scholarly journals Optimization Model Based on Reachability Guarantee for Emergency Facility Location and Link Reinforcement

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wuyang Yu ◽  
Jijun Liu
Keyword(s):  
Facility Location ◽  
Optimization Model ◽  
Location Problem ◽  
Flow Problem ◽  
Transportation Network ◽  
Operating Cost ◽  
Facility Location Problem ◽  
Demand Point ◽  
Limited Budget ◽  
Biobjective Optimization

The reasonable location of emergency facilities plays an important role in both predisaster service and postdisaster relief. Moreover, damage to the transportation network often affects the accessibility of demand points, which can seriously hamper timely rescue operations. Reasonable location of emergency facilities and reinforcement of fragile roads are two important strategies to improve the reachability of demand points. In this paper, we proposed a biobjective optimization model to determine locations of emergency facilities and links to be reinforced given a limited budget. Each demand point is allocated a primary facility and a backup facility, the former can provides normal service, and the latter is prepared for postdisaster relief. One goal of the model is to minimize the operating cost of normal services, and another goal is to maximize the reachability guarantee of demand points. The novelty and contribution of this paper are that we defined the reachability by introducing damage tolerance instead of link failure probability. Based on this, we defined the reachability guarantee to deal with the worst scenario of disasters. By embedding the max-flow problem of the reachability guarantee into the emergency facility location problem, the locations of emergency facilities and links to be reinforced can be determined simultaneously. The methodology is applied to a simplified Sioux Falls transportation network. Results such as the trade-off curve of two goals, budget efficiency, and the effect of reinforcement demonstrated the effectiveness of the model.

scholarly journals Mathematical Programming Model for the Two-Level Facility Location Problem: The Case of Tanzanian Emergence Maize Distribution Network for 2004–2010 Maize Data

2021 ◽  
Vol 47 (3) ◽  
pp. 1020-1032
Author(s):  
Said A Sima
Keyword(s):  
Mathematical Programming ◽  
Facility Location ◽  
Location Problem ◽  
Programming Model ◽  
Transportation Network ◽  
Distribution Network ◽  
Facility Location Problem ◽  
Optimal Location ◽  
Mathematical Programming Model ◽  
Maize Crop

A two-level facility location problem (FLP) has been studied in the transportation network of emergence maize crop in Tanzania. The facility location problem is defined as the optimal location of facilities or resources so as to minimize costs in terms of money, time, distance and risks with the relation to supply and demand points. Distribution network design problems consist of determining the best way to transfer goods from the supply to the demand points by choosing the structure of the network such that the overall cost is minimized. The three layers, namely production centres (PCs), distribution centres (DCs) and customer points (CPs) are considered in the two-level FLP. The flow of maize from PCs to CPs through DCs is designed at a minimum cost under deterministic mathematical programming model. The four decisions to be made simultaneously are: to determine the locations of DCs (including number of DCs), allocation of CPs to the selected DCs, allocation of selected DCs to PCs, and to determine the amount of maize crop transported from PCs to DCs and then from DCs to CPs. The modelled problem generated results through optimization with respect to optimal location-allocation strategies. The results of the optimized network shows the improvement in costs saving compared to the manually operated existing network. The results show the costs saving of up to 18% which is equivalent to $2,910 thousand (TZS 2.9 billion). Keywords:    Optimization; Maize crop; Transportation network; Deterministic model; Facility location

scholarly journals Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Eiman J. Alenezy
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Demand Point ◽  
Problem Size ◽  
Lagrangian Decomposition ◽  
Capacitated Facility Location Problem ◽  
Capacitated Facility Location ◽  
Volume Algorithm ◽  
Optimum Solution

In this research, we will focus on one variant of the problem: the capacitated facility location problem (CFLP). In many formulations of the CFLP, it is assumed that each demand point can be supplied by only one open facility, which is the simplest case of the problem. We consider the case where each demand point can be supplied by more than one open facility. We first investigate a Lagrangian relaxation approach. Then, we illustrate in the problem decomposition how to introduce tighter constraints, which solve the CFLP faster while achieving a better quality solution as well. At the same time, we apply the volume algorithm to improve both the lower and the upper bound on the optimum solution of the original problem for the large problem size.

scholarly journals Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wuyang Yu
Keyword(s):  
Robust Control ◽  
Facility Location ◽  
Optimization Model ◽  
Control Parameter ◽  
Location Problem ◽  
Facility Location Problem ◽  
Mixed Integer ◽  
Proportional Rule ◽  
Competitive Facility Location ◽  
Robust Model

When consumers faced with the choice of competitive chain facilities that offer exclusive services, current rules cannot describe these customers’ behaviors very well. So we propose a partially proportional rule to represent this kind of customer behavior. In addition, the exact demands of customers in many real-world environments are often difficult to determine. This is contradicting to the assumption in most studies of the competitive facility location problem. For the competitive facility location problem with the partially proportional rule, we establish a robust optimization model to handle the uncertainty of customers’ demands. We propose two methods to solve the robust model by studying the properties of the counterpart problem. The first method MIP is presented by solving a mixed-integer optimization model of the counterpart problem directly. The second method SAS is given by embedding a sorting subalgorithm into the simulated annealing framework, in which the sorting subalgorithm can easily solve the subproblem. The effects of the budget and the robust control parameter to the location scheme are analyzed in a quasi-real example. The result shows that changes in the robust control parameter can affect the customer demands that were captured by the new entrants, thereby changing the optimal solution for facility location. In addition, there is a threshold of the robust control parameter for any given budget. Only when the robust control parameter is larger than this threshold, the market share captured by the new entering firm increases with the increases of this parameter. Finally, numerical experiments show the superiority of the algorithm SAS in large-scare competitive facility location problems.

scholarly journals On a Leasing Variant of the Online Connected Facility Location Problem

2018 ◽  
Author(s):  
Murilo Santos De Lima ◽  
Mário César San Felice ◽  
Orlando Lee
Keyword(s):  
Facility Location ◽  
Optimization Model ◽  
Location Problem ◽  
Facility Location Problem ◽  
Scaling Factor ◽  
Total Cost ◽  
Connected Facility Location ◽  
Time Periods

In the leasing optimization model, resources are leased for K different time periods, instead of being acquired for unlimited duration. The goal is to use these temporary resources to maintain a dynamic infrastructure that serves n requests while minimizing the total cost. We propose and study a leasing variant of the online connected facility location problem, which we call the online connected facility leasing problem. In this problem each client that arrives must be connected to a temporary facility, which in turn must be connected to a root facility using permanent edges. We present an algorithm that is O(K · lg n)-competitive if the scaling factor is M = 1.  

scholarly journals Dispersing Obnoxious Facilities on a Graph

Algorithmica ◽  
2021 ◽  
Author(s):  
Alexander Grigoriev ◽  
Tim A. Hartmann ◽  
Stefan Lendl ◽  
Gerhard J. Woeginger
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Unit Length ◽  
Facility Location Problem ◽  
Np Hard ◽  
Obnoxious Facilities ◽  
Rational Parameter ◽  
Polynomially Solvable

AbstractWe study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance $$\delta$$ δ from each other. We investigate the complexity of this problem in terms of the rational parameter $$\delta$$ δ . The problem is polynomially solvable, if the numerator of $$\delta$$ δ is 1 or 2, while all other cases turn out to be NP-hard.

Sign in / Sign up

Export Citation Format

Share Document