| a1alloy.mos |
(!******************************************************
Mosel Example Problems
======================
file a1alloy.mos
````````````````
Production of alloys
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002
*******************************************************!)
model "A-1 Production of Alloys"
uses "mmxprs"
declarations
COMP = 1..3 ! Components (chemical elements)
RAW = 1..7 ! Raw materials (alloys)
P: array(RAW,COMP) of real ! Composition of raw materials (in percent)
PMIN,PMAX: array(COMP) of real ! Min. & max. requirements for components
AVAIL: array(RAW) of real ! Raw material availabilities
COST: array(RAW) of real ! Raw material costs per tonne
DEM: real ! Amount of steel to produce
use: array(RAW) of mpvar ! Quantity of raw mat. used
produce: mpvar ! Quantity of steel produced
end-declarations
initializations from 'a1alloy.dat'
P PMIN PMAX AVAIL COST DEM
end-initializations
! Objective function
Cost:= sum(r in RAW) COST(r)*use(r)
! Quantity of steel produced = sum of raw material used
produce = sum(r in RAW) use(r)
! Guarantee min. and max. percentages of every chemical element
forall(c in COMP) do
sum(r in RAW) P(r,c)*use(r) >= PMIN(c)*produce
sum(r in RAW) P(r,c)*use(r) <= PMAX(c)*produce
end-do
! Use raw materials within their limit of availability
forall(r in RAW) use(r) <= AVAIL(r)
! Satisfy the demand
produce >= DEM
! Solve the problem
minimize(Cost)
! Solution printing
declarations
NAMES: array(RAW) of string
end-declarations
initializations from 'a1alloy.dat' ! Get the names of the alloys
NAMES
end-initializations
writeln("Total cost: ", getobjval)
writeln("Amount of steel produced: ", getsol(produce))
writeln("Alloys used:")
forall(r in RAW)
if(getsol(use(r))>0) then
write(NAMES(r), ": ", getsol(use(r))," ")
end-if
write("\nPercentages (C, Cu, Mn): ")
forall(c in COMP)
write( getsol(sum(r in RAW) P(r,c)*use(r))/getsol(produce), "% ")
writeln
end-model
|
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| a2food.mos |
(!******************************************************
Mosel Example Problems
======================
file a2food.mos
```````````````
Food production for farm animals
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002
*******************************************************!)
model "A-2 Animal Food Production"
uses "mmxprs"
declarations
FOOD = 1..2 ! Food types
COMP = 1..3 ! Nutritional components
RAW = {"oat", "maize", "molasses"} ! Raw materials
P: array(RAW,COMP) of real ! Composition of raw materials (in percent)
REQ: array(COMP) of real ! Nutritional requirements
AVAIL: array(RAW) of real ! Raw material availabilities
COST: array(RAW) of real ! Raw material prices
PCOST: array(set of string) of real ! Cost of processing operations
DEM: array(FOOD) of real ! Demands for food types
use: array(RAW,FOOD) of mpvar ! Quantity of raw mat. used for a food type
produce: array(FOOD) of mpvar ! Quantity of food produced
end-declarations
initializations from 'a2food.dat'
P REQ PCOST DEM
[AVAIL, COST] as 'RAWMAT'
end-initializations
! Objective function
Cost:= sum(r in RAW,f in FOOD) COST(r)*use(r,f) +
sum(r in RAW,f in FOOD|r<>"molasses") PCOST("grinding")*use(r,f) +
sum(r in RAW,f in FOOD) PCOST("blending")*use(r,f) +
sum(r in RAW) PCOST("granulating")*use(r,1) +
sum(r in RAW) PCOST("sieving")*use(r,2)
! Quantity of food produced corresponds to raw material used
forall(f in FOOD) sum(r in RAW) use(r,f) = produce(f)
! Fulfill nutritional requirements
forall(f in FOOD,c in 1..2)
sum(r in RAW) P(r,c)*use(r,f) >= REQ(c)*produce(f)
forall(f in FOOD) sum(r in RAW) P(r,3)*use(r,f) <= REQ(3)*produce(f)
! Use raw materials within their limit of availability
forall(r in RAW) sum(f in FOOD) use(r,f) <= AVAIL(r)
! Satisfy demands
forall(f in FOOD) produce(f) >= DEM(f)
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ", getobjval)
write("Food type"); forall(r in RAW) write(strfmt(r,9))
writeln(" protein lipid fiber")
forall(f in FOOD) do
write(strfmt(f,-9))
forall(r in RAW) write(strfmt(getsol(use(r,f)),9,2))
forall(c in COMP) write(" ",
strfmt(getsol(sum(r in RAW) P(r,c)*use(r,f))/getsol(produce(f)),3,2),"%")
writeln
end-do
end-model
|
|
| a3refine.mos |
(!******************************************************
Mosel Example Problems
======================
file a3refine.mos
`````````````````
Refinery planning
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002
*******************************************************!)
model "A-3 Refinery planning"
uses "mmxprs"
declarations
CRUDES: set of string ! Set of crudes
ALLPRODS: set of string ! Intermediate and final products
FINAL: set of string ! Final products
IDIST: set of string ! Products obtained by distillation
IREF: set of string ! Products obtained by reforming
ICRACK: set of string ! Products obtained by cracking
IPETROL: set of string ! Interm. products for petrol
IDIESEL: set of string ! Interm. products for diesel
IHO={"hogasoil", "hocrknaphtha", "hocrkgasoil"}
! Interm. products for heating oil
DEM: array(FINAL) of real ! Min. production
COST: array(set of string) of real ! Production costs
AVAIL: array(CRUDES) of real ! Crude availability
OCT, VAP, VOL: array(IPETROL) of real ! Octane, vapor pressure, and
! volatility values
SULF: array(IDIESEL) of real ! Sulfur contents
DIST: array(CRUDES,IDIST) of real ! Composition of crudes (in %)
REF: array(IREF) of real ! Results of reforming (in %)
CRACK: array(ICRACK) of real ! Results of cracking (in %)
end-declarations
initializations from 'a3refine.dat'
DEM COST OCT VAP VOL SULF AVAIL DIST REF CRACK
end-initializations
finalize(FINAL); finalize(CRUDES); finalize(IPETROL); finalize(IDIESEL)
finalize(IDIST); finalize(IREF); finalize(ICRACK)
ALLPRODS:= FINAL+IDIST+IREF+ICRACK+IPETROL+IHO+IDIESEL
declarations
use: array(CRUDES) of mpvar ! Quantities used
produce: array(ALLPRODS) of mpvar ! Quantities produced
end-declarations
! Objective function
Cost:= sum(c in CRUDES) COST(c)*use(c) + sum(p in IDIST) COST(p)*produce(p)
! Relations intermediate products resulting of distillation - raw materials
forall(p in IDIST) produce(p) <= sum(c in CRUDES) DIST(c,p)*use(c)
! Relations between intermediate products
! Reforming:
forall(p in IREF) produce(p) <= REF(p)*produce("naphtha")
! Cracking:
forall(p in ICRACK) produce(p) <= CRACK(p)*produce("residue")
produce("crknaphtha") = produce("petcrknaphtha") +
produce("hocrknaphtha") + produce("dslcrknaphtha")
produce("crkgasoil") = produce("hocrkgasoil") + produce("dslcrkgasoil")
! Desulfurization:
produce("gasoil") = produce("hogasoil") + produce("dslgasoil")
! Relations final products - intermediate products
produce("butane") = produce("distbutane") + produce("refbutane") -
produce("petbutane")
produce("petrol") = sum(p in IPETROL) produce(p)
produce("diesel") = sum(p in IDIESEL) produce(p)
produce("heating") = sum(p in IHO) produce(p)
! Properties of petrol
sum(p in IPETROL) OCT(p)*produce(p) >= 94*produce("petrol")
sum(p in IPETROL) VAP(p)*produce(p) <= 12.7*produce("petrol")
sum(p in IPETROL) VOL(p)*produce(p) >= 17*produce("petrol")
! Limit on sulfur in diesel oil
sum(p in IDIESEL) SULF(p)*produce(p) <= 0.05*produce("diesel")
! Crude availabilities
forall(c in CRUDES) use(c) <= AVAIL(c)
! Production capacities
produce("naphtha") <= 30000 ! Reformer
produce("gasoil") <= 50000 ! Desulfurization
produce("residue") <= 40000 ! Cracker
! Satisfy demands
forall(p in FINAL) produce(p) >= DEM(p)
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Production costs: ", strfmt(getobjval,10,2))
forall(c in CRUDES) writeln(c, ": ", getsol(use(c)))
forall(p in ALLPRODS) writeln(p, ": ", getsol(produce(p)))
writeln("Petrol properties:")
writeln(" octane: ",
getsol(sum(p in IPETROL) OCT(p)*produce(p))/ getsol(produce("petrol")),
" vapor presure: ",
getsol(sum(p in IPETROL) VAP(p)*produce(p))/ getsol(produce("petrol")),
" volatility: ",
getsol(sum(p in IPETROL) VOL(p)*produce(p))/ getsol(produce("petrol")))
writeln("Sulfur in diesel oil: ",
getsol(sum(p in IDIESEL) SULF(p)*produce(p))/getsol(produce("diesel")) )
end-model
|
|
| a4sugar.mos |
(!******************************************************
Mosel Example Problems
======================
file a4sugar.mos
````````````````
Production of cane sugar
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002
*******************************************************!)
model "A-4 Cane sugar production"
uses "mmxprs"
declarations
NW = 11 ! Number of wagon loads of sugar
NL = 3 ! Number of production lines
WAGONS = 1..NW
SLOTS = 1..ceil(NW/NL) ! Time slots for production
LOSS: array(WAGONS) of real ! Loss in kg/hour
LIFE: array(WAGONS) of real ! Remaining time per lot
DUR: integer ! Duration of the production
process: array(WAGONS,SLOTS) of mpvar ! 1 if wagon processed in slot,
! 0 otherwise
end-declarations
initializations from 'a4sugar.dat'
LOSS LIFE DUR
end-initializations
! Objective function
TotalLoss:= sum(w in WAGONS, s in SLOTS) s*DUR*LOSS(w)*process(w,s)
! Assignment
forall(w in WAGONS) sum(s in SLOTS) process(w,s) = 1
! Wagon loads per time slot
forall(s in SLOTS) sum(w in WAGONS) process(w,s) <= NL
! Limit on raw product life
forall(w in WAGONS) sum(s in SLOTS) s*process(w,s) <= LIFE(w)/DUR
forall(w in WAGONS, s in SLOTS) process(w,s) is_binary
! Solve the problem
minimize(TotalLoss)
! Solution printing
writeln("Total loss: ", getobjval)
forall(s in SLOTS) do
write("Slot ", s, ": ")
forall(w in WAGONS)
if(getsol(process(w,s))>0) then
write("wagon ", strfmt(w,2), strfmt(" (" + s*DUR*LOSS(w) + ") ", 8))
end-if
writeln
end-do
end-model
|
|
| a5mine.mos |
(!******************************************************
Mosel Example Problems
======================
file a5mine.mos
```````````````
Opencast mining
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Feb. 2002
*******************************************************!)
model "A-5 Opencast mining"
uses "mmxprs"
declarations
BLOCKS = 1..18 ! Set of blocks
LEVEL23: set of integer ! Blocks in levels 2 and 3
COST: array(BLOCKS) of real ! Exploitation cost of blocks
VALUE: array(BLOCKS) of real ! Value of blocks
ARC: array(LEVEL23,1..3) of integer ! Arcs indicating order of extraction
extract: array(BLOCKS) of mpvar ! 1 if block b is extracted
end-declarations
initializations from 'a5mine.dat'
COST VALUE ARC
end-initializations
! Objective: maximize total profit
Profit:= sum(b in BLOCKS) (VALUE(b)-COST(b))* extract(b)
! Extraction order
! forall(b in LEVEL23) 3*extract(b) <= sum(i in 1..3) extract(ARC(b,i))
forall(b in LEVEL23)
forall(i in 1..3) extract(b) <= extract(ARC(b,i))
forall(b in BLOCKS) extract(b) is_binary
! Solve the problem
maximize(Profit)
! Solution printing
declarations
WEIGHT: integer ! Weight of blocks
end-declarations
initializations from 'a5mine.dat'
WEIGHT
end-initializations
writeln("Total profit:", strfmt(getobjval*WEIGHT,8,0))
write("Extract blocks")
forall(b in BLOCKS) write(if(getsol(extract(b))>0, " "+b, ""))
writeln
end-model
|
|
| a6electr.mos |
(!******************************************************
Mosel Example Problems
======================
file a6electr.mos
`````````````````
Production of electricity
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "A-6 Electricity production"
uses "mmxprs"
declarations
NT = 7
TIME = 1..NT ! Time periods
TYPES = 1..4 ! Power generator types
LEN, DEM: array(TIME) of integer ! Length and demand of time periods
PMIN,PMAX: array(TYPES) of integer ! Min. & max output of a generator type
CSTART: array(TYPES) of integer ! Start-up cost of a generator
CMIN: array(TYPES) of integer ! Hourly cost of gen. at min. output
CADD: array(TYPES) of real ! Cost/hour/MW of prod. above min. level
AVAIL: array(TYPES) of integer ! Number of generators per type
start: array(TYPES,TIME) of mpvar ! No. of gen.s started in a period
work: array(TYPES,TIME) of mpvar ! No. of gen.s working during a period
padd: array(TYPES,TIME) of mpvar ! Production above min. output level
end-declarations
initializations from 'a6electr.dat'
LEN DEM PMIN PMAX CSTART CMIN CADD AVAIL
end-initializations
! Objective function: total daily cost
Cost:= sum(p in TYPES, t in TIME) (CSTART(p)*start(p,t) +
LEN(t)*(CMIN(p)*work(p,t) + CADD(p)*padd(p,t)))
! Number of generators started per period and per type
forall(p in TYPES, t in TIME)
start(p,t) >= work(p,t) - if(t>1, work(p,t-1), work(p,NT))
! Limit on power production above minimum level
forall(p in TYPES, t in TIME) padd(p,t) <= (PMAX(p)-PMIN(p))*work(p,t)
! Satisfy demands
forall(t in TIME) sum(p in TYPES) (PMIN(p)*work(p,t) + padd(p,t)) >= DEM(t)
! Security reserve of 20%
forall(t in TIME) sum(p in TYPES) PMAX(p)*work(p,t) >= 1.20*DEM(t)
! Limit number of available generators; numbers of generators are integer
forall(p in TYPES, t in TIME) do
work(p,t) <= AVAIL(p)
work(p,t) is_integer
end-do
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Daily cost: ", getobjval)
write(strfmt("Time period ",-20))
ct:=0
forall(t in TIME) do
write(strfmt(ct,5), "-", strfmt(ct+LEN(t),2), "")
ct+=LEN(t)
end-do
forall(p in TYPES) do
write("\nType ", p, strfmt(" No. working ",-14));
forall(t in TIME) write(strfmt(getsol(work(p,t)),8))
write("\n", strfmt("Total output ",20));
forall(t in TIME) write(strfmt(getsol((PMIN(p)*work(p,t) + padd(p,t))),8))
write("\n", strfmt("of which add.",20));
forall(t in TIME) write(strfmt(getsol(padd(p,t)),8))
end-do
writeln
end-model
|
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