# Case Study: Optimal Tests 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_deterministic_LP_model
Maximize Linear (maximizing the value of selected tests)
subject to
Linear ≤ Const1 (constraint on resources)
Box constraints (constraints on decision variables)
——————————————————————–————–—–
Box constraints = constraints on individual decision variables
——————————————————————–————–—–

Data and solution in Run-File Environment

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset1 Problem statement Data Solution 21 20 879 0.02

Data and solution in MATLAB Environment

Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 3.50GHz (sec)
Dataset1 Matlab code Data Solution 21 20 879 0.02
PROBLEM 2: problem_robust_model
Maximize Linear (maximizing the value of selected tests)
subject to
Linear + Cvar_comp_pos ≤ Const2 (constraint on resources)
Box constraints (constraints on decision variables)
——————————————————————–————–——
Cvar_comp_pos = Cvar Component Positive
Box constraints = constraints on individual decision variables
——————————————————————–————–——

Dataset 21 20 873 0.08 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

NOTE: Problem statements can be simplified using MultiConstraint.

PROBLEM 3: problem_stochastic_model
Maximize Linear (maximizing the value of selected tests)
subject to
Prmulti_pen_ni_g ≤ Const3 (constraints on Probability Exceeding Penalty for Gain Multiple Normal Independent)
Box constraints (constraints on decision variables)
——————————————————————–————–————–—–————–———
Prmulti_pen_ni_g = Probability Exceeding Penalty for Gain Multiple Normal Independent
Box constraints = constraints on individual decision variables
——————————————————————–————–————–—–————–———

Dataset 21 20 833 0.04 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data
CASE STUDY SUMMARY
This case study considers the problem of optimal selection of tests subject to several constraints on available resources (e.g. money, times, and people). There are no partial tests: each test is assumed to be either conducted or not conducted. If each resource estimate is assumed to be accurate, then the problem of optimal selection of tests is formulated as Deterministic Linear Programming Assignment model with boolean decision variables. To take into account uncertainty in resource estimates two models are used: robust model and the stochastic model. The Robust model conservatively increases the need in each resource by 20% of its average consumption by 20% largest consumers. The Stochastic model is based on the assumption that resource consumption by each test is independent normally distributed random value. The Robust and Stochastic models provide more realistic solution of the problem of optimal selection of tests, than the Deterministic Linear Programming model. Moreover, the Stochastic model reduces many constraints to one constraint, and provides possibility of sensitivity analysis.