# Case Study: Optimal Tests Selection

** 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

——————————————————————–————–——

# of Variables |
# of Scenarios |
Objective Value |
Solving Time, PC 3.14GHz (sec) |
||||

Dataset | 21 | 20 | 873 | 0.08 | |||
---|---|---|---|---|---|---|---|

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

——————————————————————–————–————–—–————–———

# of Variables |
# of Scenarios |
Objective Value |
Solving Time, PC 3.14GHz (sec) |
||||

Dataset | 21 | 20 | 833 | 0.04 | |||
---|---|---|---|---|---|---|---|

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.