Multi-level Facility Location Research Articles

Joint Location–Allocation Model for Multi-Level Maintenance Service Network in Agriculture

The maintenance service network is always designed as a multi-level service network to provide timely maintenance service for failed machinery, and is rarely studied in agriculture. Thus, this paper focuses on a three-level maintenance service network location–allocation problem in agriculture, which contains several spare part centres, service stations, and service units. This research aims to obtain the optimal location of spare part centres and service stations while determining service vehicle allocation results for service stations, and the problem can be called a multi-level facility location and allocation problem (MLFLAP). Considering contiguity constraints and hierarchical relationships, the proposed MLFLAP is formulated as a mixed-integer linear programming (MILP) model integrating with P-region and set covering location problems to minimize total service costs, including spare part centre construction costs, service vehicle usage costs, and service mileage costs of service stations. The Benders decomposition-based solution method with several improvements is then applied to decompose the original MLFLAP into master problem and subproblems to find the optimal solutions effectively. Finally, a real-world case in China is proposed to evaluate the performance of the model and algorithm in agriculture, and sensitivity analysis is also conducted to demonstrate the impact of several parameters.

The multilevel facility location and pricing problems: the computational complexity and the stability analysis

The multilevel facility location and pricing problems: the computational complexity and the stability analysis

An approximation algorithm for stochastic multi-level facility location problem with soft capacities

Facility location problem is one of the most important problems in the combinatorial optimization. The multi-level facility location problem and the facility location with capacities are important variants for the classical facility location problem. In this work, we consider the multilevel facility location problem with soft capacities in the uncertain scenario. The uncertainty setting means the location process is stochastic. We consider a two-stage model. The soft-capacities setting means each facility has multiple capacities by paying multiple opening cost. The multi-level setting means the client needs to connect to a path. We propose a bifactor $$ (1/\alpha ,6/(1-2\alpha ) )$$-approximation algorithm for the stochastic multi-level facility location problem (SMLFLP), where $$ \alpha \in (0,0.5) $$ is a given constant. Then, we reduce the stochastic multi-level facility location problem with soft capacities to SMLFLP. The reduction implies a $$ \left( 1/\alpha + 6/(1-2\alpha ) \right) $$-approximation algorithm. The ratio is 14.9282 when setting $$ \alpha = 0.183 $$.

Multi-level facility location-allocation problem for post-disaster humanitarian relief distribution

PurposePreviously use of drones as a relief distribution vehicle was studied in several studies where required number of drones and the best locations for the relief centers were investigated. The maximum travel distance of drones without a need to recharge is limited by their endurance. Recharge stations can be used to extend the coverage area of the drones. The purpose of this paper is to find the best topology for both relief centers and recharge stations to cover a large-scale area with minimum and feasible incurred costs and waiting times.Design/methodology/approachA multi-level facility location problem (FLP) is utilized to find the optimum number of relief centers and refuel stations and their locations. It is supposed that the demand occurs according to Poisson distribution. The allocation of the demand is based on nearest neighborhood method. A hybrid genetic algorithm is proposed to solve the model. The performance of the algorithm is examined through a case study.FindingsThe proposed method delivers increased efficiency and responsiveness of the humanitarian relief system. The coverage area of the drones is extended by refuel stations, total costs of the system are reduced and the time to respond an emergency, which is an important factor in survival rate, is significantly decreased.Originality/valueThis study proposes a multi-level FLP to simultaneously account for recharge stations, relief centers and the number of required drones to cover all the demand for relief in a post-disaster period.

A congested capacitated multi-level fuzzy facility location problem: An efficient drone delivery system

Online retailers invest an enormous amount of funds in delivering products to customers. In recent years, these delivery costs have increased as a result of changes in fuel costs, which has brought new challenges to retailers in terms of offering competitive prices. Many retailers have begun to utilize a drone-based aerial delivery system as an alternative solution to overcome the problems related to the high transportation costs and traffic jams in large cities. This study provides a mathematical model for minimizing the total costs of the aerial delivery system concerned with refuel stations, warehouses, drone procurement, and transportation. The waiting time of the customers is restricted based on the M/G/K queueing system. The fuel stations and warehouses are the main components of the network. The demand (occurring at the lowest level) is ultimately satisfied via launch stations (the network's highest level). Refuel stations support drones along their long routes between the launch stations and demand points. To account for the different levels of the facilities, a multi-level facility location approach is utilized. Moreover, the nondeterministic nature of the problem is tackled using fuzzy variables. The ultimate mathematical model is a congested fuzzy capacitated multi-level facility location problem that is solved by the possibilistic approach.

Preface: advances in theoretical and practical combinatorial optimization

Preface: Advances in Theoretical and Practical Combinatorial Optimization Said Salhi1, Richard Eglese2, Eleni Hadjiconstantinou3 This issue consists of research papers dedicated, though not limited, to the International Symposium in Combinatorial Optimisation (CO2016), chaired by Said Salhi and held at the University of Kent, Canterbury, 1-3 September 2016. Of the many good papers it attracted, 35 were considered suitable for the next stage of review, resulting in 20 being accepted mostly after two rounds of reviews. We divided the issue into three parts, each covering a wider though well-defined area within combinatorial optimization (CO). These three parts, which are not completely distinct, are referred to for simplicity as Mathematically-Oriented (MO), Heuristically-Based (HB) and Practically-Focussed (PF). MO contains seven papers. These include a paper on the integration of network flows in a coloring algorithm by Koster, Scheidweiler, and Tieves; one on a polynomial time algorithm for the minimum flow problem by Khodayifar, Raayatpanah, and Pardalos, and one on a formulation in multi-level capacitated facility location by Irawan and Jones. A.Salhi, Alsoufi, and Yang provide a mixed integer program combined with an evolutionary approach for seaside operations in container ports, while Zare, Borrero, Zeng and Prokopyev have contributed a note on new linearized formulations in bilevel linear integer problems. Fuzzy logic is explored for portfolio optimization by Liagkouras and Metaxiotis, and for supplier selection by Chang. HB covers six papers. Azizi, using a genetic algorithm, explores hub and spoke networks under disruption. Knust and Xie produce a simulated annealing algorithm for nurse rostering, while Pei, Cheng, Liu, Pardalos, and Kong investigate Variable Neighbourhood Search (VNS) for single and parallel machine serial batching. A skewed VNS is adopted by Derbel, Jarbaoui, and Bhiri for the heterogeneous fleet vehicle routing problem, and an ascent-escent VNS for the detection of community (cluster) structures in a network is discussed by Džamic, Aloise, and Mladenovic. The last paper in this category is by Brimberg, Mladenovic, Todosijevic, and Urosevic, who investigate the capacitated clustering problem using a variant of VNS. PF has seven papers that treat inspiring implementations of CO for real-life applications. For example, in the area of scheduling, the use of spare parts in vessel maintenance is dealt with by Kian, Bektas, and Ouelhadj, while shift scheduling for power station staff is explored by Shuib and Kamarudin. The avoidance of obstacles in off shore wind farms is optimized by Klein and Haugland, and the costing of a product within a supply chain is performed by de Matta. In the health area, the maximization of the expected number of kidney transplants is performed by Alvelos, Klimentova, and Viana; a preventive health care network is designed by Davari; and the layout of an operating theater is produced by Chraibi, Osman, and Kharraja. Finally, we are grateful to Professor E. Boros for trusting our academic judgment in acting as guest editors of the Annals of Operations Research special issue devoted, but not restricted, to CO2016. We are also thankful to the managing editor, Katie D’Agosta, for her patience and valuable support in preparing this special issue. 1 Centre for Logistics and Heuristic Optimisation, Kent Business School, University of Kent, Canterbury, UK 2 Lancaster University Management School, Lancaster, UK 3 School of Business and Law, Frederick University Cyprus, Cyprus.

Multi-level facility location as the maximization of a submodular set function

In this paper we model the multi-level uncapacitated facility location problem as two different combinatorial optimization problems. The first model is the classical representation of the problem which uses a set of vertices as combinatorial objects to represent solutions whereas in the second model we propose the use of a set of paths. An interesting observation is that the real-valued set function associated with the first combinatorial problem does not satisfy the submodular property, whereas the set function associated with the second problem does satisfy this property. This illustrates the fact that submodularity is not a property intrinsic to an optimization problem but rather to its mathematical representation.

Primal–dual approximation algorithm for the two-level facility location problem via a dual quasi-greedy approach

The main contribution of this work is to propose a primal–dual combinatorial 3(1+ε)-approximation algorithm for the two-level facility location problem (2-LFLP) by exploring the approximation oracle concept. This result improves the previous primal–dual 6-approximation algorithm for the multilevel facility location problem, and also matches the previous primal–dual approximation ratio for the single-level facility location problem. One of the major merits of primal–dual type algorithms is their easy adaption to other variants of the facility location problems. As a demonstration, our primal–dual approximation algorithm can be easily adapted to several variants of the 2-LFLP, including models with stochastic scenario, dynamically arrived demands, and linear facility cost.

An Improved Genetic Algorithm for the Multi Level Uncapacitated Facility Location Problem

In this paper, an improved genetic algorithm (GA) for solving the multi-level uncapacitated facility location problem (MLUFLP) is presented. First improvement is achieved by better implementation of dynamic programming, which speeds up the running time of the overall GA implementation. Second improvement is hybridization of the genetic algorithm with the fast local search procedure designed specially for MLUFLP. The experiments were carried out on instances proposed in the literature which are modied standard single level facility location problem instances. Improved genetic algorithm reaches all known optimal and the best solutions from literature, but in much shorter time. Hybridization with local search improves several best-known solutions for large-scale MLUFLP instances, in cases when the optimal is not known. Overall running time of both proposed GA methods is signicantly shorter compared to previous GA approach.

A splitter location–allocation problem in designing fiber optic access networks

This paper deals with a physical access network design problem of fiber-to-the-home passive optical network (FTTH-PON). The design of FTTH-PON access network seeks the cost effective location of optical splitters that provide optical connectivity from central office to subscribers in a given service area. We formulate the problem as a multi-level capacitated facility location problem on a tree topology with nonlinear link cost. Dealing with the nonlinear link cost, we propose an objective function relaxation approach to obtain tight upper and lower bounds. We develop valid inequalities that enhance the lower bound and propose a local search heuristic procedure that improves the upper bound. Valid inequalities force integrality condition on the number of splitters placed at nodes. Local search heuristic improves the initial greedy solution by placing splitters on the sub-root nodes of a given tree network. Computational results demonstrate the effectiveness of the proposed solution procedures.

A new approximation algorithm for the multilevel facility location problem

In this paper we propose a new integer programming formulation for the multilevel facility location problem and a novel 3-approximation algorithm based on LP-rounding. The linear program that we use has a polynomial number of variables and constraints, thus being more efficient than the one commonly used in the approximation algorithms for these types of problems.

Approximate hierarchical facility location and applications to the bounded depth Steiner tree and range assignment problems

The paper concerns a new variant of the hierarchical facility location problem on metric powers ( HFL β [ h ] ), which is a multi-level uncapacitated facility location problem defined as follows. The input consists of a set F of locations that may open a facility, subsets D 1 , D 2 , … , D h − 1 of locations that may open an intermediate transmission station and a set D h of locations of clients. Each client in D h must be serviced by an open transmission station in D h − 1 and every open transmission station in D l must be serviced by an open transmission station on the next lower level, D l − 1 . An open transmission station on the first level, D 1 must be serviced by an open facility. The cost of assigning a station j on level l ⩾ 1 to a station i on level l − 1 is c i j . For i ∈ F , the cost of opening a facility at location i is f i ⩾ 0 . It is required to find a feasible assignment that minimizes the total cost. A constant ratio approximation algorithm is established for this problem. This algorithm is then used to develop constant ratio approximation algorithms for the bounded depth Steiner tree problem and the bounded hop strong-connectivity range assignment problem.

Cost-Distance: Two Metric Network Design

We present the Cost-Distance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of source-sink distances along an unrelated second metric. We give the first known $O(\log k)$ randomized approximation scheme for Cost-Distance, where $k$ is the number of sources. We reduce several common network design problems to Cost-Distance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include single-sink buy-at-bulk with variable pipe types between different sets of nodes, facility location with buy-at-bulk-type costs on edges (integrated logistics), constructing single-source multicast trees with good cost and delay properties, priority Steiner trees, and multilevel facility location. Our algorithm is also easier to implement and significantly faster than previously known algorithms for buy-at-bulk design problems.

Approximating the two-level facility location problem via a quasi-greedy approach

We propose a quasi-greedy algorithm for approximating the classical uncapacitated 2-level facility location problem (2-LFLP). Our algorithm, unlike the standard greedy algorithm, selects a sub-optimal candidate at each step. It also relates the minimization 2-LFLP problem, in an interesting way, to the maximization version of the single level facility location problem. Another feature of our algorithm is that it combines the technique of randomized rounding with that of dual fitting.This new approach enables us to approximate the metric 2-LFLP in polynomial time with a ratio of 1:77, a significant improvement on the previously known approximation ratios. Moreover, our approach results in a local improvement procedure for the 2-LFLP, which is useful in improving the approximation guarantees for several other multi-level facility location problems.

ハイブリッド型メタ戦略によるサプライチェーンネットワークの全体最適設計

We consider, in this paper, the capacitated multi-level facility location problem as a supply-chain network design. To cope with such large-scale and complicated problems, we have presented a practical method that divides first the original problem into two sub-problems, and then combine each result consistently. Each sub-problem, i.e., distribution side sub-problem and procurement one is solved likely by a hybrid method that employs meta-heuristic method like tabu search and graph algorithm for solving a transformed minimum cost flow problem in a hierarchical manner. Moreover, we have given a practical adjusting method for thus separately solved solutions associated with the Lagrangian relaxation. Through numerical experiments, we have confirmed that the proposed method can outperform a popular commercial software. On the average, the approximated rate of the obtained results was within 1.006 compared with the final solution from the commercial software.

Improved approximation algorithms for multilevel facility location problems

We show that the metric multilevel facility location problem is polynomial-time reducible within a factor of 3 to the metric uncapacitated facility location problem. This leads to a combinatorial 4.83-approximation algorithm for the metric multilevel facility location problem and to a 9-approximation algorithm for a capacitated version of it.

A note on the maximization version of the multi-level facility location problem

We show that the maximization version of the multi-level facility location problem can be approximated by a factor of 0.5. The only previously known result is a factor of 0.47 for the two-level case obtained recently by Bumb (Oper. Res. Lett. 29(4) (2001) 155).

A simple dual ascent algorithm for the multilevel facility location problem

We present a simple dual ascent method for the multilevel facility location problem which finds a solution within 6 times the optimum for the uncapacitated case and within f 2 times the optimum for the capacitated one. The algorithm is deterministic and based on the primal-dual techinique

The multi-level uncapacitated facility location problem is not submodular

Unlike the Uncapacitated Facility Location Problem submodularity does not hold for the Multi-Level Uncapacitated Facility Location Problem. This point needs to be clarified as submodularity is assumed in some published papers and may lead to erroneous procedures to tackle the problem.

The multi-level uncapacitated facility location problem is not submodular

Unlike the Uncapacitated Facility Location Problem submodularity does not hold for the Multi-Level Uncapacitated Facility Location Problem. This point needs to be clarified as submodularity is assumed in some published papers and may lead to erroneous procedures to tackle the problem.