# On mixing sets arising in chance-constrained programming

@article{Kkyavuz2012OnMS, title={On mixing sets arising in chance-constrained programming}, author={Simge K{\"u}ç{\"u}kyavuz}, journal={Mathematical Programming}, year={2012}, volume={132}, pages={31-56} }

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit inequalities for this set. We extend these inequalities to obtain valid inequalities for the mixing set… Expand

#### 105 Citations

On the mixing set with a knapsack constraint

- Mathematics, Computer Science
- Math. Program.
- 2016

On intersection of two mixing sets with applications to joint chance-constrained programs

- Mathematics, Computer Science
- Math. Program.
- 2019

A polyhedral study on chance constrained program with random right-hand side

- Mathematics, Computer Science
- Math. Program.
- 2017

On quantile cuts and their closure for chance constrained optimization problems

- Mathematics, Computer Science
- Math. Program.
- 2018

Relaxations and approximations of chance constraints under finite distributions

- Mathematics, Computer Science
- Math. Program.
- 2018

Nonanticipative duality, relaxations, and formulations for chance-constrained stochastic programs

- Mathematics, Computer Science
- Math. Program.
- 2017

#### References

SHOWING 1-10 OF 37 REFERENCES

An integer programming approach for linear programs with probabilistic constraints

- Mathematics, Computer Science
- Math. Program.
- 2010

Mixing mixed-integer inequalities

- Computer Science, Mathematics
- Math. Program.
- 2001

Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra

- Mathematics, Computer Science
- Math. Program.
- 2002

Relaxations for probabilistically constrained programs with discrete random variables

- Mathematics, Computer Science
- Oper. Res. Lett.
- 1992

Tight formulations for some simple mixed integer programs and convex objective integer programs

- Mathematics, Computer Science
- Math. Program.
- 2003

Disjunctive Programming: Properties of the Convex Hull of Feasible Points

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1998

A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems

- Mathematics, Computer Science
- Manag. Sci.
- 2004