Confined location of facilities on a graph

Location problems on a graph are usually classified according to the form that the set of located facilities takes, the specification of the demand location set and the objective function of distances between facilities and demand points. In this paper we suppose that a given number of located facilities is confined to the same number of edges. We consider eight types of optimality criteria: minirnizing(or maximizing) the minimum (or maximum) distance from a demand to its nearest (farthest) facility.     

Solving multiple facilities location problems with separated clusters

This paper examines a special case of multi-facility location problems where the set of demand points is partitioned into a given number of subsets or clusters that can be treated as smaller independent sub-problems once the number of facilities allocated to each cluster is determined. A dynamic programming approach is developed to determine the optimal allocation of facilities to clusters. The use of clusters is presented as a new idea for designing heuristics to solve general multi-facility location problems.     

A multicriteria approach to the location of public facilities

We argue that practical problems involving the location of public facilities are really multicriteria problems, and ought to be modeled as much. The general criteria are those of cost and service, but there exist several distinct criteria in each of those two categories. For the first category, fixed investment cost, fixed operating cost, variable operating cost, total operating cost, and total discounted cost are all reasonable criteria to consider. In terms of service, both demand served and response time (or distance traveled) are appropriate criteria, either agglomerated or considered on the basis of the individual clients. In this paper we treat such multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points. We show that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution. In most other cases the efficient solutions can be found through parametric solution of a GAP with additional constraints of a type which can be incorporated into an existing algorithm for the GAP. Rather than attempting to find all efficient solutions, however, we advocate an interactive approach to the resolution of multicriteria location problems and elaborate on a specific interactive algorithm for multicriteria optimization which for the present model solves a finite sequence of GAP's or GAP-type problems. Finally, some similar aspects of private sector location problems are discussed.     

Developments in network location with mobile and congested facilities

We review four facility location problems which are motivated by urban service applications and which can be thought of as extensions of the classic Q-median problem on networks. In problems P1 and P2 it is assumed that travel times on network links change over time in a probabilistic way. In P2 it is further assumed that the facilities (servers) are movable so that they can be relocated in response to new network travel times. Problems P3 and P4 examine the Q-median problem for the case when the service capacity of the facilities is finite and, consequently, some or all of the facilities can be unavailable part of the time. In P3 the facilities have stationary home locations but in P4 they have movable locations and thus can be relocated to compensate for the unavailability of the busy facilities. We summarize our main results to date on these problems.     

Sequential location of two facilities: comparing random to optimal location of the first facility

We review our recent results in the development of optimal algorithms for the minimization of a strictly convex quadratic function subject to separable convex inequality constraints and/or linear equality constraints. A unique feature of our algorithms is the theoretically supported bound on the rate of convergence in terms of the bounds on the spectrum of the Hessian of the cost function, independent of representation of the constraints. When applied to the class of convex QP or QPQC problems with the spectrum in a given positive interval and a sparse Hessian matrix, the algorithms enjoy optimal complexity, i.e., they can find an approximate solution at the cost that is proportional to the number of unknowns. The algorithms do not assume representation of the linear equality constraints by full rank matrices. The efficiency of our algorithms is demonstrated by the evaluation of the projection of a point to the intersection of the unit cube and unit sphere with hyperplanes.     

Strategic competitive location: improving existing and establishing new facilities

Competitive facility location models consider two main strategies for increasing the market share captured by a chain subject to a budget constraint. One strategy is the improvement of existing facilities. The second strategy is the construction of new facilities. In this paper we analyse these two strategies as well as the joint strategy which is a combination of the two. All three strategies are formulated as a unified model. The best solution to an individual strategy is a feasible solution to the joint one. Therefore, the joint strategy must yield solutions that are at least as good as the solutions to each of the individual strategies. Based on the results of extensive experiments, we conclude that the increase in market share captured by a chain when the joint strategy is employed can be significantly higher than increases obtained by individual strategies. A branch and bound procedure and a tabu search heuristic are constructed for the solution of the unified model. Both algorithms performed very well on a set of test problems with up to 900 demand points. A total of 62% of the test problems were optimally solved by the branch and bound procedure.     

Minisum collection depots location problem with multiple facilities on a network

We investigate the problem of locating a set of service facilities that need to service customers on a network. To provide service, a server has to visit both the demand node and one of several collection depots. We employ the criterion of minimizing the weighted sum of round trip distances. We prove that there exists a dominating location set for the problem on a general network. The properties of the solution on a tree and on a cycle are discussed. The problem of locating service facilities and collection depots simultaneously is also studied. To solve the problem on a general network, we suggest a Lagrangian relaxation imbedded branch-and-bound algorithm. Computational results are reported.     

A quadratic integer program for the location of interacting hub facilities

This paper reports a new formulation of a general hub location model as a quadratic integer program. Non-convexity of the objective function makes the problem difficult. A variety of alternative solution strategies are discussed. Computational results from two simple heuristics are presented for the task of siting 2, 3 or 4 hubs to serve interactions between sets of 10, 15, 20 and 25 U.S. cities. The effects of different computational shortcuts are examined.     

The location of public facilities intermediate to the journey to work

Location—allocation models typically locate facilities with respect to points to be served, for example to the homes of potential patrons. Certain types of facility, however, are employed by persons who travel to the facility from their homes and continue their journey to another location. Child care facilities are an example of this pattern of patronage, with parents dropping children off at a centre en route to work. The paper presents a discrete-space location—allocation model minimizing the diversion of patrons' journeys to work. The problem reduces to the structure and combinatorial dimensions of the simple P-median problem. The model is applied to the transit worktrip patterns of single parents in Edmonton, Canada. The facilities generated by the model tend to central locations in the city where workplaces are concentrated and transit connections are efficient. The model provides a compromise between ones minimizing home-facility travel times and facility-workplace travel times.     

Covering location problem of emergency service facilities in an uncertain environment

In practical location problems on networks, the response time between any pair of vertices and the demands of vertices are usually indeterminate. This paper employs uncertainty theory to address the location problem of emergency service facilities under uncertainty. We first model the location set covering problem in an uncertain environment, which is called the uncertain location set covering model. Using the inverse uncertainty distribution, the uncertain location set covering model can be transformed into an equivalent deterministic location model. Based on this equivalence relation, the uncertain location set covering model can be solved. Second, the maximal covering location problem is investigated in an uncertain environment. This paper first studies the uncertainty distribution of the covered demand that is associated with the covering constraint confidence level α. In addition, we model the maximal covering location problem in an uncertain environment using different modelling ideas, namely, the (α, β)-maximal covering location model and the α-chance maximal covering location model. It is also proved that the (α, β)-maximal covering location model can be transformed into an equivalent deterministic location model, and then, it can be solved. We also point out that there exists an equivalence relation between the (α, β)-maximal covering location model and the α-chance maximal covering location model, which leads to a method for solving the α-chance maximal covering location model. Finally, the ideas of uncertain models are illustrated by a case study.     

Capacitated dynamic location problems with opening, closure and reopening of facilities

^** Email: joana{at}fe.uc.pt In this paper a capacitated dynamic location problem with opening,closure and reopening of facilities is formulated and a primal–dualheuristic that can solve this problem is described. In thisproblem both maximum and minimum capacity restrictions are considered.The problem formulated is NP-hard. Computational results arepresented and discussed.     

Optimal location of interconnected facilities on tree networks subject to distance constraints

Optimal location of interconnected facilities on tree networks is considered in the case when some of the nodes of the network contain existing facilities. The distances between the facilities must satisfy maximum constraints. Polynomial algorithms for the solution of this problem are proposed.     

Optimizing pricing and location decisions for competitive service facilities charging uniform price

In this paper, we present the problem of optimizing the location and pricing for a set of new service facilities entering a competitive marketplace. We assume that the new facilities must charge the same (uniform) price and the objective is to optimize the overall profit for the new facilities. Demand for service is assumed to be concentrated at discrete demand points (customer markets); customers in each market patronize the facility providing the highest utility. Customer demand function is assumed to be elastic; the demand is affected by the price, facility attractiveness, and the travel cost for the highest-utility facility. We provide both structural and algorithmic results, as well as some managerial insights for this problem. We show that the optimal price can be selected from a certain finite set of values that can be computed in advance; this fact is used to develop an efficient mathematical programming formulation for our model.     

Optimization of multi-echelon repairable item inventory systems with simultaneous location of repair facilities

We study a support system for a fleet of technical systems. Our tasks are to determine the amount of spares and test equipment necessary for the support system to operate satisfactorily and to determine where repair should take place. Our decisions are made on an economical basis, or more precisely, we seek the optimal support system configuration that meets a specified life-cycle cost constraint. A mathematical framework is presented which allows for these three tasks to be solved simultaneously.     

A review of congestion models in the location of facilities with immobile servers

Capacity effects are investigated, particularly as regards congestion of facilities with immobile (or fixed) servers. A review is given of research to date in this area, together with some related work. First, general implications of facility capacities being capacitated are discussed with regard to assignment of users to facilities, time (or distance) transformations, integrality, feasibility, equity and load balancing. Then models using both system choice and user choice assignment are presented, and hierarchical problems covered briefly. Finally, there is a summary and a discussion together with some possible future research directions.     

On solving the discrete location problems when the facilities are prone to failure

The classical discrete location problem is extended here, where the candidate facilities are subject to failure. The unreliable location problem is defined by introducing the probability that a facility may become inactive. The formulation and the solution procedure have been motivated by an application to model and solve a large size problem for locating base stations in a cellular communication network. We formulate the unreliable discrete location problems as 0–1 integer programming models, and implement an enhanced dual-based solution method to determine locations of these facilities to minimize the sum of fixed cost and expected operating (transportation) cost. Computational tests of some well-known problems have shown that the heuristic is efficient and effective for solving these unreliable location problems.     

Adaptation of the plant location model for regional environmental facilities and cost allocation strategy

This paper is divided into two parts. In the first part of the paper, the plant location model is adapted for the special case of siting wastewater treatment facilities when the wastewater sources and treatment facilities are arranged in a chain or linear configuration. In this problem, flows or shipments may be merged in common pipes that provide economies of scale in transport. In order to apply the plant location model, an appropriate definition of the additional cost incurred when a waste source joins a regional facility is required. In addition, sequential priority constraints are developed in the siting model in order to make possible proper accounting of transport costs. The new siting model can be conveniently solved by linear programming.In the second part of the paper, a dual of the plant location model is explored as a cost allocation method for the fixed charge facility siting problem. The constraint sets of the dual model can be shown to imply the core conditions of the related cost game; hence, a set of the dual variables from the dual problem can be regarded as rational cost allocations. The analysis places both facility siting and cost allocation in a common framework.     

A decomposition approach for facility location and relocation problem with uncertain number of future facilities

In this paper, we discuss two challenges of long term facility location problem that occur simultaneously; future demand change and uncertain number of future facilities. We introduce a mathematical model that minimizes the initial and expected future weighted travel distance of customers. Our model allows relocation for the future instances by closing some of the facilities that were located initially and opening new ones, without exceeding a given budget. We present an integer programming formulation of the problem and develop a decomposition algorithm that can produce near optimal solutions in a fast manner. We compare the performance of our mathematical model against another method adapted from the literature and perform sensitivity analysis. We present numerical results that compare the performance of the proposed decomposition algorithm against the exact algorithm for the problem.     

求解应急医疗设施分层递进式选址问题的改进免疫算法

针对应急医疗设施的特点,提出分层递进式选址方法,对应急医疗设施进行合理选址.首先,通过熵权法对选址所需要考虑的因素进行权重计算,并进行初步选址;其次,考虑设施点的服务容量、重大公共卫生事件下轻重症患者的治疗与转移的实际情况,建立双层级整数规划模型;再次,根据模型的具体特点,设计改进的免疫优化算法对其进行求解;最后,以湖...     

Facility location for market capture when users rank facilities by shorter travel and waiting times

A firm wants to locate several multi-server facilities in a region where there is already a competitor operating. We propose a model for locating these facilities in such a way as to maximize market capture by the entering firm, when customers choose the facilities they patronize, by the travel time to the facility and the waiting time at the facility. Each customer can obtain the service or goods from several (rather than only one) facilities, according to a probabilistic distribution. We show that in these conditions, there is demand equilibrium, and we design an ad hoc heuristic to solve the problem, since finding the solution to the model involves finding the demand equilibrium given by a nonlinear equation. We show that by using our heuristic, the locations are better than those obtained by utilizing several other methods, including MAXCAP, p-median and location on the nodes with the largest demand.