scholarly journals The capacitated maximal covering location problem with heterogeneous facilities and vehicles and different setup costs: An effective heuristic approach

2021 ◽  
pp. 79-90 ◽  
Author(s):  
Masoud Hatami Gazani ◽  
Seyed Armin Akhavan Niaki ◽  
Seyed Taghi Akhavan Niaki
Keyword(s):  
Location Problem ◽  
Heuristic Method ◽  
Optimal Solution ◽  
Heuristic Approach ◽  
Mixed Integer ◽  
Solution Technique ◽  
Maximal Covering ◽  
Setup Costs ◽  
Constructive Heuristic ◽  
Solution Methods

In this research, a maximal covering location problem (MCLP) with real-world constraints such as multiple types of facilities and vehicles with different setup costs is taken into account. An original mixed integer linear programming (MILP) model is constructed in order to find the optimal solution. Since the problem at hand is shown to be NP-hard, a constructive heuristic method and a meta-heuristic approach based on genetic algorithm (GA) are developed to solve the problem. To find the most effective solution technique, a set of problems of different sizes is randomly generated and solved by the proposed solution methods. Computational results demonstrate that the heuristic method is capable of producing optimal or near-optimal solutions in a rational execution time.

scholarly journals Solving methods for the quay crane scheduling problem at port of Tripoli-Lebanon.

2020 ◽  
Author(s):  
Ali Skaf ◽  
Sid Lamrous ◽  
Zakaria Hammoudan ◽  
Marie-Ange Manier
Keyword(s):  
Dynamic Programming Algorithm ◽  
Heuristic Method ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Exact Methods ◽  
Three Solutions ◽  
Quay Crane Scheduling ◽  
Crane Scheduling

The quay crane scheduling problem (QCSP) is a global problem and all ports around the world seek to solve it, to get an acceptable time of unloading containers from the vessels or loading containers to the vessels and therefore reducing the docking time in the terminal. This paper proposes three solutions for the QCSP in port of Tripoli-Lebanon, two exact methods which are the mixed integer linear programming and the dynamic programming algorithm, to obtain the optimal solution and one heuristic method which is the genetic algorithm, to obtain near optimal solution within an acceptable CPU time. The main objective of these methods is to minimize the unloading or the loading time of the containers and therefore reduce the waiting time of the vessels in the terminals. We tested and validated our methods for small and large random instances. Finally, we compared the results obtained with these methods for some real instances in the port of Tripoli-Lebanon.

Planar Maximal Covering Location Problem with Inclined Ellipses

2011 ◽  
Vol 110-116 ◽  
pp. 4861-4866
Author(s):  
Hadi Charkhgard ◽  
Mohammad R. Akbari Jokar
Keyword(s):  
Nonlinear Programming ◽  
Heuristic Algorithm ◽  
Location Problem ◽  
Mixed Integer Nonlinear Programming ◽  
Mixed Integer ◽  
Running Time ◽  
Maximal Covering ◽  
Wireless Transmitter ◽  
Integer Nonlinear Programming ◽  
Comparison Of The Results

aximum coverage location problem is considered in this study. Extension of this problem is investigated for situations that coverage areas are elliptical; these ellipses can locate anywhere on the plane with any angle. Mixed integer nonlinear programming (MINLP) is applied for formulation. This problem can be used in many practical situations such as locating wireless transmitter towers. A heuristic algorithm named MCLPEA for solving this problem was designed. This algorithm can produce very good results in efficient running time. Finally, the comparison of the results for this study was carried done.

scholarly journals A Hybrid Approach Using an Artificial Bee Algorithm with Mixed Integer Programming Applied to a Large-Scale Capacitated Facility Location Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Guillermo Cabrera G. ◽  
Enrique Cabrera ◽  
Ricardo Soto ◽  
L. Jose Miguel Rubio ◽  
Broderick Crawford ◽  
...  
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Large Scale ◽  
Location Problem ◽  
Hybrid Approach ◽  
Optimal Solution ◽  
Facility Location Problem ◽  
Mixed Integer ◽  
Capacitated Facility Location Problem ◽  
Capacitated Facility Location

We present a hybridization of two different approaches applied to the well-known Capacitated Facility Location Problem (CFLP). The Artificial Bee algorithm (BA) is used to select a promising subset of locations (warehouses) which are solely included in the Mixed Integer Programming (MIP) model. Next, the algorithm solves the subproblem by considering the entire set of customers. The hybrid implementation allows us to bypass certain inherited weaknesses of each algorithm, which means that we are able to find an optimal solution in an acceptable computational time. In this paper we demonstrate that BA can be significantly improved by use of the MIP algorithm. At the same time, our hybrid implementation allows the MIP algorithm to reach the optimal solution in a considerably shorter time than is needed to solve the model using the entire dataset directly within the model. Our hybrid approach outperforms the results obtained by each technique separately. It is able to find the optimal solution in a shorter time than each technique on its own, and the results are highly competitive with the state-of-the-art in large-scale optimization. Furthermore, according to our results, combining the BA with a mathematical programming approach appears to be an interesting research area in combinatorial optimization.

scholarly journals Multi-Period Maximal Covering Location Problem with Capacitated Facilities and Modules for Natural Disaster Relief Services

2021 ◽  
Vol 11 (1) ◽  
pp. 397
Author(s):  
Roghayyeh Alizadeh ◽  
Tatsushi Nishi ◽  
Jafar Bagherinejad ◽  
Mahdi Bashiri
Keyword(s):  
Lower Bounds ◽  
Large Scale ◽  
Location Problem ◽  
Disaster Relief ◽  
Heuristic Method ◽  
Real Life ◽  
Planning Horizon ◽  
Upper Bounds ◽  
Maximal Covering ◽  
Large Scale Problems

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds—(LR1) and (LR2)—and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small- and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process.

scholarly journals The Electric Riverboat Charging Station Location Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Daniel Villa ◽  
Alejandro Montoya ◽  
Aura Maria Herrera
Keyword(s):  
Rural Areas ◽  
Urban Areas ◽  
Location Problem ◽  
Optimal Solution ◽  
Nonlinear Behavior ◽  
Electric Mobility ◽  
Mixed Integer ◽  
Viability Analysis ◽  
Charging Station ◽  
Station Location

Nowadays, the electric mobility is mainly focused on urban areas. However, the use of Photovoltaic-assisted Charging Stations (PVCSs) can contribute to implement the electric mobility in rural areas disconnected from the national grid. Inspired by the new river operations with an Electric Boat (EB), we introduce a new location problem named the Electric Riverboat Charging Station Location Problem (ERCSLP). This problem estimates the necessary infrastructure for an EB to be able to perform a round trip. In this case, we decide the location of the PVCSs and the size of the EB battery aiming to minimize the sum of the PVCS and the EB battery costs. In this problem, we include the nonlinear behavior of the charging function and the variation of the solar radiation. For solving this problem, we propose a Mixed-Integer Linear Programming (MILP) formulation. For testing this MILP formulation, we build a set of instances based on real river transport operations that have the potential to migrate to the electric mobility. In our computational experiments, we show that our MILP formulation can find the optimal solution of the instances. Finally, we perform a sensitivity analysis and an economic viability analysis of the electric mobility in these operations.

scholarly journals A Decomposition Heuristic for the Maximal Covering Location Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Edson Luiz França Senne ◽  
Marcos Antonio Pereira ◽  
Luiz Antonio Nogueira Lorena
Keyword(s):  
Location Problem ◽  
Optimal Solution ◽  
Real Data ◽  
Upper Bounds ◽  
Location Problems ◽  
Exact Methods ◽  
Maximal Covering ◽  
Facility Locations ◽  
Coupling Constraints ◽  
Partitioning Technique

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, are identified and relaxed in the Lagrangean way, resulting in disconnected subgraphs representing smaller subproblems that are computationally easier to solve by exact methods. The proposed technique is compared to the classical approach, using real data and instances from the available literature.

scholarly journals Two-Agent Single Machine Order Acceptance Scheduling Problem to Maximize Net Revenue

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jiaji Li ◽  
Yuvraj Gajpal ◽  
Amit Kumar Bhardwaj ◽  
Huangen Chen ◽  
Yuanyuan Liu
Keyword(s):  
Single Machine ◽  
Heuristic Method ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Order Acceptance ◽  
Net Revenue ◽  
Problem Instances ◽  
Tardy Jobs

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed-integer linear programming (MILP) formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization (PSO) is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic.

scholarly journals Mixed-integer programming approaches for the time-constrained maximal covering routing problem

OR Spectrum ◽  
2021 ◽  
Author(s):  
Markus Sinnl
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Valid Inequalities ◽  
Optimal Solution ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Routing Problem ◽  
Maximal Covering ◽  
Solution Algorithms ◽  
Number Of Customers

AbstractIn this paper, we study the recently introduced time-constrained maximal covering routing problem. In this problem, we are given a central depot, a set of facilities, and a set of customers. Each customer is associated with a subset of the facilities which can cover it. A feasible solution consists of k Hamiltonian cycles on subsets of the facilities and the central depot. Each cycle must contain the depot and must respect a given distance limit. The goal is to maximize the number of customers covered by facilities contained in the cycles. We develop two exact solution algorithms for the problem based on new mixed-integer programming models. One algorithm is based on a compact model, while the other model contains an exponential number of constraints, which are separated on-the-fly, i.e., we use branch-and-cut. We also describe preprocessing techniques, valid inequalities and primal heuristics for both models. We evaluate our solution approaches on the instances from literature and our algorithms are able to find the provably optimal solution for 267 out of 270 instances, including 123 instances, for which the optimal solution was not known before. Moreover, for most of the instances, our algorithms only take a few seconds, and thus are up to five magnitudes faster than previous approaches. Finally, we also discuss some issues with the instances from literature and present some new instances.

scholarly journals A Convex Optimization Algorithm for Electricity Pricing of Charging Stations

Algorithms ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 208 ◽  
Author(s):  
Jing Zhang ◽  
Xiangpeng Zhan ◽  
Taoyong Li ◽  
Linru Jiang ◽  
Jun Yang ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Optimization Algorithm ◽  
Model Simulation ◽  
Heuristic Method ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Electricity Pricing ◽  
Convex Optimization Problem ◽  
Low Efficiency ◽  
Charging Stations

The problem of electricity pricing for charging stations is a multi-objective mixed integer nonlinear programming. Existing algorithms have low efficiency in solving this problem. In this paper, a convex optimization algorithm is proposed to get the optimal solution quickly. Firstly, the model is transformed into a convex optimization problem by second-order conic relaxation and Karush–Kuhn–Tucker optimality conditions. Secondly, a polyhedral approximation method is applied to construct a mixed integer linear programming, which can be solved quickly by branch and bound method. Finally, the model is solved many times to obtain the Pareto front according to the scalarization basic theorem. Based on an IEEE 33-bus distribution network model, simulation results show that the proposed algorithm can obtain an exact global optimal solution quickly compared with the heuristic method.

Modeling and solution of maximal covering problem considering gradual coverage with variable radius over multi-periods

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1245-1260 ◽  
Author(s):  
Alireza Eydi ◽  
Javad Mohebi
Keyword(s):  
Simulated Annealing ◽  
Facility Location ◽  
Location Problem ◽  
Simulated Annealing Algorithm ◽  
Mixed Integer ◽  
Multiple Time ◽  
Variable Radius ◽  
Maximal Covering ◽  
Annealing Algorithm ◽  
Time Periods

Facility location is a critical component of strategic planning for public and private firms. Due to high cost of facility location, making decisions for such a problem has become an important issue which have gained a large deal of attention from researchers. This study examined the gradual maximal covering location problem with variable radius over multiple time periods. In gradual covering location problem, it is assumed that full coverage is replaced by a coverage function, so that increasing the distance from the facility decreases the amount of demand coverage. In variable radius covering problems, however, each facility is considered to have a fixed cost along with a variable cost which has a direct impact on the coverage radius. In real-world problems, since demand may change over time, necessitating relocation of the facilities, the problem can be formulated over multiple time periods. In this study, a mixed integer programming model was presented in which not only facility capacity was considered, but also two objectives were followed: coverage maximization and relocation cost minimization. A metaheuristic algorithm was presented to solve the maximal covering location problem. A simulated annealing algorithm was proposed, with its results presented. Computational results and comparisons demonstrated good performance of the simulated annealing algorithm.

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