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A model for combination of set covering and network connectivity in facility location. Rana Afzali and Shaghayegh Parhizi. Introduction Set Covering Network Connectivity Model Formulation Case Study Conclusion Future Works.

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a model for combination of set covering and network connectivity in facility location

A model for combination of set covering and network connectivity in facility location

RanaAfzali and ShaghayeghParhizi

slide2
A model for combination of set covering and network connectivity
  • Introduction
  • Set Covering
  • Network Connectivity
  • Model Formulation
  • Case Study
  • Conclusion
  • Future Works
slide3
A model for combination of set covering and network connectivity
  • One of the classical objectives in location modeling is “coverage”.
  • In many optimization problems in networking ,connectivity is a main requirement.
slide4
A model for combination of set covering and network connectivity
  • Both of these two models have been studied a lot separately, but the studies which consider these two together are rare.
  • Goal: Minimizing the total Cost ,subject to two main constraints
        • covering and connectivity.
slide5
A model for combination of set covering and network connectivity
  • The problem of locating sensors to minimize the total cost with covering demands points by using sensors while all sensors are connected to each other is considered.
        • where to put sensors
        • Each demand point is covered by which sensor
        • How sensors are connected to each other
set covering
A model for combination of set covering and network connectivity SET COVERING
  • Ensure that each customer considered to be “served” by a set of facilities has a facility within reasonable travel distance.
  • Introduced by Church and ReVelle(1974)
  • Many applications such as location of emergency services, the location of retail facilities and signal-transmission facilities (cell-phone towers, light standards, etc.)
netwok connectivity
A model for combination of set covering and network connectivity NETWOK CONNECTIVITY
  • several optimization problems with many applications, in which the network connectivity is a requirement.
  • One of those problems is the minimum cost spanning tree problem. The goal is to find a minimum cost connected subgraph of a network
  • spanning tree of the graph is a connected subgraph in which there are no cycles
minimal spanning tree

Four of the spanning trees of the graph

A model for combination of set covering and network connectivity

Minimal Spanning Tree
changing continuous region to discrete
A model for combination of set covering and network connectivity CHANGING CONTINUOUS REGION TO DISCRETE
  • feasible region for sitting sensors is continuous
  • We define the potential nodes as nodes belonging to the network intersect point set .Any point on the network that is r distance away from demand point i∈ N is a NIP. The NIPS is the set of all NIPs plus all demand points.
changing continuous region to discrete1
A model for combination of set covering and network connectivity CHANGING CONTINUOUS REGION TO DISCRETE

Define (a, x, b) a non-nodal point at a distance of x from node a on link (a, b)

When r =4,

the NIPS is {1, 2, 3, (1, 2, 2), (1, 4, 2), (2, 4, 3), (2, 6, 3), (1, 2, 3), (1, 4, 3)}.

model formulation

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A model for combination of set covering and network connectivity

MODEL FORMULATION
  • The goal :minimizing the total cost
        • cost of locating facilities
        • cost of connecting the facilities
problem size
A model for combination of set covering and network connectivity Problem Size
  • This model can solve a problem in size of 300 potential points and 500 demand points.
numerical example
A model for combination of set covering and network connectivity Numerical Example
  • Locating sensors in 20 potential capitals of states to cover all states in USA
sensitivity analysis
A model for combination of set covering and network connectivity Sensitivity Analysis
  • parameters :radius coverage and the cost of locating and connecting the facilities.
conclusion
A model for combination of set covering and network connectivity Conclusion
  • Solving a problem of a combination of set covering and network connectivity problems.
  • Developing a model
  • Applying the model for a real case
future work
A model for combination of set covering and network connectivity Future Work
  • A more reasonable model would have a gradual decline in the coverage frequency as a function of distance from the sensor.
  • Difference if demand points cover by one sensor or more.
  • Consider coverage radius as a decision variable
future work1
A model for combination of set covering and network connectivity Future Work
  • Developing heuristic
  • Using Meta-heuristics for solving the problem in Large-size