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'''Chance Constrained Programming (CCP)''' is a mathematical optimization technique used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes|Charnes]] and [[William W. Cooper|Cooper]] in 1959<ref>Charnes, A., & Cooper, W. W. (1959). Chance-Constrained Programming. ''Management Science'', 6(1), 73-79.</ref> and further developed by Miller and Wagner in 1965<ref>Miller, L. R., & Wagner, H. M. (1965). Chance-constrained programming with joint constraints. ''Operations Research'', 13(6), 930-945.</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.
== Introduction ==
'''Chance Constrained Programming (CCP)''' is a mathematical optimization technique 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. 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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=== 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>Li, P., Arellano-Garcia, H., & Wozny, G. (2007). Chance constrained programming approach to process optimization under uncertainty. ''Computers & Chemical Engineering'', 32(1-2), 25-45.</ref>.
 
=== Production Planning and Operations ===
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== References ==
{{Reflist}}
* Charnes, A., & Cooper, W. W. (1959). Chance-Constrained Programming. ''Management Science'', 6(1), 73-79.
 
* Miller, L. R., & Wagner, H. M. (1965). Chance-constrained programming with joint constraints. ''Operations Research'', 13(6), 930-945.
== External Links ==
* Li, P., Arellano-Garcia, H., & Wozny, G. (2007). Chance constrained programming approach to process optimization under uncertainty. ''Computers & Chemical Engineering'', 32(1-2), 25-45.
* [https://www.gurobi.com/ Gurobi Optimization]
* [https://www.ibm.com/analytics/cplex-optimizer IBM CPLEX Optimizer]
* [https://ampl.com/ AMPL]