Background

Problem 1. Maximizing net present value with budget constraint

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

Problem 2. Maximizing net present value with constraint on available initial capital

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

References

 

Background

This case study demonstrates an optimization setup 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” problem. We present two equivalent problem formulations: in the first one we use the PSG “linear” function with decision variables of type Boolean, in the second one the value of the items placed to the knapsack is calculated with PSG “fxchg_pos” function.

 

Problem 1

 

Simplified Problem Statement

 

Maximize Linear (maximizing net present value)

 subject to

Linear ≤ Const1 (budget constraint)

Box constraints (binary position variables, x = Boolean)

 

where

 

Box constraints = constraints on individual decision variables

 

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Solution in MATLAB Environment

 

Solved with PSG MATLAB subroutine riskprog and function tbpsg_run (General (Text) Format of PSG in MATLAB):

 

Input Files to run CS:

 

Problem 2

 

Simplified Problem Statement

 

Maximize Linear (maximizing net present value)

 subject to

Fxchg ≤ Const2 (constraint on available initial capital)

Box constraints (bounds on positions)

 

where

 

Fxchg = Fixed Charge

Box constraints = constraints on individual decision variables

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Solution in MATLAB Environment

 

Solved with PSG MATLAB subroutine riskprog and function tbpsg_run (General (Text) Format of PSG in MATLAB):

 

Input Files to run CS:

 

References

 

[1]  Luenberger, D.G. (1998): Investment Science, Oxford University Press, 494 p.