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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The significance of infeasibility for a Capacitated Facility Location Problem

I am modelling a capacitated facility location problem in R with the ompr package. When I am removing the Capacity constraint, ...
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3 votes
2 answers
127 views

Designing a multi-commodity network flow optimizer

I'm trying to solve multi commodity multi source network flow optimization problem using Python-PuLP. Here is how my problem looks like: The numbers on the arcs represent the order of priority a ...
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3 votes
0 answers
81 views

What is the general name (e.g. facility location problem) for this problem (if any)?

I would like to know if there is a general name for the following problem: We will open several facilities. Each facility has an associated facility type. There exists a given number of facility ...
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2 votes
1 answer
69 views

Capacitated Facility Location problem with a dynamic set up cost

I am trying to solve a Capacitated Facility Location Problem (CFLP) with a dynamic setup cost in R. The problem statement is this: I have the transport cost The ...
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2 votes
0 answers
52 views

Two-stage stochastic with non-linear recourse

I am working on a two-stage facility location problem as I described in this question. I am solving it with the L-shaped method (Benders decomposition). The cost value between each $(i,j)$ is a ...
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  • 429
-3 votes
1 answer
49 views

What is dynamic facility location problem ans how to formulate the same? Please help [closed]

Please explain how the problem solution looks like. basically I want model to dynamically give me multiple facility locations for a given demand.
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7 votes
1 answer
171 views

How to enforce a relation between two variables

I am having trouble formulating the following constraint: I am looking to formulate a constraint that if a facility was opened at some point in time, then $Y[j,t]$ does always have to be $1$ from that ...
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3 votes
1 answer
95 views

A tricky Bi-Level Location Problem using VISUM

I'm writing my thesis on the optimal location of Air-Taxi Stations. I'm using PTV VISUM for the transport model where I'll inherit the Origin-Destination demand matrix. I come from transportation ...
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3 votes
1 answer
142 views

Stochastic Facility Location Model

I am solving a stochastic facility location model using Benders decomposition (L-shaped algorithm). In each scenario, I want to allocate demands from origin to a fixed number of closest open ...
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  • 429
1 vote
2 answers
66 views

Prioritizing a special group in Facility Location problem

I am working on a facility location problem where I want to allocate a mix of vulnerable and non-vulnerable people to the facilities. I want to make sure that most or all vulnerable people will be ...
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  • 429
1 vote
0 answers
56 views

Why use the discrete demand setting at all?

Currently, I am working on facility location problems and I noticed why we use discrete demand setting at all. If the problem is to allocate customers to a facility and we have millions of customers, ...
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3 votes
0 answers
47 views

Popup facility location

I was searching through articles for popup facility location and could not find anything devoted to it. If anyone has come across it, can someone guide me to some papers?
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2 votes
1 answer
129 views

Demand allocation to facilities

I'm facing the following problem as I am trying to model a problem where people visit facilities according to their age and per a time horizon. Additionally, I am trying to allocate specific commodity ...
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1 vote
1 answer
82 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. ...
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1 vote
0 answers
66 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 ...
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5 votes
0 answers
120 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 ...
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2 votes
1 answer
51 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 ...
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4 votes
1 answer
76 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 ...
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  • 379
3 votes
1 answer
74 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\}\...
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  • 33
6 votes
0 answers
63 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 ...
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1 vote
1 answer
82 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 ...
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  • 415
9 votes
2 answers
364 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 ...
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  • 1,229
3 votes
1 answer
206 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 ...
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  • 141
3 votes
0 answers
62 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 ...
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  • 507
2 votes
1 answer
99 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 ...
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3 votes
2 answers
96 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 ...
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  • 507
4 votes
1 answer
117 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 ...
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  • 173
2 votes
1 answer
81 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 ...
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9 votes
1 answer
73 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 ...
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15 votes
1 answer
176 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 ...
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8 votes
2 answers
349 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 ...
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  • 159
11 votes
2 answers
231 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: ...
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  • 1,059
10 votes
1 answer
166 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(\...
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  • 569
33 votes
4 answers
937 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 ...
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11 votes
2 answers
166 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 ...
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