An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure

In this paper we examine the Uncapacitated Facility Location Problem (UFLP) with a special structure of the objective function coefficients. For each customer the set of potential locations can be partitioned into subsets such that the objective function coefficients in each are identical. This structure exists in many applications, including the Maximum Cover Location Problem. For the problems possessing this structure, we develop a new integer programming formulation that has all the desirable properties of the standard formulation, but with substantially smaller dimensionality, leading to significant improvement in computational times. While our formulation applies to any instance of the UFLP, the reduction in dimensionality depends on the degree to which this special structure is present. This work was supported by grants from NSERC.     

The Ordered Gradual Covering Location Problem on a Network

In this paper we develop a network location model that combines the characteristics of ordered median and gradual cover models resulting in the Ordered Gradual Covering Location Problem (OGCLP). The Gradual Cover Location Problem (GCLP) was specifically designed to extend the basic cover objective to capture sensitivity with respect to absolute travel distance. The Ordered Median Location problem is a generalization of most of the classical locations problems like p-median or p-center problems. The OGCLP model provides a unifying structure for the standard location models and allows us to develop objectives sensitive to both relative and absolute customer-to-facility distances. We derive Finite Dominating Sets (FDS) for the one facility case of the OGCLP. Moreover, we present efficient algorithms for determining the FDS and also discuss the conditional case where a certain number of facilities is already assumed to exist and one new facility is to be added. For the multi-facility case we are able to identify a finite set of potential facility locations a priori, which essentially converts the network location model into its discrete counterpart. For the multi-facility discrete OGCLP we discuss several Integer Programming formulations and give computational results.     

Covering models and optimization techniques for emergency response facility location and planning: a review

With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed demands. It is often problematic due to the intrinsic complexity of these problems. This paper reviews covering models and optimization techniques for emergency response facility location and planning in the literature from the past few decades, while emphasizing recent developments. We introduce several typical covering models and their extensions ordered from simple to complex, including Location Set Covering Problem (LSCP), Maximal Covering Location Problem (MCLP), Double Standard Model (DSM), Maximum Expected Covering Location Problem (MEXCLP), and Maximum Availability Location Problem (MALP) models. In addition, recent developments on hypercube queuing models, dynamic allocation models, gradual covering models, and cooperative covering models are also presented in this paper. The corresponding optimization techniques to solve these models, including heuristic algorithms, simulation, and exact methods, are summarized.     

The return plant location problem: Modelling and resolution

The formulation and analysis of a new plant location problem is presented. The problem studied, herein referred to as the Return Plant Location Problem (RPLP), is that of cost minimization in a system of suppliers and customers in which there exists a return product from each customer. Lagrangian decomposition based heuristic and exact solution methods are given. The methods are applied to test problems with different structures and compared with the classical subgradient optimization approach.     

A branch-and-cut algorithm for a generalization of the Uncapacitated Facility Location Problem

Summary We introduce a generalization of the well-know Uncapacitated Facility Location Problem, in which clients can be served not only by single facilities but also by sets of facilitities. The problem, calledGaneralized Uncapacitated Facility Lacition Problem (GUFLP), was inspired by the Index Selection Problem in physical database design. We for mulate GUFLP as a Set Packing Problem, showing that our model contains all the clique inequalities (in polynomial number). Moreover, we describe and exact separation procedure for odd-hole inequalities, based on the particular structure of the problem. These results are used within a branch-and-cut algorithm for the exact solution of GUFLP. Computational results on two different classes of test problems are given.     

Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.     

基于遗传算法的固定起讫点危险品配送路线优化

为科学选择危险品配送路线,保障运输安全,将传统TSP(Travelling SalesmanProblem)问题加以推广和延伸,建立以路段交通事故率、路侧人口密度、环境影响因子和路段运输费用为指标的固定起讫点危险品配送路线优化模型.以遗传算法基本框架为基础,引入新的遗传算子,构建了可用于实现模型的多目标遗传算法.实例仿真表明,所建模型和算法在求解固定起讫点危险品配送路线优化问题中有较好的实用性.     

Enumeration and Search Procedures for a Hub Location Problem with Economies of Scale

Within a communications or transportation network, in which a number of locations exchange material or information, hubs can be used as intermediate switching points. In this way, traffic can be consolidated on inter-hub links and, thus, achieve economies of scale in transport costs. Recently, O'Kelly and Brian in 1998 proposed a model (termed the FLOWLOC model) that treats these economies of scale by means of piecewise-linear concave cost functions on the interhub arcs. We show that, for a fixed set of hubs, the FLOWLOC model can be solved using the classic Uncapacitated Facility Location Problem (UFLP). This observation then motivates an optimal enumeration procedure for the FLOWLOC model, as well as some search heuristics that are based upon tabu search and greedy random adaptive search procedures (GRASP). These search procedures would be especially applicable for large-sized problems. Some computational experience is described.     

A Branch-and-Price algorithm for the Single Source Capacitated Plant Location Problem

This paper considers the Single Source Capacitated Plant Location Problem (SSCPLP). We propose an exact algorithm in which a column generation procedure for finding upper and lower bounds is incorporated within a Branch-and-Price framework. The bounding procedure exploits the structure of the problem by means of an iterative approach. At each iteration, a two-level optimization problem is considered. The two levels correspond with the two decisions to be taken: first, the selection of a subset of plants to be opened and then, the allocation of clients within the subset of open plants. The second level subproblem is solved using column generation. The algorithm has been tested with different sets of test problems and the obtained results are satisfactory.     

Branch-and-Bound Algorithms for a Regional Water Authority Distribution Problem

A problem put forward recently by a Regional Water Authority differs from the well-known Capacitated Warehouse Location Problem only in that there are both weeks of normal demand levels and weeks of peak demand levels. We describe how Lagrangian relaxation based branch-and-bound algorithms have been adapted for the new problem. Computational results are given, enabling a comparison of the different approaches tried.     

A fuzzy multi-objective programming for optimization of fire station locations through genetic algorithms

Location of fire stations is an important factor in its fire protection capability. This paper aims to determine the optimal location of fire station facilities. The proposed method is the combination of a fuzzy multi-objective programming and a genetic algorithm. The original fuzzy multiple objectives are appropriately converted to a single unified ‘min–max’ goal, which makes it easy to apply a genetic algorithm for the problem solving. Compared with the existing methods of fire station location our approach has three distinguish features: (1) considering fuzzy nature of a decision maker (DM) in the location optimization model; (2) fully considering the demands for the facilities from the areas with various fire risk categories; (3) being more understandable and practical to DM. The case study was based on the data collected from the Derbyshire fire and rescue service and used to illustrate the application of the method for the optimization of fire station locations.     

Location coverage models with demand originating from nodes and paths: Application to cellular network design

Location covering problems, though well studied in the literature, typically consider only nodal (i.e. point) demand coverage. In contrast, we assume that demand occurs from both nodes and paths. We develop two separate models – one that handles the situation explicitly and one which handles it implicitly. The explicit model is formulated as a Quadratic Maximal Covering Location Problem – a greedy heuristic supported by simulated annealing (SA) that locates facilities in a paired fashion at each stage is developed for its solution. The implicit model focuses on systems with network structure – a heuristic algorithm based on geometrical concepts is developed. A set of computational experiments analyzes the performance of the algorithms, for both models. We show, through a case study for locating cellular base stations in Erie County, New York State, USA, how the model can be used for capturing demand from both stationary cell phone users as well as cell phone users who are in moving vehicles.     

考虑后悔规避与匹配意愿的直觉模糊双边匹配方法

针对直觉模糊偏好信息的双边匹配问题,提出一种考虑匹配主体后悔规避心理行为和匹配意愿的双边匹配方法。首先,将双边主体的直觉模糊偏好信息转化为效用值;然后,依据后悔理论的思想,通过一方主体将另一方主体进行两两比较计算每个主体的后悔值和欣喜值,进而计算每个主体的总体后悔欣喜值,构建匹配满意度计算规则,建立双边匹配多目标优化模型,通过分析现有匹配意愿系数确定方法的不足,给出一种新的匹配意愿系数确定方法,在此基础上,考虑双边主体的匹配意愿,采用线性加权法将多目标优化模型转化为单目标规划模型进行求解,获得双边匹配结果;最后,通过一个算例验证了提出方法的可行性和有效性。     

Bees Algorithm for constrained fuzzy multi-objective two-sided assembly line balancing problem

Bees Algorithm is one of the swarm intelligence based heuristics which tries to model natural behaviour of honey bees in food foraging and used to solve optimization problems. On the other hand, Two-sided Assembly Line Balancing Problem is a generalization of simple Assembly Line Balancing Problem where different assembly tasks are carried out on the same product in parallel at both left and right sides of the line. Two-sided assembly lines are generally employed for the assembly of large-sized products such as buses and trucks. Furthermore, many real life problems contain imprecise objectives and Fuzzy Multi-objective Programming gives an opportunity to handle such situations. In this study, Two-sided Assembly Line Balancing Problem is considered more realistically by employing positional, zoning and synchronous task constraints and by utilizing fuzzy approaches so as to maximize work slackness index and line efficiency, and minimize total balance delay. For solving this problem Bees Algorithm is used as a search mechanism for obtaining good solutions and extensive computational results are presented.     

A stochastic and dynamic model for the single-vehicle pick-up and delivery problem

In this paper a stochastic and dynamic model for the Pick-up and Delivery Problem is developed and analyzed. Demands for service arrive according to a Poisson process in time. The pick-up locations of the demands are independent and uniformly distributed over a service region. A single vehicle must transport the demands from the pick-up to the delivery location. Once a demand has been picked up it can only be dropped off at its desired delivery location. The delivery locations are independent and uniformly distributed over the region, and they are independent of the pick-up locations. The objective is to minimize the expected time in the system for the demands. Unit-capacity vehicle and multiple-capacity vehicle variations are considered. For each variation, bounds on the performance of the routing policies are derived for light and heavy traffic. The policies are analyzed using both analytical methods and simulation.     

货运列车的编组调度问题

主要通过建立组合优化的模型,将原问题等价为一个TSP问题,运用遗传算法来求解.问题一:以到达场列车解体次序为决策变量,车辆"中时"最小为目标,分阶段建立组合优化模型;问题二:在问题一的基础上将含有军用车辆的列车和含有去向目的站点S1车辆的列车优先考虑解体,得到解编方案;问题三,将待解编列车的范围向后延伸2小时;问题四,将到达场列车中去向目的站点S1和S2以远的车辆分别排在目的站点E 3和E 4以南之间;问题五,由于编组完成的列车都能及时发出,当排完前一时段留下的车辆后,对于当前时段到达的列车采用随到随解策略进行解编;问题六,给出改进编组调度方案的建议和意见.     

Lagrangean heuristics applied to a variety of large capacitated plant location problems

A series of performance improving heuristics are developed and embedded into the procedure of Lagrangean heuristics. The principles and ideas of these heuristics are used to build a general framework with which a variety of large Capacitated Plant Location Problems (CPLP) are solved, including the multi-capacitated case. A significant improvement over the results discussed in the literature is recorded. The single-source multi-Capacitated Plant Location Problem, which has not been addressed in the literature, is also tackled with encouraging results.     

Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach

The Solid Transportation Problem (STP) arises when bounds are given on three item properties. The Fuzzy Solid Transportation Problem (FSTP) appears when the nature of the data problem is fuzzy. This paper deals with the FSTP in the case in which the fuzziness affects the constraint set, and a fuzzy solution to the problem is required. Moreover, an arbitrary linear or nonlinear objective function is considered. In order to find a fuzzy solution to the problem, a parametric approach is used to obtain an auxiliary Parametric Solid Transportation Problem (PSTP) associated to the original problem. As there are no well-known solution methods proposed in literature to solve effectively the PSTP, in this paper an Evolutionary Algorithm (EA) based solution method is proposed to solve it, which can finally be applied to find a “good” fuzzy solution to the FSTP. Comparisons with another conventional method are presented and the results show the EA based approach to be better as a whole.     

The crew timetabling problem: An extension of the crew scheduling problem

In some urban transportation companies driving periods are short when compared with the total duty time, leading to long non-driving periods that can be used as cover time. This paper presents the Crew Timetabling Problem, an extension of the Crew Scheduling Problem in which crew timetables are obtained by levelling the cover crew resources. An objective function for this problem is proposed in order to balance the number of driving and cover crews. A Lisbon Underground case study is used to illustrate the Crew Timetabling Problem. The problem is represented in a multigraph and solved by a tabu search-based heuristic.     

A cutting plane algorithm for the Capacitated Connected Facility Location Problem

We consider a network design problem that arises in the cost-optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design problem and the single-source capacitated facility location problem. We refer to it as the Capacitated Connected Facility Location Problem. We develop a basic integer programming model based on single-commodity flows. Based on valid inequalities for the capacitated network design problem and the single-source capacitated facility location problem we derive several (new) classes of valid inequalities for the Capacitated Connected Facility Location Problem including cut set inequalities, cover inequalities and combinations thereof. We use them in a branch-and-cut framework and show their applicability and efficacy on a set of real-world instances.