| h1loan.mos |
(!******************************************************
Mosel Example Problems
======================
file h1loan.mos
```````````````
Choice of loans
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "H-1 Loan choice"
uses "mmxprs"
declarations
BANKS = 1..3 ! Set of banks
SHOPS = {"London", "Munich", "Rome"} ! Set of shops
DUR: integer ! Duration of loans
PRICE: array(SHOPS) of integer ! Price of shops
RATE: array(BANKS,SHOPS) of real ! Interest rates offered by banks
VMAX: integer ! Maximum loan volume per bank
borrow: array(BANKS,SHOPS) of mpvar ! Loan taken from banks per project
end-declarations
initializations from 'h1loan.dat'
PRICE RATE VMAX DUR
end-initializations
! Objective: interest payments
Interest:=
sum(b in BANKS, s in SHOPS) borrow(b,s)*RATE(b,s)/(1-(1+RATE(b,s))^(-DUR))
! Finance all projects
forall(s in SHOPS) sum(b in BANKS) borrow(b,s) = PRICE(s)
! Keep within maximum loan volume per bank
forall(b in BANKS) sum(s in SHOPS) borrow(b,s) <= VMAX
! Solve the problem
minimize(Interest)
! Solution printing
writeln("Total interest: ", getobjval)
forall(s in SHOPS) do
write("Shop in ", s, ": ")
forall(b in BANKS)
write( if(getsol(borrow(b,s))>0,
" bank " + b + ": " + getsol(borrow(b,s))/1000000 + " million",
""))
writeln
end-do
end-model
|
|
| h2publ.mos |
(!******************************************************
Mosel Example Problems
======================
file h2publ.mos
```````````````
Planning a publicity campaign for a new product
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "H-2 Publicity"
uses "mmxprs"
declarations
MEDIA = 1..6 ! Set of media types
REACH: array(MEDIA) of integer ! Number of people reached
COST: array(MEDIA) of integer ! Unitary cost
MAXUSE: array(MEDIA) of integer ! Maximum use
SCORE: array(MEDIA) of integer ! Quality rating (best=highest value)
BUDGET: integer ! Available publicity budget
TARGET: integer ! Number of people to be reached
use: array(MEDIA) of mpvar ! Use made of different media
end-declarations
initializations from 'h2publ.dat'
REACH COST MAXUSE SCORE BUDGET TARGET
end-initializations
! Objective: quality of perception of the campaign
Perceive:= sum(m in MEDIA) SCORE(m)*use(m)
! Budgetary limit
sum(m in MEDIA) COST(m)*use(m) <= BUDGET
! Outreach of campaign
sum(m in MEDIA) REACH(m)*use(m) >= TARGET
forall(m in MEDIA) do
use(m) is_integer
use(m) <= MAXUSE(m)
end-do
! Solve the problem
maximize(Perceive)
! Solution printing
declarations
NAMES: array(MEDIA) of string
end-declarations
initializations from 'h2publ.dat'
NAMES
end-initializations
writeln("Perception: ", getobjval, " units (",
getsol(sum(m in MEDIA) REACH(m)*use(m)), " people)")
forall(m in MEDIA) writeln(NAMES(m), ": ", getsol(use(m)))
end-model
|
|
| h3portf.mos |
(!******************************************************
Mosel Example Problems
======================
file h3portf.mos
````````````````
Composition of an investment portfolio
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "H-3 Portfolio"
uses "mmxprs"
parameters
MAXTECH = 0.3 ! Maximum investment into tech. values
MINEU = 0.5 ! Minimum investment into European shares
VMIN = 5000 ! Minimum amount for a single value
VMAX = 40000 ! Maximum amount for a single value
end-parameters
declarations
SHARES = 1..6 ! Set of shares
RET: array(SHARES) of real ! Estimated return in investment
CAPITAL: integer ! Capital to invest
EU: set of integer ! European values among the shares
TECHNOLOGY: set of integer ! Technology values among shares
buy: array(SHARES) of mpvar ! Amount of values taken into portfolio
end-declarations
initializations from 'h3portf.dat'
RET CAPITAL EU TECHNOLOGY
end-initializations
! Objective: total return
Return:= sum(s in SHARES) RET(s)/100*buy(s)
! Requirements concerning portfolio composition
sum(s in TECHNOLOGY) buy(s) <= MAXTECH*CAPITAL
sum(s in EU) buy(s) >= MINEU*CAPITAL
! Total capital to invest
sum(s in SHARES) buy(s) = CAPITAL
forall(s in SHARES) do
VMIN <= buy(s);
! buy(s) is_semcont(VMIN)
buy(s) <= VMAX
end-do
! Solve the problem
maximize(Return)
! Solution printing
writeln("Total return: ", getobjval)
forall(s in SHARES) writeln(s, ": ", getsol(buy(s)))
end-model
|
|
| h4retire.mos |
(!******************************************************
Mosel Example Problems
======================
file h4retire.mos
`````````````````
Financing an early retirement scheme
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "H-4 Retirement"
uses "mmxprs"
declarations
BONDS = {"SNCF","Fujitsu","Treasury"} ! Set of bonds
NT = 7 ! Length of planning period
YEARS = 1..NT
DEM: array(YEARS) of integer ! Annual payments for retirement
VALUE: array(BONDS) of real ! Unit price of bonds
RATE: array(BONDS) of real ! Remuneration rates paid by bonds
RET: array(BONDS) of real ! Unit annual interest of bonds
DUR: array(BONDS) of real ! Duration of loans
INTEREST: real ! Interest for other secure investment
buy: array(BONDS) of mpvar ! Number of bonds acquired
invest: array(YEARS) of mpvar ! Other annual investment
capital: mpvar ! Total capital required
end-declarations
initializations from 'h4retire.dat'
DEM VALUE RATE DUR INTEREST
end-initializations
forall(b in BONDS) RET(b):= VALUE(b)*RATE(b)/100
! Annual balances
capital - sum(b in BONDS) VALUE(b)*buy(b) - invest(1) = DEM(1)
forall(t in 2..NT)
sum(b in BONDS | DUR(b)+1>=t) (RET(b)*buy(b) +
if(DUR(b)+1=t, VALUE(b)*buy(b), 0)) +
(1+INTEREST/100)*invest(t-1) - if(t<NT, invest(t), 0) = DEM(t)
forall(b in BONDS) buy(b) is_integer
! Solve the problem: minimize invested capital
minimize(capital)
! Solution printing
writeln("Total capital: ", getobjval)
writeln("Number of bonds to buy:")
forall(b in BONDS) write(b, ": ", getsol(buy(b)),
" (price: ", VALUE(b)*getsol(buy(b)), ") ")
writeln("\nOther investment:")
forall(t in 1..NT-1) write(" year ", t)
writeln
forall(t in 1..NT-1) write(strfmt(getsol(invest(t)),9,3))
writeln
end-model
|
|
| h4retire.mos |
(!******************************************************
Mosel Example Problems
======================
file h4retire.mos
`````````````````
Financing an early retirement scheme
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "H-4 Retirement"
uses "mmxprs"
declarations
BONDS = {"SNCF","Fujitsu","Treasury"} ! Set of bonds
NT = 7 ! Length of planning period
YEARS = 1..NT
DEM: array(YEARS) of integer ! Annual payments for retirement
VALUE: array(BONDS) of real ! Unit price of bonds
RATE: array(BONDS) of real ! Remuneration rates paid by bonds
RET: array(BONDS) of real ! Unit annual interest of bonds
DUR: array(BONDS) of real ! Duration of loans
INTEREST: real ! Interest for other secure investment
buy: array(BONDS) of mpvar ! Number of bonds acquired
invest: array(YEARS) of mpvar ! Other annual investment
capital: mpvar ! Total capital required
end-declarations
initializations from 'h4retire.dat'
DEM VALUE RATE DUR INTEREST
end-initializations
forall(b in BONDS) RET(b):= VALUE(b)*RATE(b)/100
! Annual balances
capital - sum(b in BONDS) VALUE(b)*buy(b) - invest(1) = DEM(1)
forall(t in 2..NT)
sum(b in BONDS | DUR(b)+1>=t) (RET(b)*buy(b) +
if(DUR(b)+1=t, VALUE(b)*buy(b), 0)) +
(1+INTEREST/100)*invest(t-1) - if(t<NT, invest(t), 0) = DEM(t)
forall(b in BONDS) buy(b) is_integer
! Solve the problem: minimize invested capital
minimize(capital)
! Solution printing
writeln("Total capital: ", getobjval)
writeln("Number of bonds to buy:")
forall(b in BONDS) write(b, ": ", getsol(buy(b)),
" (price: ", VALUE(b)*getsol(buy(b)), ") ")
writeln("\nOther investment:")
forall(t in 1..NT-1) write(" year ", t)
writeln
forall(t in 1..NT-1) write(strfmt(getsol(invest(t)),9,3))
writeln
end-model
|
|
| h6expand.mos |
(!******************************************************
Mosel Example Problems
======================
file h6expand.mos
`````````````````
Planning the expansion of a company
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "H-6 Expansion"
uses "mmxprs"
forward procedure print_sol
declarations
PROJECTS = 1..5 ! Set of possible projects
TIME = 1..5 ! Planning period
COST: array(PROJECTS,TIME) of real ! Annual costs of projects
CAP: array(TIME) of real ! Annually available capital
RET: array(PROJECTS) of real ! Estimated profits
DESCR: array(PROJECTS) of string ! Description of projects
choose: array(PROJECTS) of mpvar ! 1 if project is chosen, 0 otherwise
end-declarations
initializations from 'h6expand.dat'
COST CAP RET DESCR
end-initializations
! Objective: Total profit
Profit:= sum(p in PROJECTS) RET(p)*choose(p)
! Limit on capital availability
forall(t in TIME) sum(p in PROJECTS) COST(p,t)*choose(p) <= CAP(t)
forall(p in PROJECTS) choose(p) is_binary
! Solve the problem
maximize(XPRS_LIN, Profit)
write("LP solution: ")
print_sol
maximize(Profit)
write("MIP solution: ")
print_sol
! Force acceptance of project 1
choose(1)=1
maximize(Profit)
write("Forcing project 1 (", DESCR(1), "): ")
print_sol
!-----------------------------------------------------------------
! Solution printing
procedure print_sol
writeln("Total profit: ", getobjval)
forall(p in PROJECTS)
if(getsol(choose(p))>0) then
writeln(" ", DESCR(p), " (", getsol(choose(p)),")")
end-if
end-procedure
end-model
|
|
| h7qportf.mos |
(!******************************************************
Mosel Example Problems
======================
file h7qportf.mos
`````````````````
Mean-variance portfolio selection
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Aug. 2002, rev. Sep. 2017
*******************************************************!)
model "H-7 QP Portfolio"
uses "mmxprs", "mmnl"
parameters
TARGET = 7.0 ! Minimum target yield
MAXASSETS = 4 ! Maximum number of assets in portfolio
end-parameters
declarations
SECS = 1..4 ! Set of securities
RET: array(SECS) of real ! Expected yield of securities
VAR: array(SECS,SECS) of real ! Variance/covariance matrix of
! estimated returns
frac: array(SECS) of mpvar ! Fraction of capital used per security
end-declarations
initializations from 'h7qportf.dat'
RET VAR
end-initializations
! **** First problem: unlimited number of assets ****
! Objective: mean variance
Variance:= sum(s,t in SECS) VAR(s,t)*frac(s)*frac(t)
! Spend all the capital
sum(s in SECS) frac(s) = 1
! Target yield
sum(s in SECS) RET(s)*frac(s) >= TARGET
! Solve the problem
minimize(Variance)
! Solution printing
declarations
NAMES: array(SECS) of string
end-declarations
initializations from 'h7qportf.dat' ! Get the names of the assets
NAMES
end-initializations
writeln("With a target of ", TARGET, " minimum variance is ", getobjval)
forall(s in SECS) writeln(NAMES(s), ": ", getsol(frac(s))*100, "%")
! **** Second problem: limit total number of assets ****
declarations
buy: array(SECS) of mpvar ! 1 if asset is in portfolio, 0 otherwise
end-declarations
! Limit the total number of assets
sum(s in SECS) buy(s) <= MAXASSETS
forall(s in SECS) do
buy(s) is_binary
frac(s) <= buy(s)
end-do
! Solve the problem
minimize(Variance)
writeln("With a target of ", TARGET," and at most ", MAXASSETS,
" assets, minimum variance is ", getobjval)
forall(s in SECS) writeln(NAMES(s), ": ", getsol(frac(s))*100, "%")
end-model
|
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