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
h6expand.mos
(!******************************************************
Mosel Example Problems
======================
file h6expand.mos
`````````````````
Planning the expansion of a company
A company aims to expand and has a series of candidate
projects for a planning horizon of five years. Every
project has an annual cost and expected benefit after
five years. The forecast annual costs of the projects
for the next five years as well as the available yearly
funds are known. Which project(s) should the company
choose now to maximize the total benefit after five years?
A simple IP model with binary decision variables is
implemented. For each period, we ensure that the
annual cost of the project is at most the available
funds for the specific year. The problem solving is
started repeatedly, initially solving only the root
LP relaxation.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)
model "H-6 Expansion"
uses "mmxprs"
forward procedure printsol
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: ")
printsol
maximize(Profit)
write("MIP solution: ")
printsol
! Force acceptance of project 1 (='rounding' of an almost integer LP solution value)
choose(1)=1
maximize(Profit)
write("Forcing project 1 (", DESCR(1), "): ")
printsol
!-----------------------------------------------------------------
! Solution printing
procedure printsol
writeln("Total profit: ", getobjval)
forall(p in PROJECTS | getsol(choose(p))>0)
writeln(" ", DESCR(p), " (", getsol(choose(p)), ")")
end-procedure
end-model
| 
