The identification of the distribution of air passengers among airports is an important task of the airport planner. It would be useful to understand how trip makers choose among competing airports. The ultimate purpose of this study is to research into , passengers' choice of airport so that the airport system can be planned on a more reliable basis. The choice of airport of passengers originating from central England in 1975 is explained by constructing multinomial disaggregate behavioural models of logit form. The data used for model calibration, were collected during two Civil Aviation Authority surveys. This work makes contribution to: -The definition of the major determinants of airport choice, -The responsiveness of passengers, choice to changes in these determinants, - The policy implications for the regional airports - The transferability of the model in time and space. The method of analysis has been selected after outlining the potential advantages and shortcomings of logit and probit models and after a test on the validity of the Independence from Irrelevant Alternatives (I.I.A.) property has been carried out. The results show that the multinomial logit model used for the airport choice is good in terms of its explanatory ability and successful in predicting the choices actually made. Travel time to the airport, frequency of flights and air fare are found to be decisive factors for a passenger to select a given airport but are not of equal importance. By influencing-these factors, it appears that there exists room for the transport planner to shift traffic from one airport to another to have an economically and/or environmentally efficient airport system. In their original form, the models have been tested and found not to be transferable to the London area in 1978. However, after a Bayesian updating procedure was applied, the business and inclusive tours models were transferable. The leisure model was not statistically transferable but had a good predictive ability while the domestic model was not transferable. Finally, subsequent directions ·for further research are outlined.

Facility Location problem refers to placing facilities (mostly vehicles) in appropriate locations to yield the best coverage with respect to other important factors which are specific to the problem. For instance in a fire station some of the important factors are traffic time, distribution of stations, time of the service and so on. Furthermore, budget limitation, time constraints and the great importance of the operation, make the optimum allocation very complex. In the past few years, several research in this area have been done to help managers by designing some effective algorithm to allocating facilities in the best way possible. Most early proposed models were focused on static and deterministic methods. In static models, once a facility assigns to a location, it will not relocate anymore. Although these methods could be utilized in some simple settings, there are so many factors in real world that make a static model of limited application. The demands may change over time or facilities may be dropped or added. In these cases a more flexible model is desirable, thus dynamic models are proposed to be used in such cases. Facilities can be located and relocated based on the situations. More recently, dynamic models became more popular but there were still many aspects of facility allocation problems which were challenging and would require more complex solutions. The importance of facility location problem becomes significantly more relevant when it relates to hospitals and emergency responders. Even one second of improvement in response time is important in this area. For this reason, we selected ambulance facility allocation problem as a case study to analyze this problem domain. Much research has been done on ambulances allocation. We will review some of these models and their advantages and disadvantages. One of the best model in this areas introduced by Rajagopalan. In this work, his model is analyzed and its major drawback is addressed by applying some modifications to its methodology. Genetic Algorithm is utilized in this study as a heuristic method to solve the allocation model.

We consider the lower-bounded facility location (LBFL) problem (, also known as load-balanced facility location), which is a generalization of uncapacitated facility location (UFL) problem where each open facility is required to serve a minimum number of clients. More formally, in the LBFL problem, we are given a set of clients Ɗ , a set of facilities Ƒ, a non-negative facility-opening cost f_i for each i ∈ Ƒ, a lower bound M, and a distance metric c(i,j) on the set Ɗ ∪ Ƒ, where c(i,j) denotes the cost of assigning client j to facility i. A feasible solution S specifies the set of open facilities F_S ⊆ Ƒ and the assignment of each client j to an open facility i(j) such that each open facility serves at least M clients. Our goal is to find feasible solution S that minimizes ∑_{i ∈ F_S} f_i + ∑_j c(i,j). The current best approximation ratio for LBFL is 550. We substantially advance the state-of-the-art for LBFL by devising an approximation algorithm for LBFL that achieves a significantly-improved approximation guarantee of 83.

We consider the lower-bounded facility location (LBFL) problem (, also known as load-balanced facility location), which is a generalization of uncapacitated facility location (UFL) problem where each open facility is required to serve a minimum number of clients. More formally, in the LBFL problem, we are given a set of clients Ɗ , a set of facilities Ƒ, a non-negative facility-opening cost f_i for each i ∈ Ƒ, a lower bound M, and a distance metric c(i,j) on the set Ɗ ∪ Ƒ, where c(i,j) denotes the cost of assigning client j to facility i. A feasible solution S specifies the set of open facilities F_S ⊆ Ƒ and the assignment of each client j to an open facility i(j) such that each open facility serves at least M clients. Our goal is to find feasible solution S that minimizes ∑_{i ∈ F_S} f_i + ∑_j c(i,j). The current best approximation ratio for LBFL is 550. We substantially advance the state-of-the-art for LBFL by devising an approximation algorithm for LBFL that achieves a significantly-improved approximation guarantee of 83.

Spatial facility location problems (SFLPs) involve the placement of facilities in continuous demand regions. One approach to solving SFLPs is to aggregate demand into discrete points, and then solve the point-based model as a conventional facility location problem (FLP) according to a surrogate model. Solution performance is measured in terms of the percentage of continuous space actually covered in the original SFLP. In this dissertation I explore this approach and examine factors contributing to solution quality. Three error sources are discussed: point representation spacing, multiple possible solutions to the surrogate point-based model, and round-off errors induced by the computer representation of numbers. Some factors—including boundary region surrogate points and surrogate point location—were also found to make significant contributions to coverage errors. A surrogate error measure using a point-based surrogate model was derived to characterize relationships among spacing, facility coverage area, and spatial coverage error. Locating continuous space facilities with full coverage is important but challenging. Demand surrogate points were initially used as a continuous space for constructing the MIP model, and a point-based surrogate FLP was enhanced for extracting multiple solutions with additional constraints that were found to reduce coverage error. Next, a best initial solution was applied to a proposed heuristic algorithm to serve as an improvement procedure. Algorithm performance was evaluated and applied to a problem involving the location of emergency warning sirens in the city of Dublin, Ohio. The effectiveness of the proposed method for solving this and other facility location/network design problems was demonstrated by comparing the results with those reported in recently published papers.

We consider how the optimal decision can be made if the optimality criterion of maximizing profit changes to that of maximizing return on investment for the general uncapacitated facility location problem. We show that the inherent structure of the proposed model can be exploited to make a significant computational reduction.

The facility location problem is the task of optimally placing a given number of facilities in a certain subset of the plane. In this thesis, we present various mathematical programming formulations of the planar facility location problem, where potential facility locations are not specified. We first consider mixed-integer programming formulations of the planar facility locations problems with squared Euclidean and rectangular distance metrics to solve this problem to provable optimality. We also investigate a heuristic approach to solving the problem by extending the $K$-means clustering algorithm and formulating the facility location problem as a variant of a semidefinite programming problem, leading to a relaxation algorithm. We present computational results for the mixed-integer formulations, as well as compare the objective values resulting from the relaxation algorithm and the modified $K$-means heuristic. In addition, we briefly discuss some of the practical issues related to the facility location model under the continuous customer distribution.

The facility location problem is the task of optimally placing a given number of facilities in a certain subset of the plane. In this thesis, we present various mathematical programming formulations of the planar facility location problem, where potential facility locations are not specified. We first consider mixed-integer programming formulations of the planar facility locations problems with squared Euclidean and rectangular distance metrics to solve this problem to provable optimality. We also investigate a heuristic approach to solving the problem by extending the $K$-means clustering algorithm and formulating the facility location problem as a variant of a semidefinite programming problem, leading to a relaxation algorithm. We present computational results for the mixed-integer formulations, as well as compare the objective values resulting from the relaxation algorithm and the modified $K$-means heuristic. In addition, we briefly discuss some of the practical issues related to the facility location model under the continuous customer distribution.

The capacitated facility location problem is a well known problem in combinatorial optimization and operations research. In it, we are given a set of clients and a set of possible facility locations. Each client has a certain demand that needs to be satisfied from open facilities, without exceeding their capacity. Whenever we open a facility we incur in a corresponding opening cost. Whenever demand is served, we incur in an assignment cost; depending on the distance the demand travels. The goal is to open a set of facilities that satisfy all demands while minimizing the total opening and assignment costs. In this thesis, we present two novel LP-based approximation algorithms for the capacitated facility location problem. The first algorithm is based on LP-rounding techniques, and is designed for the special case of the capacitated facility location problem where capacities are uniform and assignment costs are given by a tree metric. The second algorithm follows a primal-dual approach, and works for the general case. For both algorithms, we obtain an approximation guarantee that is linear on the size of the problem. To the best of our knowledge, there are no LP-based algorithms known, for the type of instances that we focus on, that achieve a better performance.

This dissertation is focused on investigating the integration of inventory and facility location decisions in different supply chain settings. Facility location and inventory decisions are interdependent due to the economies of scale that are inherent in transportation and replenishment costs. The facility location decisions have an impact on the transportation and replenishment costs which, in turn, affect the optimal inventory policy. On the other hand, the inventory policy dictates the frequency of shipments to replenish inventory which, in turn, affects the number of deliveries, and, hence, the transportation costs, between the facilities. Therefore, our main research objectives are to: • compare the optimal facility location, determined by minimizing total transportation costs, to the one determined by the models that also consider the timing and quantity of inventory replenishments and corresponding costs, • investigate the effect of facility location decisions on optimal inventory decisions, and • measure the impact of integrated decision-making on overall supply chain cost performance. Placing a special emphasis on the explicit modeling of transportation costs, we develop several novel models in mixed integer linear and nonlinear optimization programming. Based on how the underlying facility location problem is modeled, these models fall into two main groups: 1) continuous facility location problems, and 2) discrete facility location problems. For the stylistic models, the focus is on the development of analytical solutions. For the more general models, the focus is on the development of efficient algorithms. Our results demonstrate • the impact of explicit transportation costs on integrated decisions, • the impact of different transportation cost functions on integrated decisions in the context of continuous facility location problems of interest, • the value of integrated decision-making in different supply chain settings, and • the performance of solution methods that jointly optimize facility location and inventory decisions.