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1500 questions
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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
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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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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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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
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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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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
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7
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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
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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…
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…
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
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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
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7
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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
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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
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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…
7
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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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