# 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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### Move circles from initial positions such that they do not overlap and total shift is minimized

I have a set of circles of varying radii residing in 2D space. Some of these circles overlap. I would like to rearrange the circles such that a) they do not overlap; and b) the total distance that the ...
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### Warehouse placement problem in

I’m curious about the warehouse placement problem. Suppose N nodes exist, each with average demand across all products (or a single product for simplicity.) the problem is to position M warehouses ...
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### Single Facility Problem

Hi, Can someone explain to me how this works or refer to any page that tells how the single facility problem works step by step?
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### Guidance on selecting locals for waste treatment installation

I am seeking guidance for a study in which I have the coordinates of 3 wastewater treatment plants (WTPs) shown in blue, and 54 farms shown in red (see the figure below). My goal is to calculate ...
833 views

### Modeling: How to force customers visit their NEAREST facility

Let set $I$ denote the facility location set, $N$ denote the customer set, and $d_{ni}, \forall n\in N, i \in I$ is the distance between customer $n$ and facility $i$. The problem is to locate ...
727 views

### Writing a constraint of an integer programming in a linear form

I modeled an optimization problem in an integer programming format. The main constraint I came up with is now nonconvex. I would like to see if there is another equivalent formulation in which the ...
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### Modelling a Capacitated Facility Location Problem in such a way that a few candidate locations are always selected

I am trying to model a MIP for a Capacitated Facility Location problem in a way that a number of selected candidate locations will always be there. How can I model it? My approach: Add a cost ...
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1 vote
147 views

### How to model this problem?

I have recently tasked with a problem in which I have to locate electric vehicle charging points (new) keeping in mind that there continue to exist older charging points. The problem is to model the ...
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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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### 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 ...
102 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 ...
147 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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### 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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Please explain how the problem solution looks like. basically I want model to dynamically give me multiple facility locations for a given demand.
178 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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### 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 ...
357 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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1 vote
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### 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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1 vote
60 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, ...
52 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?
170 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 ...
173 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
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### 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 ...
280 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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### 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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### 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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### 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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### 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
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
81 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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### 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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### 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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### 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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