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1500 questions
7
votes
1 answer
Gurobi: can you retrieve the dual solution from each node of the B&B tree using callbacks
When solving a MIP with Gurobi, one can use the cbGetNodeRel() function to extract the primal solution to the LP relaxation at each node in the branch and bound tree. Is there similar functionality to extract the dual solution as well? It seems…
David M.
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7
votes
1 answer
Solution time out for VRPTW in or-tools
I am experimenting around with or-tools and somehow I can't get a solution for the VRPTW problem for any of the instances I have tested from Gehring & Homberger datasets.
The smallest dataset I have tested is with 200 nodes (+1 for the depot) and…
k88
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7
votes
1 answer
How to find the idle intervals in integer programming?
I have a scheduling problem with one machine and one job. I defined a binary variable $z_t$ that is 1 iff the job is scheduled at time $t$ (the job can be served in multiple times that are not consecutive). I would like to find the intervals where…
zdm
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7
votes
0 answers
Modeling traffic in a city
I am trying to model traffic in a city, $(i,j)$ represents a road in a city.
There are $H$ vehicles in a city they have some prescheduled set of destinations to visit, $A_{j,h}$ denotes arrival time of vehicle $h$ at node $j$ and $D_{j,h}$ is…
ooo
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7
votes
1 answer
Linearizing the square root of two binary summations
My question is similar to this one though a bit more complicated. Though my question also includes indices, I am removing them to ease readability.
Let binary variables $x,y\in\{0,1\}$, non-negative continuous variable $z\in\mathbb{R}^+$ and the…
tcokyasar
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- 12
7
votes
3 answers
Constraint that checks for an undirected graph whether it is connected?
I would like to create a constraint with AMPL that checks whether I am able to reach from one node $v$ to all other nodes of a set but I don't really know how to formulate it (especially in AMPL (+CPLEX)).
(I am not interested in finding the…
baxbear
- 319
- 1
- 7
7
votes
2 answers
The general meaning of "constraint relaxation" in the context of the Shortest Path Problem
I've read that in the context of the Shortest Path Problem, the use of the term "relaxation" ("relaxing edges")
[...][the use of the term "relaxation"] is historical. The outcome of a relaxation step can be viewed as a relaxation
of the…
Alexey
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7
votes
1 answer
An upper-bound on the value of $S$ in $(s,S)$ policy
I recently have come across a problem which can be categorized as a stochastic optimization. The problem seems simple, but I haven't been able to solve it yet. It has a major impact on algorithm design for real business problems.
Assume that there…
farshid evazabadian
- 171
- 3
7
votes
3 answers
No solution found from n MIP starts
Currently, I am working on the implementation of a MILP formulation with lazy constraints for an optimization problem, and I am using the MIP Start strategy. I am generating the integer feasible solution to the MIP Start through a heuristic, the…
Matheus Diógenes Andrade
- 1,238
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- 14
7
votes
1 answer
Ridge Regression lagrange duality
In every machine learning book we see that it is roughly mentioned that the ridge regression:
$$p_1^* = \min\limits_{\beta} \ \left( \mathrm{RSS} + \lambda\sum_{j=1}^p \beta_j^2 \right)$$
is equivalent to:
$$ p_2^* = \min_{\beta} \left\{…
independentvariable
- 3,980
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- 36
7
votes
0 answers
Building the Scheurman's Model II constraints for a multi period linear program
Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also shown in this paper, if you can't access the first.…
dassouki
- 153
- 8
7
votes
2 answers
MPX Queuing Software for Manufacturing with the GTHUBS Case
I'm teaching an Operations Management Class. A long time ago, there was a simple DOS-based product called MPX. It was based on queuing theory and let you model manufacturing processes. There was nice case that went with it call GTHUBS-- something…
Michael Watson
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7
votes
1 answer
Negative reduced cost for basic variable
I am observing something unusual : after solving a linear program, some basic variables have negative reduced costs (instead of $0$) :
CPLEX> display which sensitivity analysis: objective *
Variable Name Reduced Cost Down …
Kuifje
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7
votes
1 answer
Aggregate production planning
I'm looking for an optimization model about production planning that takes the following into consideration:
Single site
Multi products
One machine/resource
Sequence-dependent
Fixed batch size
Set-up times
No back orders
Capacity…
Ulrich_Peters
- 129
- 2
7
votes
2 answers
How to formulate problems in the language of mathematical programming?
The question says it all. I am having difficulties formulating general problems (meaning no numbers just variables). When I read the solution, I understand but I can't figure how to formulate myself in new problems. I need some tips or what to look…
paulaxa1
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