Chance constrained programming: Difference between revisions

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'''Chance Constrained Programming (CCP)''' is a [[mathematical optimization]] approach used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes|Charnes]] and [[William W. Cooper|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal |last1=Charnes |first1=Abraham |last2=Cooper |first2=William W. |title=Chance-Constrained Programming |journal=Management Science |date=1959 |volume=6 |issue=1 |pages=73-7973–79 |doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal |last1=Miller |first1=L. R. |last2=Wagner |first2=H. M. |title=Chance-constrained programming with joint constraints |journal=Operations Research |date=1965 |volume=13 |issue=6 |pages=930-945930–945 |doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.

== Theoretical Background ==

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== Practical Applications ==

Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for portfolio selection.<ref name=pu/> It has been applied to [[renewable energy]] integration,<ref>{{cite book |last1=Zhang |first1=Ning |last2=Kang |first2=Chongqing |last3=Du |first3=Ershun |last4=Wang |first4=Yi |title=Analytics and Optimization for Renewable Energy Integration |date=2019 |publisher=CRC Press |isbn=9780429847707 |page=180}}</ref> generating flight trajectory for [[UAV]]s,<ref>{{cite book |last1=Chai |first1=Runqi |title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles |date=2023 |publisher=Springer Nature Singapore |isbn=9789819943111 |page=131}}</ref> and robotic space exploration.<ref>{{cite journal |last1=Ono |first1=Masahiro |last2=Pavone |first2=Marco |last3=Kuwata |first3=Yoshiaki |last4=Balaram |first4=J. |title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration |journal=Autonomous Robots |date=2015 |volume=39 |issue=4 |pages=555-571555–571 |doi=10.1007/s10514-015-9467-7}}</ref>

=== Process Optimization Under Uncertainty ===

CCP is used in [[chemical engineering|chemical]] and [[process engineering]] to optimize operations considering uncertainties in operating conditions and model parameters. For example, in optimizing the design and operation of chemical plants, CCP helps in achieving desired performance levels while accounting for uncertainties in feedstock quality, demand, and environmental conditions.<ref name=pu>{{cite journal |last1=Pu |first1=Pu |last2=Arellano-Garcia |first2=Harvey |last3=Wozny |first3=Günter |title=Chance constrained programming approach to process optimization under uncertainty |journal=Computers and Chemical Engineering |date=2008 |volume=32 |issue=1-21–2 |pages=25-4525–45 |doi=10.1016/j.compchemeng.2007.05.009}}</ref>

=== Production Planning and Operations ===