Questions tagged [facility-location]

For questions related to optimization problems for choosing the optimal locations of facilities such as warehouses, factories, fire stations, etc.

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1answer
48 views

Calculating the Obj Value manually in Gurobi

I have been working on the problem on Facility Location Problem with Gurobi using the example provided by the Gurobi team. ...
1
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0answers
60 views

Facility location over time - Parameter

I'm trying to model this scenario that each population group gets assigned to a hospital over a period of time. The time is divided into say a period of 30 weeks, and I have about 8 age-wise ...
4
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0answers
107 views

Which software to use for Voronoi diagrams?

I have recently been looking at some facility location problems and how they change in the presence of the motorway (or highway, freeway) etc. Tried to visualize some observations with the Voronoi ...
2
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1answer
41 views

How to interpret no-overlap constraints with rotation as a mixed integer programming

Suppose, we want to locate some given facilities $\left \{ (i,j) \ |\ (i,j) \in \text[{1,\cdots, N}]\right \}$ in a specific area. Each facility has a predefined dimension with a length $l_{i}$ and ...
4
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1answer
67 views

Does the facility layout problem with zero and one matrices have a specific name?

I have an facility layout problem where the flow between any two departments is either zero or one. Also the distance between each location pair has the same nature (zero or one). I am curious whether ...
3
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1answer
53 views

Strict inclusion for facility location formula and aggregate facility location formula

I am trying to prove that $P_{FL} \subset P_{AFL}$ where \begin{align}P_{FL}&=\left\{({\bf x},{\bf y})\,\,\middle\vert\,\,\forall i,j:\sum_{j=1}^nx_{ij}=1,x_{ij}\le y_j,0\le x_{ij},y_j\le1\right\}\...
6
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0answers
57 views

Estimating multistop routing costs

In many OR problems, it is sometimes a good idea (or necessary) to relax routing constraints. An example of this occurs in the classical facility location problem, where a warehouse can send out a ...
1
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1answer
76 views

A discrete location problem

I have a discrete optimization problem in which there are some predetermined nodes in the set A. a vehicle must visit them as the traveling salesman problem. there are some other nodes in the set B ...
9
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2answers
268 views

Facility Location Problem over Continuous Space

I am reviewing the facility location problem (FLP) literature. Here, Daskin and Dean (2004) provided a short literature on discrete space FLPs, which was useful to distinguish different types of ...
3
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1answer
110 views

Benders implementation on Cplex is very slow

I'm working on a location problem and I have an issue with the Benders decomposition. I'm using Cplex with Python. I coded a single cut and a multi-cut to compare. The single-cut implementation takes ...
3
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0answers
57 views

Under what conditions is the optimal solution to the warehouse location problem the same for a subset of customers?

I am wondering whether there exists some general insight for when the optimal solution to the warehouse location problem is still optimal for a given subset of customers. For example: Does the ...
2
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1answer
85 views

How to design and scale sales territory?

My first naive approach is: Given N number of salesmen. Cluster an area to be N clusters with almost equal number of clients [1] with some kind of same-size clustering/facility location algorithm ...
3
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2answers
80 views

Adding robustness to the objective function of the facility location problem

Let us first define a simplified facility location problem as follows: $$\min \sum_{i=1}^{n}\sum_{j=1}^{m}d(i,j)x_{i.j}$$ subjected to: $$\sum_{i=1}^{n} x_{i,j}\geq1, \forall j$$ (Every customer ...
4
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1answer
112 views

Mobile Sensor Placement for Optimal Coverage

I have come across the paper that deals with spatial positioning of mobile sensors to optimally detect sound source, or position mobile cellphone towers to maximize the coverage. The region $Q$ is ...
2
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1answer
73 views

What is the state of the art on the Weber problem?

I'm trying to get up to speed on the Weber problem. I'm very much not an expert, unfortunately. I would really appreciate recent literature recommendations / surveys / potted histories, however ...
9
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1answer
71 views

Using Spatial Multi Criteria Analysis for simultaneously locating various facilities?

Is it possible to use SMCA (Spatial Multi Criteria Analysis) for determining simultaneously where to locate various facilities? Suppose, for example, I'm planing to build a new city and everything ...
15
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1answer
174 views

Symmetric undirected $p$-median instance with fractional LP solution?

The $p$-median problem is NP-hard, so its LP relaxation does not naturally have all-integer solutions. However, it very often does; in fact, it can be hard to find an instance for which the LP ...
8
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2answers
322 views

Linear facility location problem for large size problems (police station)

Considering a set of $m$ existing weighted demand points (very large) and $n$ different-sized facilities, what is the best approach for locating new facilities to maximise coverage? I have used the ...
11
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2answers
198 views

partitioning hub assignment models

When solving large-scale hub assignment models (1000+ candidate hubs and 1000+ demand nodes), it is possible that parts of a cost matrix are not connected to one another. A typical workflow would be: ...
10
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1answer
134 views

Algorithmic gap for Hochbaum's (greedy) algorithm for (metric) uncapacitated facility location

In Jain et al. (2003)1, at the bottom of page 801, they construct an instance of (metric) uncapacitated facility location for which they claim the greedy (Hochbaum's) algorithm has gap $\Omega\left(\...
33
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4answers
808 views

Why are integer minimax problems hard?

Problems that have a minimax-type structure are notoriously hard to solve. For example, the $p$-median problem from facility location (choose $p$ facilities to minimize demand-weighted distance to ...
11
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2answers
162 views

How to quantify the “griddiness” of a set of points?

We're working on a facility location problem in which it is desirable for the facilities to be laid out as close as possible to a grid. In our problem, a lattice is overlaid on the region, and the ...