Location models for airline hubs behaving as M/D/c queues

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and {\em c} servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of {\em b} airplanes in queue, to be lesser than a value $\alpha$. Due to the computational complexity of the formulation. The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.Hub location, congestion, tabu-search

Hierarchical location-allocation models for congested systems

In this paper we address the issue of locating hierarchical facilities in the presence of congestion. Two hierarchical models are presented, where lower level servers attend requests first, and then, some of the served customers are referred to higher level servers. In the first model, the objective is to find the minimum number of servers and their locations that will cover a given region with a distance or time standard. The second model is cast as a Maximal Covering Location formulation. A heuristic procedure is then presented together with computational experience. Finally, some extensions of these models that address other types of spatial configurations are offered.Hierarchical location, congestion, queueing

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

Hub Network Design and Discrete Location: Economies of Scale, Reliability and Service Level Considerations

In this thesis, we study three related decision problems in location theory. The first part of the dissertation presents solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p-hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a greedy randomized adaptive search algorithm that is used to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed solution algorithms. In the second part of this dissertation, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes. In the last part of this dissertation we study the dynamic facility location problem with service level constraints (DFLPSL). The DFLPSL seeks to locate a set of facilities with sufficient capacities over a planning horizon to serve customers at minimum cost while a service level requirement is met. This problem captures two important sources of stochasticity in facility location by considering known probability distribution functions associated with processing and routing times. We present a nonlinear mixed integer programming formulation and provide feasible solutions using two heuristic approaches. We present the results of computational experiments to analyze the impact and potential benefits of explicitly considering service level constraints when designing distribution systems

Integrated Management of Emergency Vehicle Fleet

The growing public concerns for safety and the advances in traffic management systems, that have made the availability of real-time traffic information a reality, have created an opportunity to build integrated decision support systems that can improve the coordination and sharing of information between agencies that are responsible for public safety and security and transportation agencies to provide more efficient Emergency Response Service. In an Emergency Response System, reduction of the duration of response time can yield substantial benefits. The response time plays a crucial role in minimizing the adverse impacts: fatalities and loss of property can be greatly reduced by reducing the response time for emergencies. In this dissertation, we have developed an integrated model that can assist emergency response fleet dispatchers in managing the fleet. This model can help reduce the response time and improve service level by specifically accounting for the following: Vehicle Deployment: given real-time information about the status of the emergency response fleet, traffic information and the status of emergency calls, select proper fleet assignment schemes that satisfy various operation requirements. Vehicle Routing: given real-time traffic information, provide real-time route guidance for drivers of dispatched vehicles. This goal is achieved by applying various shortest path algorithms into the solution procedure. Planning and Evaluation: given the status of the fleet and the frequency of emergency calls in various areas of a region, the model can help evaluate the performance of the current system and help plan for potential sites for the relocation of vehicles and allocate an appropriate fleet of vehicles to these sites. The vehicle deployment problem is formulated as an integer optimization problem. Since this problem has been shown to be NP-hard and because of the nature of emergency response, we developed heuristics which can provide quality solutions with short computational times. Several test algorithms are proposed to solve the emergency response vehicle deployment problem. Different methods for obtaining lower bounds for the value of objective function are analyzed in this dissertation. To evaluate the performance of the system under various scenarios, a simulation model is developed. The simulation system is calibrated based on real-world data. The results of simulation and analysis show the proposed system can effectively improve the emergency response service level. Application of this model in facility allocation illustrates its usage in other relevant operational scenarios

Emergency Medical Service Ambulance System Planning: History and Models

Integer linear programming models that incorporate probabilistic and stochastic components represent one approach for capturing the stochastic nature of emergency medical service ambulance systems. This includes modeling non-deterministic call arrival and servicing rates and congestion in the ambulance network (i.e., ambulance unavailability). These models focus on maximizing the total population that can find an available ambulance within a set service time standard (s) with a probability of at least α%. In MALP the concept of local vehicle busyness estimates is introduced to estimate the availability of service in a neighborhood given the neighborhood’s level of demand and the number of ambulance vehicles located in the neighborhood. QMALP is an extension of MALP where queue-theory derived parameters are implemented in the MALP model framework in order to relax the assumption that the probability of different ambulances being busy are independent. Despite this considerable development, several concerns remained about MALP and QMALP, namely the districting assumption where its assumed that a neighborhood’s calls for service are served only by an ambulance in the area, that ambulances in a neighborhood only serve calls for service originating within the neighborhood, or that at least the flow of ambulance service to and from external neighborhoods was roughly equal. Questions have been raised about the validity of MALP and QMALP’s reliability estimates, that is, whether a neighborhood actually received α-reliable service.To address these issues, we developed the Resource-Constrained Queue-based Maximum Availability Location Problem (RC-QMALP). This model is based on a location-allocation framework that (1) assigns workload from neighborhoods to ambulances located within s and ambulance idle capacity to neighborhoods and (2) includes additional constraints designed to help ensure the validity of the original MALP and QMALP constraints used to establish whether a neighborhood can find an available ambulance with α-reliability. We also implemented a secondary minsum objective that minimizes the average travel distance between ambulances and the neighborhoods they service while maintaining the priority of the MALP and QMALP coverage objective.In this thesis, we validated RC-QMALP by comparing the reliable coverage levels predicted by the RC-QMALP to the ambulance system simulations that used the locational configurations suggested by the RC-QMALP. We found that MALP 2 and QMALP provided higher levels of reliable coverage and that RC-QMALP’s secondary objective has a negligible impact on system performance. However, RC-QMALP-based models provide more accurate estimates of reliable coverage and location solutions whose simulated reliable coverage performance was always within 5% of the optimal solution with the same system parameters (we tested 1,080 different model configurations). Our work suggests that (1) simulation models must be developed to handle the modeling assumptions that underlie location optimization models and that (2) service reliability location models should consider additional factors such as ambulance workloads (and their distribution)