Questions tagged [stochastic-programming]

For questions about optimization problems in which one or more parameters are stochastic, with known probability distributions or discrete scenarios. The goal is often, but not always, to minimize or maximize the expected value of the objective function.

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9
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0answers
61 views

Sources to learn about Sample Average Approximation for practitioners

I want to start learning Stochastic Programming, beginning with SAA (Sample Average Approximation) and keeping a practitioner's perspective in mind, i.e. I would like my sources to collectively cover ...
10
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1answer
102 views

Scenario Generation and Reduction in Stochastic Optimization

I have to generate scenarios for a stochastic optimization program. I want to reduce this number of scenarios but the assignment of a probability to each scenario is my problem. How can I assign a ...
11
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1answer
300 views

Why is the sample variance of a Sample Average Approximation calculated in this way?

I am going through the great tutorial on Stochastic Programming by Shapiro and Philpott. When talking about Monte Carlo techniques, I get confused by the way they calculate the sample variance (page ...
8
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0answers
101 views

Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
10
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2answers
161 views

Optimal set order to maximize stochastic reward

You have a ticket allowing you to visit up to $n$ of $M$ carnival booths offering games of chance. At each booth you have probability $p_{i}$ of winning a reward with average value $r_{i}$. Each booth ...
6
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1answer
73 views

Alternative definition for the value of stochastic solution

I have a two-stage stochastic programming problem in which the expected-value solution results in a quite different first-stage solution than the recourse problem. Although the value of VSS (defined ...
11
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1answer
136 views

Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm

Recently, I've been working on some two-stage stochastic programming problems. Due to the presence of integer second-stage variables in the model, I've preferred to use the Progressive Hedging ...
15
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4answers
752 views

Modeling the uncertainty of the input parameters

There are many approaches to deal with the uncertainty such as stochastic programming, robust optimization and fuzzy programming. Finding a suitable approach that is applicable in the real situations ...
10
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2answers
191 views

Infinite horizon versus finite horizon MDP

When can we approximate a finite horizon MDP with infinite horizon? Can we use infinite horizon stochastic shortest path problem on a directed acyclic graph?
9
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1answer
87 views

Advantages/disadvantages of different representations of non-anticipativity constraints

When reading various papers about two-stage (or multi-stage) stochastic programs with recourse, a common representation of the non-anticipativity constraints is: $$ \sum_{i}H_ix_i=h, $$ where $i$ ...
15
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3answers
257 views

Benchmark problems for scenario-based stochastic optimization

$\newcommand{\E}{\mathbb{E}}$I am working on numerical algorithms for solving convex large-scale multistage scenario-based problems and I am looking for some standard benchmarks problems. I have so ...
25
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4answers
342 views

Stochastic programming MIP solvers

I am aware that Benders Decomposition is readily available in CPLEX and in SCIP; but are there any (free) solvers that provide off the shelf stochastic programming MIP algorithms or a nice to work ...
12
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1answer
146 views

2 stage stochastic programming to approximate many stage problems

There are many naturally multi-stage (i.e., more than two) stochastic programming problems that are approximated by a two-stage stochastic programming model due to the complete intractability of the '...