model-data
2 solutiondvelopment validation
3 result interpretation - sensitivity andlysis
H1
Modelling
:
*
terminology :
·
teasible solution : satisfies all the constraints
optimal solution : teasible solution with longest objective A. value
·
1 1 :
.
Formulation
* Stopperplan :
Step 1 : Define decision variables X =
. . .
i X =...
Step 2 :
Formulate objectiveAunction Max Min CM1 + C2 X2 +... -
Step 3 : Formulate constraints an X1 + &e-X2 +... & be
& 2 X2.
+ &e2X2 +.. -
X b2
Step 4 : Formulate
Sign restrictions X-30 ; Xa40 0 ,
1
,*
assumptions< limitations of LP
·
certainty : all parameters o t m are known constants
Linearity the objective functions constraints are linear functions
·
: -
Proportionality the contribution of each activity to the value of
·
:
Objective A. is proportional to the level of activity X
;
Additivity every function is the sum oft contributions of all dec
·
: . Var.
Divisibility dec have tractional values
Val can
moninteger
·
: .
.
1
. 2 :
Graphic solution method
Im for LDs with 2 or 3 variables
Stapperplen
↓2 1d
* : 20
Step 1 : Determine functional region GD
↓ a Draw constraints 2 1D
N
In 3 Determine set of points that
satisfies requirements
&
all
Step 2 :
Determine optimal solution
on a Draw Objective function line X
3
on Move Objective function line
an c stop moving optimal solution
*
types of teasible regions :
non-existent simple point line
polygon unbounded
-
bounded
* optimal solutions are
always corne points =
extreme points
2
, H2 : The simplex method
.
2 1 : The principles
*
terminology :
live that toms boundary
constraint
boundly :
! Always= never or
·
,
cornce-point feasible cof solution point on corner of tensible
region
· =
:
solacent solution CP' cojacent it caste, bound
op I are
they share n-1
·
:
* stappeplen :
Iteration 0 : Initialization
↓ start in
origin
Iteration 1 : Current (X -, ...,
Xn) =
(0 , . . .
.
d)
Step ptimality test
·
1 :
it has
CPFS
agacent CPFS' that are better optimal
*
a no in
·
Step 2 : Determine entering variable
i move to cojacent CPFS
in choose variable with
highest rate of improvement (
Determine
Step 3 :
leaving variable
·
Iminimal reltio test : RHS
cott of .
entering var.
·
Step 4 : Rewrite equations in canonical torm
*
using elementary row operations
*
pivot row :
equation with leaving variable
Iteration 2 : Same as 1 ,
until solution is optimal
3
Linear programming
Ho : Introduction
*
types of modus :
·
physical/iconic models :
easy to comprehend
analog model harder to comprehend
·
:
·
symbolic mods hardest to comprehend :
* moder building proces :
1 formulation of model-data
2 solutiondvelopment validation
3 result interpretation - sensitivity andlysis
H1
Modelling
:
*
terminology :
·
teasible solution : satisfies all the constraints
optimal solution : teasible solution with longest objective A. value
·
1 1 :
.
Formulation
* Stopperplan :
Step 1 : Define decision variables X =
. . .
i X =...
Step 2 :
Formulate objectiveAunction Max Min CM1 + C2 X2 +... -
Step 3 : Formulate constraints an X1 + &e-X2 +... & be
& 2 X2.
+ &e2X2 +.. -
X b2
Step 4 : Formulate
Sign restrictions X-30 ; Xa40 0 ,
1
,*
assumptions< limitations of LP
·
certainty : all parameters o t m are known constants
Linearity the objective functions constraints are linear functions
·
: -
Proportionality the contribution of each activity to the value of
·
:
Objective A. is proportional to the level of activity X
;
Additivity every function is the sum oft contributions of all dec
·
: . Var.
Divisibility dec have tractional values
Val can
moninteger
·
: .
.
1
. 2 :
Graphic solution method
Im for LDs with 2 or 3 variables
Stapperplen
↓2 1d
* : 20
Step 1 : Determine functional region GD
↓ a Draw constraints 2 1D
N
In 3 Determine set of points that
satisfies requirements
&
all
Step 2 :
Determine optimal solution
on a Draw Objective function line X
3
on Move Objective function line
an c stop moving optimal solution
*
types of teasible regions :
non-existent simple point line
polygon unbounded
-
bounded
* optimal solutions are
always corne points =
extreme points
2
, H2 : The simplex method
.
2 1 : The principles
*
terminology :
live that toms boundary
constraint
boundly :
! Always= never or
·
,
cornce-point feasible cof solution point on corner of tensible
region
· =
:
solacent solution CP' cojacent it caste, bound
op I are
they share n-1
·
:
* stappeplen :
Iteration 0 : Initialization
↓ start in
origin
Iteration 1 : Current (X -, ...,
Xn) =
(0 , . . .
.
d)
Step ptimality test
·
1 :
it has
CPFS
agacent CPFS' that are better optimal
*
a no in
·
Step 2 : Determine entering variable
i move to cojacent CPFS
in choose variable with
highest rate of improvement (
Determine
Step 3 :
leaving variable
·
Iminimal reltio test : RHS
cott of .
entering var.
·
Step 4 : Rewrite equations in canonical torm
*
using elementary row operations
*
pivot row :
equation with leaving variable
Iteration 2 : Same as 1 ,
until solution is optimal
3
