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What is the impact of making flow fractional rather than integer?

When creating a network flow formulation you can set up sinks with integer flow requirement $\ge 1$. This yields solutions with the total amount of flow along an edge. I have also seen this as a real positive number between $0$ and $1$, the latter…
fhk
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A Question on A tutorial on column generation and branch-and-price for vehicle routing problems by Dominique Feillet

I am reading A tutorial on column generation and branch-and-price for vehicle routing problems by Dominique Feillet to learn the column generation approach, but I have a problem. in section 3.3 entitled Subproblem I can't understand how Expression…
Bhr
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Best way to solve an allocation problem

I have the following problem: I have products with different attributes (price, weight, category) and I have a list of clients. Every client has an "affinity value" with every product, the more affinity a person has, the more likely they will like…
RenanSchwyz
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Are there any good models for min-max vehicle routing problem?

I am trying to model a min-max VRP problem with multiple delivery vehicles and I have come up with a model using branch and cut but I do not think it is strong enough as it takes lot of time to converge. Is there any model which is basic enough to…
Morpheus
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Minimize binary variable's distance with respect to the index values

For a given binary decision variable $x[i,j,k]$ my goal is to get as dense results in terms of k for successive values of j. Distance of k value to be kept as close as possible throughout j values: $d = \sum_{j=2}^n (|k\cdot x[1,j,k] - k\cdot…
Psyndrom Ventura
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Simplex Multiplier

I am reading through a book which provides an example of a linear program given by \begin{align}\min&\quad-24y_{1}-28y_{2}\\\text{s.t.}&\quad6y_{1}+10y_{2} \leq 2400\\&\quad8y_{1}+5y_{2} \leq 1600\\&\quad0\leq y_{1} \leq 500\\&\quad0\leq y_{2} \leq…
Jonn
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What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money $m$ to spend over $r$ different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability of my total winnings across all raffles being a…
winterwyvern
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How to linearize a quadratic constraint to add it then via a callback function

Suppose we have a positive continuous variables $0 \le x \le UB$ where $UB$ is a known upper bound. How can we linearize the term $x^2$? Detailled problem: Suppose that via a callback we compute a factor namely $A_i \in ]0,1]$. After computing this…
Farouk Hammami
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Complexity of solving a certain commodity flow problem

Does anyone know the complexity of obtaining the optimal solution to the integral multi-commodity network flow problem with unit demands, integral capacities, but the cost of using an arc varies across different commodities? As a follow-up, the same…
batwing
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Books in applied Online Optimization

What are books on Online Optimization other than Introduction to Online Convex Optimization? Preferably: more on applied side, rather than theoretical not limited to convex only
Rizky Luthfianto
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Local optimum of dual of non-linear program

In general, suppose you have a non-convex optimization problem with constraints and you form the dual problem. If you find a local optimum for the dual problem, will the corresponding primal solution always be feasible? If not, when is it not…
George Chang
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Installing COIN-OR solvers in Ubuntu (Azure)

For a side project, I'm looking to install COIN-OR project solvers on a Microsoft Azure Ubuntu VM. (I will be running Pyomo optimization models on this VM as well; using NEOS isn't cutting it.) Anybody have any experience in installing these…
Ralph
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Linearizing a constraint with square root of a variable

I am trying to linearize the constraint set (2) in the following simplified program. The parameters: $A,C,D,T\in\mathbb{R}^+$. The set $\mathcal{J}$ is polynomially-sized. \begin{alignat}2\min &\quad…
tcokyasar
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How can I optimize this integer programming constraint problem without running out of memory?

I am trying to run this constraint problem but the memory runs out, $$S_{i}$$ are 1975 Students that need to be assigned to one of 188 teacher assistants classes, each teacher assistant has to chose a time slot $$TA_{j}$$ from out of 8. Each Teacher…
jeroaranda
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Polynomial algorithm for a special ILP problem

Given the following problem: \begin{align} & z=\min \sum_{ij} x_{ij}\\ \text{s.t.} & \quad \sum_i d_{ij} x_{ij} \ge s_j, \quad \forall j \tag1 \\ & \quad \sum_j x_{ij} \le 1, \quad \forall i \tag2 \\ & \quad x_{ij} \in \left\{0, 1\right\}, \quad…
dgamboz
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