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1500 questions
10
votes
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Variable Sensitivity Analysis
I am working with the following MIP :
\begin{alignat}2\min&\quad\sum_{j\in J} c_j x_j\\\text{s.t.}&\quad l_j \le f(x_j,t_j) \le u_j \quad &\forall j \in J \\&\quad x_j \in \mathbb{N} \quad &\forall j \in J \\&\quad t_j \in \mathbb{R}^+ \quad…
Kuifje
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10
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3 answers
Do solvers use GUB/SOS1 branching?
GUB/SOS1 branching is an old and well-known idea (see for example page 9 of Jeff Linderoth's notes).
Is this implemented in commercial solvers these days?
The Gurobi documentation mentions SOS1 constraints, but never mentions SOS1 branching.
Austin Buchanan
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2 answers
Linearization $\max(c_1 x_2, c_2 x_2, \ldots, c_nx_n) \geq q$ constraint
I have a MIP minimization problem where I have a maximization in the constraints:
$$\max(c_1x_2,\, c_2x_2,\, \ldots,\, c_nx_n) \geq q$$
Where:
$c_n$ constants
$x_n$ binary variables
$q$ constant
$x_n$ is not part of the objective function. How can…
Tim
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10
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1 answer
MIP: If integer variable $>0$ it should be equal to other integer variables $>0$
I have an MIP problem where $n$ different types of cars are delivering packages. Sometimes multiple types of cars are required to go to a single location. For example if car $1$ makes two deliveries to location $z$, car $2$ needs to make an equal…
Tim
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10
votes
1 answer
Linear programming with if-then-else (big-M)
I am trying to formulate the following in linear programming.
\begin{cases}\text{if}\,\,a>b\,\,\text{then}\,\,c=a\\\text{else}\,\,c=b.\end{cases}
I tried some things with big $M$, like $$a + my > b+m(1-y),$$ so that $y$ (binary) can be used to pick…
Harry van t Kamp
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10
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4 answers
Integer programming problem with simple quadratic objective function in Python
I have $n$ objects that need to be divided among $k$ groups. Each group must receive at least $5$ objects. In addition, the percentage of objects in group $i$ should be as close as possible to $p_i$ where $\sum\limits_{i=1}^k p_i = 1$. I was…
Rohit Pandey
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10
votes
2 answers
Advantages generic cplex callback within branch-and-cut
What are the advantages of using the generic callback compared to the old user/lazy callbacks within a branch-and-cut framework?
IBM states on its website that the major benefit of the new generic callback is that it allows for dynamic search…
Michiel uit het Broek
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10
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1 answer
How to access neighboring extreme points to an optimal extreme point of an LP?
Suppose that I have access to an optimal non-degenerate extreme point of an LP. I need to find some $\epsilon$-optimal extreme points. That is, a point $x$ where $c'x \le z^{*} + \epsilon$.
One way to do this is to add this constraint to the…
Hamed Rahimian
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3 answers
Is there a heuristic approach to the MILP problem?
I have the following optimization problem which is a MILP. I can solve it with a MILP solver.
\begin{align}\min_t&\quad t\\\text{s.t.}&\quad d_{c}-t\le \sum_{n=1}^{N} B_{n,c}x_{n}\le d_{c}+t,\quad\forall c\in\{1,2,\cdots,C\}\\&\quad\sum_{n=1}^{N}…
KGM
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1 answer
Wild oscillation of dual infeasibility in Gurobi mixed-integer solver
As the question says, I am wondering what happens "behind the scene" when the Dual Infeasibility column of the Gurobi runtime log oscillates wildly, before Gurobi eventually quits with infeasibility. I am solving a mixed-integer model. More…
user22363
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10
votes
2 answers
How to use warm start to solve MIPs efficiently?
I'm working on the scheduling model which takes a long time to solve to optimality (even for a small instance), therefore I would like to use a warm start (MIP start) to solve the problem. I'm using the following two different methods:
Determine a…
A.Omidi
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2 answers
Linear Programming: Objective function goodness if variable holds value above a given constant value
In a Linear Programming formulation, stating that a punishment is to be introduced in an objective minimization function if a variable $S$ holds a value above a given constant $K$ ($K = 35$ in the below example), is quite easy:
Variable $M$ is…
10
votes
1 answer
Solving convex programs defined by separation oracles?
General question: What software can solve convex programs defined by a separation oracle?
The objective function is concave, and the feasible set is a polytope. By a separation oracle I mean that I would program a function that, on input a point,…
Elle Najt
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10
votes
3 answers
Holding cost vs carrying cost vs storage cost
I was reading an article on supply chain management and encountered a number of inventory costs like ordering, carrying, shortage, holding, storage costs. I cannot understand the difference between holding, carrying and storage cost. Literally these…
Harry
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10
votes
2 answers
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 can be visited once at most. You can visit the…
sedge
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