| c1bike.mos |
(!******************************************************
Mosel Example Problems
======================
file c1bike.mos
```````````````
Planning the production of bicycles
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-1 Bicycle production"
uses "mmxprs"
declarations
TIMES = 1..12 ! Range of time periods
DEM: array(TIMES) of integer ! Demand per months
CNORM,COVER: integer ! Prod. cost in normal / overtime hours
CSTOCK: integer ! Storage cost per bicycle
CAP: integer ! Monthly capacity in normal working hours
ISTOCK: integer ! Initial stock
pnorm:array(TIMES) of mpvar ! No. of bicycles produced in normal hours
pover:array(TIMES) of mpvar ! No. of bicycles produced in overtime hours
store:array(TIMES) of mpvar ! No. of bicycles stored per month
end-declarations
initializations from 'c1bike.dat'
DEM CNORM COVER CSTOCK CAP ISTOCK
end-initializations
! Objective: minimize production cost
Cost:= sum(t in TIMES) (CNORM*pnorm(t) + COVER*pover(t) + CSTOCK*store(t))
! Satisfy the demand for every period
forall(t in TIMES)
pnorm(t) + pover(t) + if(t>1, store(t-1), ISTOCK) = DEM(t) + store(t)
! Capacity limits on normal and overtime working hours per month
forall(t in TIMES) do
pnorm(t) <= CAP
pover(t) <= 0.5*CAP
end-do
! Solve the problem
minimize(Cost)
! Solution printing
declarations
MONTHS: array(TIMES) of string ! Names of months
end-declarations
initializations from 'c1bike.dat'
MONTHS
end-initializations
writeln("Total cost: ", getobjval)
write(" ")
forall(t in TIMES) write(strfmt(MONTHS(t),4))
write("\nDemand ")
forall(t in TIMES) write(strfmt(DEM(t)/1000,4))
write("\nNormal ")
forall(t in TIMES) write(strfmt(getsol(pnorm(t))/1000,4))
write("\nAdd. ")
forall(t in TIMES) write(strfmt(getsol(pover(t))/1000,4))
write("\nStore ")
forall(t in TIMES) write(strfmt(getsol(store(t))/1000,4))
writeln
end-model
|
|
| c2glass.mos |
(!******************************************************
Mosel Example Problems
======================
file c2glass.mos
````````````````
Planning the production of glasses
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-2 Glass production"
uses "mmxprs"
declarations
NT = 12 ! Number of weeks in planning period
WEEKS = 1..NT
PRODS = 1.. 6 ! Set of products
CAPW,CAPM: integer ! Capacity of workers and machines
CAPS: integer ! Storage capacity
DEM: array(PRODS,WEEKS) of integer ! Demand per product and per week
CPROD: array(PRODS) of integer ! Production cost per product
CSTOCK: array(PRODS) of integer ! Storage cost per product
ISTOCK: array(PRODS) of integer ! Initial stock levels
FSTOCK: array(PRODS) of integer ! Min. final stock levels
TIMEW,TIMEM: array(PRODS) of integer ! Worker and machine time per unit
SPACE: array(PRODS) of integer ! Storage space required by products
produce: array(PRODS,WEEKS) of mpvar ! Production of products per week
store: array(PRODS,WEEKS) of mpvar ! Amount stored at end of week
end-declarations
initializations from 'c2glass.dat'
CAPW CAPM CAPS DEM CSTOCK CPROD ISTOCK FSTOCK TIMEW TIMEM SPACE
end-initializations
! Objective: sum of production and storage costs
Cost:=
sum(p in PRODS, t in WEEKS) (CPROD(p)*produce(p,t) + CSTOCK(p)*store(p,t))
! Stock balances
forall(p in PRODS, t in WEEKS)
store(p,t) = if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) - DEM(p,t)
! Final stock levels
forall(p in PRODS) store(p,NT) >= FSTOCK(p)
! Capacity constraints
forall(t in WEEKS) do
sum(p in PRODS) TIMEW(p)*produce(p,t) <= CAPW ! Workers
sum(p in PRODS) TIMEM(p)*produce(p,t) <= CAPM ! Machines
sum(p in PRODS) SPACE(p)*store(p,t) <= CAPS ! Storage
end-do
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
writeln("Production plan:")
write(" Week")
forall(t in WEEKS) write(strfmt(t,7))
writeln
forall(p in PRODS) do
write(p,": Prod. ")
forall(t in WEEKS) write(strfmt(getsol(produce(p,t)),7))
writeln
write(" Store ")
forall(t in WEEKS) write(strfmt("("+getsol(store(p,t))+")",7))
writeln
end-do
writeln("\nCapacities used:")
writeln("Week",strfmt("Workers",8),strfmt("Machines",9),strfmt("Space",7))
forall(t in WEEKS)
writeln(strfmt(t,2),
strfmt(getsol(sum(p in PRODS) TIMEW(p)*produce(p,t)),8),
strfmt(getsol(sum(p in PRODS) TIMEM(p)*produce(p,t)),10,2),
strfmt(getsol(sum(p in PRODS) SPACE(p)*store(p,t)),9,2) )
end-model
|
|
| c3toy.mos |
(!******************************************************
Mosel Example Problems
======================
file c3toy.mos
``````````````
Planning the production of toy lorrys
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-3 Toy production"
uses "mmxprs"
declarations
ITEMS: set of string ! Set of all products
FINAL: set of string ! Set of final products
ASMBL: set of string ! Set of assembled products
PREPROD: set of string ! Set of preproducts
CAP: array(ASMBL) of integer ! Capacity of assembly lines
DEM: array(FINAL) of integer ! Demand of lorrys
CPROD: array(ASMBL) of real ! Assembly costs
CBUY: array(ITEMS) of real ! Purchase costs
REQ: array(ASMBL,PREPROD) of integer ! Items req. for assembling a product
end-declarations
initializations from 'c3toy.dat'
DEM CBUY REQ
[CPROD, CAP] as 'ASSEMBLY'
end-initializations
finalize(ASMBL); finalize(PREPROD); finalize(FINAL); finalize(ITEMS)
declarations
produce: array(ASMBL) of mpvar ! Quantity of items produced
buy: array(PREPROD) of mpvar ! Quantity of items bought
end-declarations
! Objective: total costs
Cost:= sum(p in PREPROD) CBUY(p)*buy(p) +
sum(p in ASMBL) CPROD(p)*produce(p)
! Satisfy demands
forall(p in FINAL) produce(p) >= DEM(p)
! Assembly balance
forall(p in PREPROD) buy(p) + if(p in ASMBL, produce(p), 0) >=
sum(q in ASMBL) REQ(q,p)*produce(q)
! Limits on assembly capacity
forall(p in ASMBL) produce(p) <= CAP(p)
forall(p in PREPROD) buy(p) is_integer
forall(p in ASMBL) produce(p) is_integer
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
writeln("Buy:")
forall(p in PREPROD)
writeln(" ", strfmt(p,-18), ": ", strfmt(getsol(buy(p)),5))
writeln("Produce:")
forall(p in ASMBL)
writeln(" ", strfmt(p,-18), ": ", strfmt(getsol(produce(p)),5))
end-model
|
|
| c4compo.mos |
(!******************************************************
Mosel Example Problems
======================
file c4compo.mos
````````````````
Planning the production of electronic components
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-4 Electronic components"
uses "mmxprs"
declarations
NT = 6 ! Number of time periods (months)
MONTHS = 1..NT
PRODS = 1..4 ! Set of components
DEM: array(PRODS,MONTHS) of integer ! Demand of components per month
CPROD: array(PRODS) of integer ! Production costs
CSTOCK: array(PRODS) of real ! Storage costs
CADD,CRED: real ! Cost of additional/reduced prod.
ISTOCK,FSTOCK: array(PRODS) of integer ! Initial and final stock levels
produce: array(PRODS,MONTHS) of mpvar ! Quantities produced per month
store: array(PRODS,MONTHS) of mpvar ! Stock levels at end of every month
reduce: array(MONTHS) of mpvar ! Reduction of production per month
add: array(MONTHS) of mpvar ! Increase of production per month
end-declarations
initializations from 'c4compo.dat'
DEM CPROD CSTOCK CADD CRED ISTOCK FSTOCK
end-initializations
! Objective: total cost of production, storage, and change of prod. level
Cost:= sum(p in PRODS, t in MONTHS) (CPROD(p)*produce(p,t) +
CSTOCK(p)*store(p,t)) +
sum(t in 2..NT) (CRED*reduce(t) + CADD*add(t))
! Stock balance constraints (satisfy demands)
forall(p in PRODS, t in MONTHS)
store(p,t) = if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) - DEM(p,t)
! Changes to the level of production
forall(t in 2..NT)
sum(p in PRODS) (produce(p,t) - produce(p,t-1)) = add(t) - reduce(t)
! Guarantee final stock levels
forall(p in PRODS) store(p,NT) >= FSTOCK(p)
! Solve the problem
minimize(Cost)
! Solution printing
declarations
PNAME: array(PRODS) of string ! Product names
end-declarations
initializations from 'c4compo.dat'
PNAME
end-initializations
writeln("Total cost: ",getobjval)
write(strfmt("Month",13))
forall(t in MONTHS) write(strfmt(t,5))
forall(p in PRODS) do
write("\n", PNAME(p), ": Prod. ")
forall(t in MONTHS) write(strfmt(getsol(produce(p,t)),5))
write("\n", strfmt("Store ",14))
forall(t in MONTHS) write(strfmt("("+getsol(store(p,t))+")",5))
end-do
write("\nTotal ")
forall(t in MONTHS) write(strfmt(sum(p in PRODS) getsol(produce(p,t)),5))
writeln
end-model
|
|
| c5fiber.mos |
(!******************************************************
Mosel Example Problems
======================
file c5fiber.mos
````````````````
Planning the production of fiberglass
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, rev. Nov. 2017
*******************************************************!)
model "C-5 Fiberglass"
uses "mmxprs"
declarations
NODES: range ! Production and demand nodes
! odd numbers: production capacities
! even numbers: demands
ARC: dynamic array(NODES,NODES) of real ! Cost of flow on arcs
WEIGHT: array(NODES) of integer ! Node weights (capacities/demand)
flow: dynamic array(NODES,NODES) of mpvar ! Flow on arcs
end-declarations
initializations from 'c5fiber.dat'
ARC WEIGHT
end-initializations
forall(m,n in NODES | exists(ARC(m,n))) create(flow(m,n))
! Objective: total cost of production and storage
Cost:= sum(m,n in NODES | exists(ARC(m,n))) ARC(m,n)*flow(m,n)
! Satisfy demands (flow balance constraints)
forall(n in NODES | isodd(n)=FALSE)
if(n>2, flow(n-2,n), 0) + flow(n-1,n) =
if(n<getlast(NODES), flow(n,n+2), 0) + WEIGHT(n)
! Production capacities
forall(n in NODES | isodd(n)) flow(n,n+1) <= WEIGHT(n)
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
write("Week")
forall(t in 1..integer(getlast(NODES)/2)) write(strfmt(t,5))
write("\nProd.")
forall(n in NODES | isodd(n))
write(strfmt(getsol(sum(m in NODES) flow(n,m)),5))
write("\nStock")
forall(n in NODES | not(isodd(n)))
write(strfmt(getsol(sum(m in NODES) flow(n,m)),5))
writeln
end-model
|
|
| c6assign.mos |
(!******************************************************
Mosel Example Problems
======================
file c6assign.mos
`````````````````
Machine assignment for production batches
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-6 Machine assignment"
uses "mmxprs"
declarations
MACH = 1..5 ! Set of machines
PRODS = 1..10 ! Set of production batches
CAP: array(MACH) of integer ! Machine capacities
DUR: array(MACH,PRODS) of integer ! Production durations
COST: array(MACH,PRODS) of integer ! Production costs
use: array(MACH,PRODS) of mpvar ! 1 if machine assigned to batch,
! 0 otherwise
end-declarations
initializations from 'c6assign.dat'
DUR CAP COST
end-initializations
! Objective: total production cost
Cost:= sum(m in MACH, p in PRODS) COST(m,p)*use(m,p)
! Assign a single machine to every batch
forall(p in PRODS) sum(m in MACH) use(m,p) = 1
! Limits on machine capacities
forall(m in MACH) sum(p in PRODS) DUR(m,p)*use(m,p) <= CAP(m)
forall(m in MACH, p in PRODS) use(m,p) is_binary
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
forall(m in MACH) do
write("Machine ", m, ": ")
forall(p in PRODS)
if (getsol(use(m,p))=1) then
write(p, " ")
end-if
writeln(" (total duration: ", getsol(sum(p in PRODS) DUR(m,p)*use(m,p)), ")")
end-do
end-model
|
|
