# Case Study: Project Selection

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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).

Dataset 7 1 610 0.01 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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).

Dataset 7 1 610 0.01 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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.