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1500 questions
9
votes
1 answer
Graphical method in linear programming
This page describes the graphical method to solve a linear program. The formulation is as follows.
$$\begin{alignat}{2} \max &\quad Z = 200W + 100B\\ \text{s.t.} &\quad 1W + 0.8B &&\leq 4000\\ &\quad 0.004W + 0.001B &&\leq 10\\ &\quad W, B &&\geq…
Mark K
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Solving large-scale stochastic mixed integer program
What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the problem in consideration is not bilevel). I am…
S_Scouse
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9
votes
2 answers
Convexity of a QP
In quadratic programming (QP), you encounter an objective of the following form:
$$x^TQx + c^Tx$$
and often it's desirable to know if the QP is convex. One method to check for convexity is by determining whether matrix $Q$ is positive semidefinite…
Josh Allen
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9
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Do the KKT conditions hold for mixed integer nonlinear problems?
I was wondering if the KKT conditions are applicable for for MINLPs, and if not, why not? What about the case when the integer variables are modeled using constraints involving just continuous variables?
Josh Allen
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9
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3 answers
Examples of problems with non-convex constraint functions but convex feasible region
I'm looking for examples of (classes of) problems with a non-convex, non-linear formulation, but convex feasible region.
That is, a problem of the sort:
$$
\begin{array}{lll}
\text{minimize} & c^Tx & \\
\text{subject to} & g_i(x) \le 0 &…
Robert Schwarz
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9
votes
1 answer
Constraint to state the relation between 2 binary variables
I'm trying to deal with a process planning and machine layout allocation simultaneously.
I have the following variables:
$X_p{_w}_{cj}=1$ if an operation $p$ is done by a machine $w$ with a configuration $c$ at process plan position $j$, and zero…
campioni
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9
votes
2 answers
Reading an LP/MPS file using Pyomo software
I would like to know is it possible to read an LP/MPS file into the Pyomo software and solve the problem? If so, how can I do that?
A.Omidi
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9
votes
1 answer
Should I factor in time as a parameter or a variable in a scheduling problem with MILP?
I am trying to formulate a problem that will spit out an optimal schedule for my tasks to be completed. To keep the information confidential, I will refer to my tasks as papers that need to be written. Here is the premise of my problem.
There are…
Dom
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votes
1 answer
A variant of the Shortest Path Problem
Consider a layerwise directed acyclic graph DAG, $G=(V,E)$ and two vertices $s$ and $t$. $s$ is connected to all vertices in $L_0$, $L_0$ is connected to all vertices in $L_1$ and so forth. Consider all possible paths between $s$ and $t$. In…
ephemeral
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9
votes
1 answer
Pyomo: Looping Over A Variable Method
I am trying to extract my variable values into unique lists so that I can pass them to a panadas dataframe and eventually export the dataframe to Excel after I solve my model. The idea is to have the variables of interest in a much more readable and…
GrayLiterature
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9
votes
1 answer
How can I model regression with an asymmetric loss function?
Mosek provided a concrete example of using the Huber loss function,
Huber loss, which is great!
One problem I am trying to tackle is to use asymmetric loss, as described in the answer of asymmetric loss.
Simply speaking, instead of using a classic…
eight3
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9
votes
2 answers
CVRP With Unconstrained Fleet Size: Upper Bound on Optimal Fleet Size
Given a CVRP where the number of trucks is not constrained, is there an upper bound on the number of trucks used in an optimal solution in terms of number of customers, some distances, capacities, and demands?
At the most general level I would like…
Bo Jones
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9
votes
3 answers
Vehicle routing benchmark instances
I recently started working on the classical split delivery vehicle routing problem (SDVRP). I appreciate if someone could let me know where to download benchmark instances for this problem? I am also interested to know what problem instances are…
rasul
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votes
2 answers
When should I use a solver for IP and MIP and can I just use a library from Python, R, Matlab, etc...?
Are there any rules of thumb for figuring out when you need to use a solver like Gurobi or CPLEX, and when you can just solve you problems directly with a Python, R, or Matlab package?
Is it just a question of the size of the problem, or are there…
Skander H.
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9
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2 answers
Could reserving a hotel room potentially lead to a suboptimal allocation of rooms?
Suppose you have a standard hotel with a set of rooms. If you have booked a room for a fixed period of time, would allocating a specific room in advance potentially cause a conflict when trying to allocate rooms for other bookings in the future?
I…
Double M
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