University of Florida

Stan Uryasev

Skip to main Content   Search   Main Navigation   Resources   Website   Social   Address   What is this view

Main Navigation

Home   Research   Test Problems for NonLinear, Stochastic, Mixed-Integer Optimization   Financial Engineering Case Studies (Portfolio Optimization Replication, Hedging, VaR, CVaR, Drawdown, CDaR, Probability, Credit Risk, Cash Matching, Options, Structuring CDO, Mortgage) Case Study: Project Selection

Case Study: Project Selection

Back to main page

Case study background and problem formulations

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.
PROBLEM 1: problem_CS_Project_Selection_FXCHG
Maximize Linear (maximizing net present value)
subject to
Fxchg ≤ Const (constraint on available initial capital)
Box constraints (bounds on positions)
——————————————————————–——–——–
Fxchg = Fixed Charge
Box constraints = constraints on individual decision variables
——————————————————————–——–——–
The same problem is solved with two different solvers: CAR and CARGRB (which needs GUROBI).

# of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec)
Dataset 7 1 610 0.01
Environments
Run-File Problem Statement Data Solution
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab Code Data
R R Code Data
PROBLEM 2: problem_CS_Project_Selection_linear
Maximize Linear (maximizing net present value)
subject to
Linear ≤ Const (budget constraint)
Box constraints (binary position variables, x = Boolean)
——————————————————————–——–——–
Box constraints = constraints on individual decision variables
——————————————————————–——–——–
The same problem is solved with two different solvers: VAN and VANGRB (which needs GUROBI).

# of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec)
Dataset 7 1 610 0.01
Environments
Run-File Problem Statement Data Solution
Run-File Problem Statement Data Solution
Matlab Toolbox Data
Matlab Subroutines Matlab Code Data
R R Code Data
CASE STUDY SUMMARY
This case study demonstrates an optimization setup and relevant graphs for a project selection problem. A similar problem is described in Luenberger (1998), p. 104. The model allows selecting among several different projects. Each project, if chosen, requires an initial capital outlay. Projects are selected to maximize the net present value of the investment subject to constraint on the initial available capital. This problem belongs to the class of “knapsack optimization” problems. We present two equivalent problem formulations having different presentation of the knapsack constraint: the first formulation uses a linear function with Boolean decision variables, and the second one uses PSG “fxchg_pos” function.

References
• Luenberger, D.G. (1998): Investment Science, Oxford University Press.

Footer

Resources

Website

Social links

Address

What is this view?

You are using a dynamic assistive view of the University of Florida site. It has all the same data and features of the original site but formatted just with assistive users in mind. It has links and content reorganized to aid assistive users and has controls at the bottom under assistive options that allow you to control key aspects such as font size and contrast colors etc.
This is not a separate text-only site, it's a dynamic view that uses unique technology from Usablenet to give assistive users better, more accessible access to the same content and features as all users that use the graphic view of the site.

Assistive Options

Top of page


Assistive Options

Open the original version of this page.

Usablenet Assistive is a Usablenet product. Usablenet Assistive Main Page.