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An uncertainty management framework for industrial applications

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Abstract

Uncertainty affects industrial systems in many ways. It may describe the amount of system variability. It may influence the way we make decisions. This paper provides a novel framework that maps the effects of uncertainty to existing mathematical methods. In addition, new techniques to assess, adjust and abate parametric uncertainty are presented. Due to the computational burden associated with solving uncertain models of large-scale industrial processes, some simplification techniques may be required, including scenarios with the different parameter realizations. Issues regarding scenario generation, comparison, assessment, management and practical implementation are also discussed.

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Abbreviations

A :

Left-hand side coefficients

B :

Left-hand side coefficients

c :

Objective function coefficients

E(.) :

Expected value operator

f :

Flexibility index

g(.):

Inequality constraints

h(.):

Equality constraints

L(.):

Lagrangian function

MaxR(.) :

Maximum regret function

n g :

Number of inequality constraints

n h :

Number of equality constraints

p :

Probability

R(.) :

Regret function

S :

Set of all scenarios

x :

Decision variable

y :

Slack variable

λ :

Lagrange multipliers for inequality constraints

μ :

Lagrange multipliers for equality constraints

θ:

Parameters

1 :

First-stage decisions

2 :

Second-stage decisions

d :

Deterministic

eq :

Equality constraint

in :

Inequality constraint

LB:

Lower bound

N:

Nominal value

s :

Scenario

u :

Uncertain

UB:

Upper bound

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  1. Hatch, 4342 Queen St., Niagara Falls, ON, Canada

    Danielle Zyngier

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  1. Danielle Zyngier
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Correspondence to Danielle Zyngier.

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Zyngier, D. An uncertainty management framework for industrial applications. Optim Eng 18, 179–202 (2017). https://doi.org/10.1007/s11081-016-9309-2

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  • DOI: https://doi.org/10.1007/s11081-016-9309-2

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