A network location-allocation model trading off flow capturing andp-median objectives

The flow capturing and thep-median location—allocation models deal quite differently with demand for service in a network. Thep-median model assumes that demand is expressed at nodes and locates facilities to minimize the total distance between such demand nodes and the nearest facility. The flow-capturing model assumes that demand is expressed on links and locates facilities to maximize the one-time exposure of such traffic to facilities. Demand in a network is often of both types: it is expressed by passing flows and by consumers centred in residential areas, aggregated as nodes. We here present a hybrid model with the dual objective of serving both types of demand. We use this model to examine the tradeoff between serving the two types of demand in a small test network using synthetic demand data. A major result is the counter-intuitive finding that thep-median model is more susceptible to impairment by the flow capturing objective than is the flow capturing model to thep-median objective. The results encourage us to apply the model to a real-world network using actual traffic data.     

带危险度瓶颈限制的服务站截流选址－分配模型研究

该文考虑带危险度瓶颈限制的服务站截流选址－分配问题(FCLM). 假设网络中各边有两个向量:长度和危险度. 对于有一个起点和多个讫点的FCLM问题,网络的安全费用是一个关于可抵御最大危险度等级的非递减函数. 该问题考虑如何选取可抵御最大危险度的等级和服务站的位置使得建站费用和安全费用之和最小. 文中建立了该问题的模型并提出了基于后序遍历的替代算法.     

Network hub location problems: The state of the art

Hubs are special facilities that serve as switching, transshipment and sorting points in many-to-many distribution systems. The hub location problem is concerned with locating hub facilities and allocating demand nodes to hubs in order to route the traffic between origin–destination pairs. In this paper we classify and survey network hub location models. We also include some recent trends on hub location and provide a synthesis of the literature.     

Asymptotic Analysis of a Greedy Heuristic for the Multi-Period Single-Sourcing Problem: The Acyclic Case

The multi-period single-sourcing problem that we address in this paper can be used as a tactical tool for evaluating logistics network designs in a dynamic environment. In particular, our objective is to find an assignment of customers to facilities, as well as the location, timing and size of production and inventory levels, that minimizes total assignment, production, and inventory costs. We propose a greedy heuristic, and prove that this greedy heuristic is asymptotically optimal in a probabilistic sense for the subclass of problems where the assignment of customers to facilities is allowed to vary over time. In addition, we prove a similar result for the subclass of problems where each customer needs to be assigned to the same facility over the planning horizon, and where the demand for each customer exhibits the same seasonality pattern. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. These results suggest that the greedy heuristic may be asymptotically optimal even for the cases that we were unable to analyze theoretically.     

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.     

Location of slaughterhouses under economies of scale

The facility location problem described in this paper comes from an industrial application in the slaughterhouse industry of Norway. Investigations show that the slaughterhouse industry experiences economies of scale in the production facilities. We examine a location-allocation problem focusing on the location of slaughterhouses, their size and the allocation of animals in the different farming districts to these slaughterhouses. The model is general and has applications within other industries that experience economies of scale.We present an approach based on linearization of the facility costs and Lagrangean relaxation. We also develop a greedy heuristic to find upper bounds. We use the method to solve a problem instance for the Norwegian Meat Co-operative and compare our results to previous results achieved using standard branch-and-bound in commercial software.     

A fuzzy programming approach for dynamic virtual hub location problem

Hub location problem has been used in transportation network to exploit economies of scale. For example, a controversial issue in the planning of air transportation networks is inclement weather or emergency conditions. In this situation, hub facilities would not be able to provide a good service to their spoke nodes temporarily. Thus, some other kinds of predetermined underutilized facilities in the network are used as virtual hubs to host some or all connections of original hubs to recover the incurred incapacitation and increase network flexibility and demand flow. In such an unexpected situation, it is not unreasonable to expect that some information be imprecise or vague. To deal with this issue, fuzzy concept is used to pose a more realistic problem. Here, we present a fuzzy integer liner programming approach to propose a dynamic virtual hub location problem with the aim of minimizing transportation cost in the network. We examine the effectiveness of our model using the well-known CAB data set.     

Location and sizing of facilities on a line

The location-allocation problem in its basic form assumes that the number of new facilities to be located is known and the capacities are unlimited. When the locations of the facilities and demand points (or customers) are restricted to the real line, the basic model may be solved efficiently by dynamic programming. In this note, we show that when the number of facilities and their capacities are included in the decision process, the problem may actually be easier to solve.     

Locating flow-capturing units on a network with multi-counting and diminishing returns to scale

In the paper we consider the problem of locating flow-capturing units (facilities) on a transportation network, where the level of consuming service by customers depends on the number of facilities that they encounter on their pre-planned tour (the effect of multi-counting). Two location problems are considered: Problem 1 — minimizing the number of facilities required to ensure the maximal level of consumption, and Problem 2 — maximizing the total consumption given a restriction on the number of facilities. Both problems are NP-hard on general networks. Integer programming formulations of the problems are given. For Problem 2, a heuristic with worst-case analysis is presented. It is shown that Problem 2 is NP-hard even on a tree (and even without multi-counting). For Problem 1 on a tree a polynomial algorithm is presented. If it is required additionally that at most one facility can be located at each node and locations are restricted to nodes, then both problems are NP-hard on trees.     

Solving the logit-based stochastic user equilibrium problem with elastic demand based on the extended traffic network model

This paper proposes a novel extended traffic network model to solve the logit-based stochastic user equilibrium (SUE) problem with elastic demand. In this model, an extended traffic network is established by properly adding dummy nodes and links to the original traffic network. Based on the extended traffic network, the logit-based SUE problem with elastic demand is transformed to the SUE problem with fixed demand. Such problem is then further converted to a linearly constrained convex programming and addressed by a predictor–corrector interior point algorithm with polynomial complexity. A numerical example is provided to compare the proposed model with the method of successive averages (MSA). The numerical results indicate that the proposed model is more efficient and has a better convergence than the MSA.     

A Transportation Network Model as a Tool to Solve Urban Planning Location Problems

The aim of this paper is to formulate a transportation network model conceived as a basis of possible tools to be used by administrators and planners to approach location problems in a urban context. The key element of this model is a static representation of the transportation network, made of oriented links and nodes, connecting the facilities located in a prespecified urban area. Such a representation is based on an analogy of electric nature, thus allowing to exploit conventional electric networks solvers to determine the relevant features of the traffic flow in each link of the transportation network. The facility quality level is also taken into account in a quantitative fashion. Relying on the proposed model, different related results, such as the minimum path matrix and the induced traffic in each link of the network can be retrieved.     

Optimization models for assessing the peak capacity utilization of intelligent transportation systems

With limited economic and physical resources, it is not feasible to continually expand transportation infrastructure to adequately support the rapid growth in its usage. This is especially true for traffic coordination systems where the expansion of road infrastructure has not been able to keep pace with the increasing number of vehicles, thereby resulting in congestion and delays. Hence, in addition to striving for the construction of new roads, it is imperative to develop new intelligent transportation management and coordination systems. The effectiveness of a new technique can be evaluated by comparing it with the optimal capacity utilization. If this comparison indicates that substantial improvements are possible, then the cost of developing and deploying an intelligent traffic system can be justified. Moreover, developing an optimization model can also help in capacity planning. For instance, at a given level of demand, if the optimal solution worsens significantly, this implies that no amount of intelligent strategies can handle this demand, and expanding the infrastructure would be the only alternative. In this paper, we demonstrate these concepts through a case study of scheduling vehicles on a grid of intersecting roads. We develop two optimization models namely, the mixed integer programming model and the space-time network flow model, and show that the latter model is substantially more effective. Moreover, we prove that the problem is strongly NP-hard and develop two polynomial-time heuristics. The heuristic solutions are then compared with the optimal capacity utilization obtained using the space-time network model. We also present important managerial implications.     

Inventory sharing in integrated network design and inventory optimization with low-demand parts

Service Parts Logistics (SPL) problems induce strong interaction between network design and inventory stocking due to high costs and low demands of parts and response time based service requirements. These pressures motivate the inventory sharing practice among stocking facilities. We incorporate inventory sharing effects within a simplified version of the integrated SPL problem, capturing the sharing fill rates in 2-facility inventory sharing pools. The problem decides which facilities in which pools should be stocked and how the demand should be allocated to stocked facilities, given full inventory sharing between the facilities within each pool so as to minimize the total facility, inventory and transportation costs subject to a time-based service level constraint. Our analysis for the single pool problem leads us to model this otherwise non-linear integer optimization problem as a modified version of the binary knapsack problem. Our numerical results show that a greedy heuristic for a network of 100 facilities is on average within 0.12% of the optimal solution. Furthermore, we observe that a greater degree of sharing occurs when a large amount of customer demands are located in the area overlapping the time windows of both facilities in 2-facility pools.     

A hub covering network design problem for cargo applications in Turkey

Hub location problems involve locating hub facilities and allocating demand nodes to hubs in order to provide service between origin–destination pairs. In this study, we focus on cargo applications of the hub location problem. Through observations from the Turkish cargo sector, we propose a new mathematical model for the hub location problem that relaxes the complete hub network assumption. Our model minimizes the cost of establishing hubs and hub links, while designing a network that services each origin–destination pair within a time bound. We formulate a single-allocation hub covering model that permits visiting at most three hubs on a route. The model is then applied to the realistic instances of the Turkish network and to the Civil Aeronautics Board data set.     

Combining very large scale and ILP based neighborhoods for a two-level location problem

In this paper we tackle a generalization of the Single Source Capacitated Facility Location Problem in which two sets of facilities, called intermediate level and upper level facilities, have to be located; the dimensioning of the intermediate set, the assignment of clients to intermediate level facilities, and of intermediate level facilities to upper level facilities, must be optimized, as well. Such problem arises, for instance, in telecommunication network design: in fact, in hierarchical networks the traffic arising at client nodes often have to be routed through different kinds of facility nodes, which provide different services. We propose a heuristic approach, based on very large scale neighborhood search to tackle the problem, in which both ad hoc algorithms and general purpose solvers are applied to explore the search space. We report on experimental results using datasets from the capacitated location literature. Such results show that the approach is promising and that Integer Linear Programming based neighborhoods are significantly effective.     

A hierarchical location-allocation model with travel based on expected referral distances

The hierarchical p-median location-allocation model assumes that patrons always travel to the closest facility of appropriate level and that their interests are best served when the distances they must travel to do this are minimized. This assumption about travel behavior is unrealistic, patrons in the real world are known, for instance, to bypass lower level facilities that can serve their needs to attend higher level facilities. We introduce the concept of “expected distance under referral” to deal with such irrationality and incorporate it into a location-allocation model that minimizes the negative effects of such irrational behavior. We demonstrate the model with several types of non-optimal travel behavior.     

Network flow problems with pricing decisions

This paper considers a class of network flow problems in which the demand levels of the nodes are determined through pricing decisions representing the revenue received per unit demand at the nodes. We must simultaneously determine the pricing decisions and the network flow decisions in order to maximize profits, i.e., the revenues received from the pricing decisions minus the cost of the network flow decisions. Specializations of this class of problems have numerous applications in supply chain management. We show that the class of problems with a single pricing decision throughout the network can be solved in polynomial time under both continuous pricing restrictions and integer pricing restrictions. For the class of problems with customer-specific pricing decisions, we provide conditions under which the problem can be solved in polynomial-time for continuous pricing restrictions and prove that the problem is NP-hard for integer pricing restrictions.     

竞争环境下截流设施选址问题

研究企业新建设施时,市场上已有设施存在的情况下,使本企业总体利润最大的截流设施选址问题。在一般截留设施选址模型的基础上引入引力模型,消费者到某个设施接受服务的概率与偏离距离及设施的吸引力相关,同时设施的建设费用与设施吸引力正相关,建立非线性整数规划模型并使用贪婪算法进行求解。数值分析表明,该算法求解速度快,模型计算精度较高。     

Optimal Control for Traffic Flow Networks

We consider traffic flow models for road networks where the flow is controlled at the nodes of the network. For the analytical and numerical optimization of the control, the knowledge of the gradient of the objective functional is useful. The adjoint calculus introduced below determines the gradient in two ways. We derive the adjoint equations for the continuous traffic flow network model and derive also the adjoint equations for a discretized model. Numerical examples for the solution of problems of optimal control for traffic flow networks are presented.This author was supported by Deutsche Forschungsgemeinschaft (DFG), Grant KL 1105/5.     

The \alpha -cost minimization model for capacitated facility location-allocation problem with uncertain demands

Facility location-allocation problem aims at determining the locations of some facilities to serve a set of spatially distributed customers and the allocation of each customer to the facilities such that the total transportation cost is minimized. In real life, the facility location-allocation problem often comes with uncertainty for lack of the information about the customers’ demands. Within the framework of uncertainty theory, this paper proposes an uncertain facility location-allocation model by means of chance-constraints, in which the customers’ demands are assumed to be uncertain variables. An equivalent crisp model is obtained via the \(\alpha \) -optimistic criterion of the total transportation cost. Besides, a hybrid intelligent algorithm is designed to solve the uncertain facility location-allocation problem, and its viability and effectiveness are illustrated by a numerical example.