| approx.mos |
(!******************************************************
Mosel Example Problems
======================
file approx.mos
```````````````
Function approximation with SOS2
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Sep. 2006
*******************************************************!)
model "Approximation"
uses "mmxprs"
declarations
NB = 5
BREAKS = 1..NB
R,F: array(BREAKS) of real ! Coordinates of break points
x,f: mpvar ! Decision variables
y: array(BREAKS) of mpvar ! Weight variables
end-declarations
R:: [1, 2.2, 3.4, 4.8, 6.5]
F:: [2, 3.2, 1.4, 2.5, 0.8]
RefRow:= sum(i in BREAKS) R(i)*y(i)
x = RefRow
f = sum(i in BREAKS) F(i)*y(i)
! Convexity constraint
sum(i in BREAKS) y(i) = 1
! SOS2 definition
RefRow is_sos2
! Alternative SOS definition (to be used for 0-valued RefRow coefficients):
! makesos2(union(i in BREAKS) {y(i)}, RefRow)
(! Alternative formulation using binaries instead of SOS2:
declarations
b: array(1..NB-1) of mpvar
end-declarations
sum(i in 1..NB-1) b(i) = 1
forall(i in 1..NB-1) b(i) is_binary
forall(i in BREAKS) y(i) <= if(i>1, b(i-1), 0) + if(i<NB, b(i), 0)
!)
! Bounds
1<=x; x<=6.5
! Solve the problem
minimize(f)
writeln("Objective value: ", getobjval)
writeln("x: ", getsol(x))
end-model
|
|
| approx.mos |
(!******************************************************
Mosel Example Problems
======================
file approx.mos
```````````````
Function approximation with SOS2
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Sep. 2006
*******************************************************!)
model "Approximation"
uses "mmxprs"
declarations
NB = 5
BREAKS = 1..NB
R,F: array(BREAKS) of real ! Coordinates of break points
x,f: mpvar ! Decision variables
y: array(BREAKS) of mpvar ! Weight variables
end-declarations
R:: [1, 2.2, 3.4, 4.8, 6.5]
F:: [2, 3.2, 1.4, 2.5, 0.8]
RefRow:= sum(i in BREAKS) R(i)*y(i)
x = RefRow
f = sum(i in BREAKS) F(i)*y(i)
! Convexity constraint
sum(i in BREAKS) y(i) = 1
! SOS2 definition
RefRow is_sos2
! Alternative SOS definition (to be used for 0-valued RefRow coefficients):
! makesos2(union(i in BREAKS) {y(i)}, RefRow)
(! Alternative formulation using binaries instead of SOS2:
declarations
b: array(1..NB-1) of mpvar
end-declarations
sum(i in 1..NB-1) b(i) = 1
forall(i in 1..NB-1) b(i) is_binary
forall(i in BREAKS) y(i) <= if(i>1, b(i-1), 0) + if(i<NB, b(i), 0)
!)
! Bounds
1<=x; x<=6.5
! Solve the problem
minimize(f)
writeln("Objective value: ", getobjval)
writeln("x: ", getsol(x))
end-model
|
|
| burglar1.mos |
(!******************************************************
Mosel Example Problems
======================
file burglar1.mos
`````````````````
Knapsack problem
(c) 2008 Fair Isaac Corporation
author: R.C. Daniel, Jul. 2002
*******************************************************!)
model "Burglar 1"
uses "mmxprs"
declarations
ITEMS = 1..8 ! Index range for items
WTMAX = 102 ! Maximum weight allowed
VALUE: array(ITEMS) of real ! Value of items
WEIGHT: array(ITEMS) of real ! Weight of items
take: array(ITEMS) of mpvar ! 1 if we take item i; 0 otherwise
end-declarations
! Item: 1 2 3 4 5 6 7 8
VALUE :: [15, 100, 90, 60, 40, 15, 10, 1]
WEIGHT:: [ 2, 20, 20, 30, 40, 30, 60, 10]
! Objective: maximize total value
MaxVal:= sum(i in ITEMS) VALUE(i)*take(i)
! Weight restriction
sum(i in ITEMS) WEIGHT(i)*take(i) <= WTMAX
! All variables are 0/1
forall(i in ITEMS) take(i) is_binary
maximize(MaxVal) ! Solve the MIP-problem
! Print out the solution
writeln("Solution:\n Objective: ", getobjval)
forall(i in ITEMS) writeln(" take(", i, "): ", getsol(take(i)))
end-model
|
|
| burglar2.mos |
(!******************************************************
Mosel Example Problems
======================
file burglar2.mos
`````````````````
Knapsack problem
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Aug. 2002
*******************************************************!)
model "Burglar 2"
uses "mmxprs"
declarations
ITEMS: set of string ! Set of items
WTMAX = 102 ! Maximum weight allowed
VALUE: array(ITEMS) of real ! Value of items
WEIGHT: array(ITEMS) of real ! Weight of items
end-declarations
initializations from 'burglar.dat'
VALUE
WEIGHT
end-initializations
(! alternatively:
initializations from 'burglar2.dat'
[VALUE, WEIGHT] as 'KNAPSACK'
end-initializations
!)
declarations
take: array(ITEMS) of mpvar ! 1 if we take item i; 0 otherwise
end-declarations
! Objective: maximize total value
MaxVal:= sum(i in ITEMS) VALUE(i)*take(i)
! Weight restriction
sum(i in ITEMS) WEIGHT(i)*take(i) <= WTMAX
! All variables are 0/1
forall(i in ITEMS) take(i) is_binary
maximize(MaxVal) ! Solve the MIP-problem
! Print out the solution
writeln("Solution:\n Objective: ", getobjval)
forall(i in ITEMS) writeln(" take(", i, "): ", getsol(take(i)))
end-model
|
|
| burglari.mos |
(!******************************************************
Mosel Example Problems
======================
file burglari.mos
`````````````````
Knapsack problem
-- Using string indices --
(c) 2008 Fair Isaac Corporation
author: R.C. Daniel, Jul. 2002
*******************************************************!)
model "Burglar 1 (index set)"
uses "mmxprs"
declarations
ITEMS = {"camera", "necklace", "vase", "picture", "tv", "video",
"chest", "brick"} ! Set for items
WTMAX = 102 ! Maximum weight allowed
VALUE: array(ITEMS) of real ! Value of items
WEIGHT: array(ITEMS) of real ! Weight of items
take: array(ITEMS) of mpvar ! 1 if we take item i; 0 otherwise
end-declarations
VALUE("camera") := 15; WEIGHT("camera") := 2
VALUE("necklace"):=100; WEIGHT("necklace"):= 20
VALUE("vase") := 90; WEIGHT("vase") := 20
VALUE("picture") := 60; WEIGHT("picture") := 30
VALUE("tv") := 40; WEIGHT("tv") := 40
VALUE("video") := 15; WEIGHT("video") := 30
VALUE("chest") := 10; WEIGHT("chest") := 60
VALUE("brick") := 1; WEIGHT("brick") := 10
(! Alternative data initialization:
VALUE :: (["camera", "necklace", "vase", "picture", "tv", "video",
"chest", "brick"])[15, 100, 90, 60, 40, 15, 10, 1]
WEIGHT:: (["camera", "necklace", "vase", "picture", "tv", "video",
"chest", "brick"])[ 2, 20, 20, 30, 40, 30, 60, 10]
!)
! Objective: maximize total value
MaxVal:= sum(i in ITEMS) VALUE(i)*take(i)
! Weight restriction
sum(i in ITEMS) WEIGHT(i)*take(i) <= WTMAX
! All variables are 0/1
forall(i in ITEMS) take(i) is_binary
maximize(MaxVal) ! Solve the MIP-problem
! Print out the solution
writeln("Solution:\n Objective: ", getobjval)
forall(i in ITEMS) writeln(" take(", i, "): ", getsol(take(i)))
end-model
|
|
| burglar_rec.mos |
(!******************************************************
Mosel Example Problems
======================
file burglar_rec.mos
````````````````````
Use of records.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, July 2006
*******************************************************!)
model "Burglar (records)"
uses "mmxprs"
declarations
WTMAX = 102 ! Maximum weight allowed
ITEMS = {"camera", "necklace", "vase", "picture", "tv", "video",
"chest", "brick"} ! Index set for items
I: array(ITEMS) of record
VALUE: real ! Value of items
WEIGHT: real ! Weight of items
end-record
take: array(ITEMS) of mpvar ! 1 if we take item i; 0 otherwise
end-declarations
initializations from 'burglar_rec.dat'
I
end-initializations
! Objective: maximize total value
MaxVal:= sum(i in ITEMS) I(i).VALUE*take(i)
! Weight restriction
sum(i in ITEMS) I(i).WEIGHT*take(i) <= WTMAX
! All variables are 0/1
forall(i in ITEMS) take(i) is_binary
maximize(MaxVal) ! Solve the MIP-problem
! Print out the solution
writeln("Solution:\n Objective: ", getobjval)
forall(i in ITEMS) writeln(" take(", i, "): ", getsol(take(i)))
end-model
|
|
| chess.mos |
(!******************************************************
Mosel Example Problems
======================
file chess.mos
``````````````
Production of chess boards
(c) 2008 Fair Isaac Corporation
author: R.C. Daniel, Jul. 2002
*******************************************************!)
model Chess
uses "mmxprs"
declarations
xs, xl: mpvar ! Decision variables: produced quantities
end-declarations
Profit:= 5*xs + 20*xl ! Objective function
Boxwood:= 1*xs + 3*xl <= 200 ! kg of boxwood
Lathe:= 3*xs + 2*xl <= 160 ! Lathehours
maximize(Profit) ! Solve the problem
writeln("LP Solution:") ! Solution printing
writeln(" Objective: ", getobjval)
writeln("Make ", getsol(xs), " small sets")
writeln("Make ", getsol(xl), " large sets")
end-model
|
|
| chess2.mos |
(!******************************************************
Mosel Example Problems
======================
file chess2.mos
```````````````
Production of chess boards
(c) 2008 Fair Isaac Corporation
author: R.C. Daniel, Jul. 2002
*******************************************************!)
model "Chess 2"
uses "mmxprs"
declarations
xs, xl: mpvar ! Decision variables: produced quantities
end-declarations
Profit:= 5*xs + 20*xl ! Objective function
Boxwood:= 1*xs + 3*xl <= 200 ! kg of boxwood
Lathe:= 3*xs + 2*xl <= 160 ! Lathehours
maximize(Profit) ! Solve the problem
writeln("LP Solution:") ! Solution printing
writeln(" Objective: ", getobjval)
writeln("Make ", getsol(xs), " small sets")
writeln("Make ", getsol(xl), " large sets")
writeln("Activities/Dual Values")
writeln(" Lathe: ", getact(Lathe)," / ", getdual(Lathe))
writeln(" Boxwood: ", getact(Boxwood)," / ", getdual(Boxwood))
writeln("Reduced Costs")
writeln(" xs: ", getrcost(xs))
writeln(" xl: ", getrcost(xl))
end-model
|
|
| pricebrai.mos |
(!******************************************************
Mosel Example Problems
======================
file pricebrai.mos
``````````````````
Modeling price breaks:
All item discount pricing
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Sep. 2006
*******************************************************!)
model "All item discount"
uses "mmxprs"
declarations
NB = 3 ! Number of price bands
BREAKS = 1..NB
COST: array(BREAKS) of real ! Cost per unit
x: array(BREAKS) of mpvar ! Number of items bought at a price
b: array(BREAKS) of mpvar ! Indicators of price bands
B: array(0..NB) of real ! Break points of cost function
end-declarations
DEM:= 150 ! Demand
B:: [0, 50, 120, 200]
COST:: [ 1, 0.7, 0.5]
forall(i in BREAKS) b(i) is_binary
(! Alternatively
sum(i in BREAKS) B(i)*b(i) is_sos1
!)
! Objective: total price
TotalCost:= sum(i in BREAKS) COST(i)*x(i)
! Meet the demand
sum(i in BREAKS) x(i) = DEM
! Lower and upper bounds on quantities
forall(i in BREAKS) do
B(i-1)*b(i) <= x(i); x(i) <= B(i)*b(i)
end-do
! The quantity bought lies in exactly one interval
sum(i in BREAKS) b(i) = 1
! Solve the problem
minimize(TotalCost)
! Solution printing
writeln("Objective: ", getobjval,
" (price per unit: ", getobjval/DEM, ")")
forall(i in BREAKS)
writeln("x(", i, "): ", getsol(x(i)), " (price per unit: ", COST(i), ")")
end-model
|
|
| pricebrinc.mos |
(!******************************************************
Mosel Example Problems
======================
file pricebrinc.mos
```````````````````
Incremental pricebreaks formulated with SOS2
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Sep. 2006
*******************************************************!)
model "Incremental pricebreaks (SOS2)"
uses "mmxprs"
declarations
NB = 3 ! Number of price bands
BREAKS = 0..NB
COST: array(1..NB) of real ! Cost per unit within price bands
w: array(BREAKS) of mpvar ! Weight variables
x: mpvar ! Total quantity bought
B,CBP: array(BREAKS) of real ! Break points, cost break points
end-declarations
DEM:= 150 ! Demand
B:: [0, 50, 120, 200]
COST:: [0.8, 0.5, 0.3]
CBP(0):= 0
forall(i in 1..NB) CBP(i):= CBP(i-1) + COST(i) * (B(i)-B(i-1))
! Objective: total price
TotalCost:= sum(i in BREAKS) CBP(i)*w(i)
! Meet the demand
x = DEM
! Definition of x
Defx:= x = sum(i in BREAKS) B(i)*w(i)
! Weights sum up to 1
sum(i in BREAKS) w(i) = 1
! Definition of SOS2
! (we cannot use 'is_sos2' since there is a 0-valued coefficient)
makesos2(union(i in BREAKS) {w(i)}, Defx)
! Solve the problem
minimize(TotalCost)
! Solution printing
writeln("Objective: ", getobjval,
" (price per unit: ", getobjval/DEM, ")")
forall(i in BREAKS)
writeln("w(", i, "): ", getsol(w(i)), " (price per unit: ",
if(i>0, CBP(i)/B(i), CBP(i)), ")")
end-model
|
|
| pricebrinc2.mos |
(!******************************************************
Mosel Example Problems
======================
file pricebrinc2.mos
````````````````````
Incremental pricebreaks formulated with
binary variables
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Sep. 2006
*******************************************************!)
model "Incremental pricebreaks (binaries)"
uses "mmxprs"
declarations
NB = 3 ! Number of price bands
BREAKS = 1..NB
COST: array(BREAKS) of real ! Cost per unit
x: array(BREAKS) of mpvar ! Number of items bought at a price
b: array(BREAKS) of mpvar ! Indicators of price bands
B: array(0..NB) of real ! Break points of cost function
end-declarations
DEM:= 150 ! Demand
B:: [0, 50, 120, 200]
COST:: [0.8, 0.5, 0.3]
forall(i in BREAKS) b(i) is_binary
! Objective: total price
TotalCost:= sum(i in BREAKS) COST(i)*x(i)
! Meet the demand
sum(i in BREAKS) x(i) = DEM
! Lower and upper bounds on quantities
forall(i in 1..NB-1) (B(i)-B(i-1)) * b(i+1) <= x(i)
forall(i in BREAKS) x(i) <= (B(i)-B(i-1)) * b(i)
! Sequence of price intervals
forall(i in 1..NB-1) b(i) >= b(i+1)
! Solve the problem
minimize(TotalCost)
! Solution printing
writeln("Objective: ", getobjval,
" (price per unit: ", getobjval/DEM, ")")
forall(i in BREAKS)
writeln("x(", i, "): ", getsol(x(i)), " (price per unit: ", COST(i), ")")
end-model
|
|
