STOCHASTIC INTEGER PROGRAMMING BY DYNAMIC PROGRAMMING

Stochastic Dual Dynamic Integer Programming

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, suc...

Stochastic Integer Programming Bibliography

Stochastic Integer Programming

1. Books and Surveys 2. Theory 2.1 Structural properties of the EVF 2.2 Complexity related results 3. General Purpose Algorithms 3.1 Benders’ decomposition methods 3.2 Gröbner basis methods 3.3 Convex approximations of SIR models 3.4 Other methods 4. Solution of Specific Problems 4.1 Production planning and scheduling problems 4.2 Network and routing problems 4.3 Location problems 4.4 Other pro...

Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming

Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed-integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for ...

Approximation in Stochastic Integer Programming

Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly rem...