Two hyperfinite constructions of the brownian bridge

Infinitesimal Analysis is used to give two constructions of the brownian bridge process. In the first construction a hyperfinite tied down random walk is used and a brownian bridge is obtained via the standard part map. As a consequence it is shown that the brownian bridge is the weak limit of a sequence of normalized tied down random walks. The second construction is based on a hyperfinite uniform empirical process. This construction gives an almost trivial proof of Donsker's Invariance Principle for the uniform empirical process     

On a bulk arrival bulk service infinite service queue

This paper considers an infinite server queue in continuous time in which arrivals are in batches of variable size X and service is provided in groups of fixed size R. We obtain analytical results for the number of busy servers and waiting customers at arbitrary time points. For the number of busy servers, we obtain a recursive relation for the partial binomial moments both in transient and steady states. Special cases are also discussed     

Two-player simultaneous location game: Preferential rights and overbidding

Competitive location problems can be characterized by the fact that the decisions made by others will affect our own payoffs. In this paper, we address a discrete competitive location game in which two decision-makers have to decide simultaneously where to locate their services without knowing the decisions of one another. This problem arises in a franchising environment in which the decision-makers are the franchisees and the franchiser defines the potential sites for locating services and the rules of the game. At most one service can be located at each site, and one of the franchisees has preferential rights over the other. This means that if both franchisees are interested in opening the service in the same site, only the one that has preferential rights will open it. We consider that both franchisees have budget constraints, but the franchisee without preferential rights is allowed to show interest in more sites than the ones she can afford. We are interested in studying the influence of the existence of preferential rights and overbidding on the outcomes for both franchisees and franchiser. A model is presented and an algorithmic approach is developed for the calculation of Nash equilibria. Several computational experiments are defined and their results are analysed, showing that preferential rights give its holder a relative advantage over the other competitor. The possibility of overbidding seems to be advantageous for the franchiser, as well as the inclusion of some level of asymmetry between the two decision-makers.     

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered. A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.     

Multiperiod Location-Routing with Decoupled Time Scales

This paper focuses on a multiperiod discrete facility location problem where transportation costs are considered together with location costs to design the operating facility pattern along a time horizon. The problem captures the difference in the scope of the location and routing decisions by considering different scales within the time horizon. Thus, solutions to this problem reflect the stability of locational decisions along time. The high complexity of this problem makes it impossible to be solved in practice with commercial software. For this reason, an approximation based on replacing vehicle routes by spanning trees is proposed, and its capability for providing good quality solutions is assessed in a series of computational experiments.     

基于期望视角的感知服务质量与顾客满意度区别研究

从期望出发,比较顾客视角的感知服务质量与满意度的区别。首先对期望概念进行明确界定,借鉴卡诺模型分类方法划分期望类别,基于重要性维度得到期望的三个类别:核心属性期望、重要属性期望和附加属性期望。以餐饮行业为实证研究背景,比较期望视角下的顾客满意度和感知服务质量的区别。发现核心属性期望、重要属性期望对顾客的服务质量评价影响更大,而附加属性期望对顾客的满意度评价影响更大。最后,给出企业对顾客期望、服务质量与顾客满意度的管理意义。     

US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology

We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.     

Some heuristic methods for solving p-median problems with a coverage constraint

The aim of this paper is to solve p-median problems with an additional coverage constraint. These problems arise in location applications, when the trade-off between distance and coverage is being calculated. Three kinds of heuristic algorithms are developed. First, local search procedures are designed both for constructing and improving feasible solutions. Second, a multistart GRASP heuristic is developed, based on the previous local search methods. Third, by employing Lagrangean relaxation methods, a very efficient Lagrangean heuristic algorithm is designed, which extends the well known algorithm of Handler and Zang, for constrained shortest path problems, to constrained p-median problems. Finally, a comparison of the computational efficiency of the developed methods is made between a variety of problems of different sizes.     

Integer linear programming models for grid-based light post location problem

Selecting optimal location is a key decision problem in business and engineering. This research focuses to develop mathematical models for a special type of location problems called grid-based location problems. It uses a real-world problem of placing lights in a park to minimize the amount of darkness and excess supply. The non-linear nature of the supply function (arising from the light physics) and heterogeneous demand distribution make this decision problem truly intractable to solve. We develop ILP models that are designed to provide the optimal solution for the light post problem: the total number of light posts, the location of each light post, and their capacities (i.e., brightness). Finally, the ILP models are implemented within a standard modeling language and solved with the CPLEX solver. Results show that the ILP models are quite efficient in solving moderately sized problems with a very small optimality gap.     

Uncertain models for single facility location problems on networks

In practical location problems on networks, the vertex demand is usually non-deterministic. This paper employs uncertainty theory to deal with this non-deterministic factor in single facility location problems. We first propose the concepts of satisfaction degree for both vertices and the whole network, which are used to evaluate products assignment. Based on different network satisfaction degree, two models are constructed. The solution to these models is based on Hakimi’s results, and some examples are given to illustrate these models.