14 votes

How can I approximate a chance constraint in a computationally tractable way?

In general, chance constraints are difficult to handle computationally. Given a fixed $x$, is it often very difficult to even compute the value of $\Pr[F(x,\xi)\leq0]$, making the incorporation of ...
David M.'s user avatar
  • 2,077
12 votes

How can I approximate a chance constraint in a computationally tractable way?

In addition to David M's excellent answer, another approach which sometimes can be useful is to use integer programming. Specifically, if your distribution of $\xi$ is discrete (e.g. taking a sample-...
Ryan Cory-Wright's user avatar
8 votes

Difference between Chance constraints and logical constraints

These two types of constraint are totally different in terms of their applications in modeling. In fact, the way of using these constraint types (based on your modeling approach) end up in two totally ...
Oguz Toragay's user avatar
  • 8,652
8 votes

Difference between Chance constraints and logical constraints

Logical constraints do not involve probability, except perhaps for the implicit probability of one or zero. Chance constraints specify conditions (constraints) which must hold with a(t least) ...
Mark L. Stone's user avatar
7 votes

Software for multi-objective optimization

You may be interested in the following paper because it uses chance-constrained programming and bi-objective optimization together in a transportation application: https://link.springer.com/article/...
Hadi C.'s user avatar
  • 71
4 votes

Decomposition methods for two-stage stochastic program with integer variables

To solve stochastic programming models with integer recourse, there are some methods. Most stochastic programming textbooks cover these methods. For example, chapter 7 of Introduction to Stochastic ...
Ehsan's user avatar
  • 2,463
3 votes
Accepted

Static stochastic knapsack problem: unbounded version

Couldn't you just introduce binary variables $x_{ij}$ and consider the sum $$ Pr\left(\sum_{i \in I}\sum_{j=0}^{\text{max}} \tilde{w}_{ij} x_{ij} \le C \right)\ge 1-\alpha $$ where max is chosen ...
J Fabian Meier's user avatar
2 votes

Create constraint only for a recourse problem in stochastic linear programming

Ok, my last post for this Q perhaps: regarding: update 2, Stage 3, you can introduce a recourse variable, a random variable for each section to capture overbooking like: S[s,c] - c >= O[c] where O[...
Sutanu Majumdar's user avatar
2 votes

Create constraint only for a recourse problem in stochastic linear programming

I know this is a lengthy problem; you can skip the complete solution and cite the central conceptual part This too is a hard challenge. Stochastic programming is difficult to explain, and I find the ...
Oscar Dowson's user avatar
2 votes
Accepted

Decomposition methods for two-stage stochastic program with integer variables

You can try a master problem of the form \begin{alignat*}{1} \min & \quad \gamma\\ \textrm{s.t.} & \quad \sum_{s=1}^{S}P_{s}Y_{s}\le\alpha\\ & \quad \gamma\ge\gamma_{T}\left[\sum_{s\in T}(...
prubin's user avatar
  • 39.1k
2 votes
Accepted

Scenario based approach to value-at-risk optimization using mixed-integer programming

How about \begin{align}\min&\quad\gamma\\\text{s.t.}&\quad(-r^s)^\top X\leq \gamma + M Y_s \qquad s=1,\ldots,S\\&\quad\sum_{s=1}^SP_sY_s \leq \alpha\\&\quad \sum_{i=1}^nx_i=1\\&\...
k88074's user avatar
  • 1,661

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