Economics and finance
Description
| Problem name and type, features | Difficulty | Related examples |
| H‑1 | Choice of loans | * | |
|---|
| calculation of net present value |
| H‑2 | Publicity campaign | * | |
|---|
| forall-do |
| H‑3 | Portfolio selection | ** | h7qportf.mos |
|---|
| sets of integers, second formulation with semi-continuous, parameters |
| H‑4 | Financing an early retirement scheme | ** | |
|---|
| inline if, selection with `|' |
| H‑5 | Family budget | ** | |
|---|
| formulation of monthly balance constraints including different payment frequencies; as, mod, inline if, selection with `|' |
| H‑6 | Choice of expansion projects | ** | capbgt_graph.mos |
|---|
| experiment with solutions: solve LP problem explicitly, ``round'' some almost integer variable and re-solve |
| H‑7 | Mean variance portfolio selection: Quadratic Programming problem | *** | folioqp_graph.mos |
|---|
| parameters, forall-do, min, max, loop over problem solving |
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 13: Economics and finance problems
Source Files
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Data Files
h5budget.mos
(!******************************************************
Mosel Example Problems
======================
file h5budget.mos
`````````````````
Planning the family budget
A mother wants to plan her family's annual budget. A
list of monthly expenses is provided as well as the
family salary and allowances. Each month, the mother
pays at least a given amount for leisure, but she would
like to spend more in such activities. How should she
balance the budget through the year to maximize the money
available for leisure?
This is a LP model similar to a production planning
model where money can be transferred from one time
period to the next one. To deal with the different
periodicities of the expenses, the Mosel operator 'mod'
is introduced. For the savings at the beginning of the
first period, the conditional 'if' is used in the constraint
formulation.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)
model "H-5 Family budget"
uses "mmxprs"
declarations
MONTHS = 1..12 ! Time period
ITEMS: set of string ! Set of shops
INCOME, ALLOW: integer ! Monthly income and allowance
HMIN: integer ! Min. amount required for hobbies
EXPENSE: array(ITEMS) of integer ! Expenses
FREQ: array(ITEMS) of integer ! Frequency (periodicity) of expenses
hobby: array(MONTHS) of mpvar ! Money to spend for leisure/hobbies
saving: array(MONTHS) of mpvar ! Savings
end-declarations
initializations from 'h5budget.dat'
INCOME ALLOW HMIN
[EXPENSE, FREQ] as 'PAYMENT'
end-initializations
! Objective: money for hobby
Leisure:= sum(m in MONTHS) hobby(m)
! Monthly balances
forall(m in MONTHS)
sum(i in ITEMS | m mod FREQ(i) = 0) EXPENSE(i) + hobby(m) +
saving(m) <= INCOME + ALLOW + if(m>1, saving(m-1), 0)
forall(m in MONTHS) hobby(m) >= HMIN
! Solve the problem
maximize(Leisure)
! Solution printing
writeln("Money for hobby: ", getobjval)
write("Month ")
forall(m in MONTHS) write(" ", strfmt(m,4))
setparam("realfmt", "%4g") ! Reserve 4 char.s for display of real numbers
write("\nHobby: ")
forall(m in MONTHS) write(" ", getsol(hobby(m)))
write("\nSavings:")
forall(m in MONTHS) write(" ", getsol(saving(m)))
writeln
end-model
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