Solving the Capacitated Multifacility Weber Problem approximately

In this study, we consider the capacitated multifacility Weber problem which is concerned with locating m facilities in the plane, and allocating their limited capacities to n customers at minimum total cost. In this group of location-allocation problems, the only cost dealt with is the transportation cost that is proportional to the distance between the facility and the customer. The capacities of each facility and the demands and the locations of each customer are predetermined and given as parameters. This problem is an intractable non-convex optimization problem and difficult to solve. Therefore, using approximation strategies to compute efficient and accurate lower and upper bounds for the capacitated multifacility Weber problem can be a good approach. We first concentrate on the alternating location allocation heuristics. Then we continue with the discretization strategies and the Lagrangean relaxations of the approximating models. Some specific lower bounding algorithms are also defined by using the special properties of some of the distance functions. In addition to them, the relaxation of the main model is investigated and a Lagrangean heuristic is devised. In this heuristic, either a linear relaxation or exact solution of the Lagrangean subproblem is found by using column generation and branch and price algorithms combined with concave minimization. Although an exact solution methodology is not found, the approximation methods give accurate results. The tight bounds calculated by using these algorithms can be convenient in searching the exact solutions for this group of problems

Exploring the Effect of Variability of Urban Systems Characteristics in the Network Capacity

Mobility and transportation are two of the leading indicators of economic growth of a society. As cities around the world grow rapidly and more people and modes compete for limited urban space to travel, there is an increasing need to understand how this space is used for transportation and how it can be managed to improve accessibility for everyone. In a recent paper, Daganzo and Geroliminis explored the connection between network structure and a network’s MFD for urban neighborhoods with cars controlled by traffic signals and derived an analytical theory for the MFD using Variational Theory. Information needed to estimate this network MFD’s are average network (total length of roads in lane-km, number of lanes, length of links), control (signal offsets, green phase and cycle time) and traffic (free flow speed, congested wave speed, jam density, capacity) characteristics. However in previous studies, Variational Theory has been applied only in cities with deterministic values of the above variables for the whole network and by ignoring the effect of turns. In our study we are aiming to generate an MFD for streets with variable link lengths and signal characteristics and understand the effect of variability for different cities and signal structures. Furthermore, this variability gives the opportunity to mimic the effect of turning movements and heterogeneity in drivers’ behavior. This will be a key issue in planning the signal regimes such a way that maximizes the network capacity and/or the density range of the capacity

Extended Hypercube Models for Location Problems with Stochastic Demand

In spatial queues, servers travel to the customers and provide service on the scene. This property makes them applicable to emergency response (e.g. ambulances, police) and on-demand transportation systems (e.g. paratransit, taxis) location problems. However, in spatial queues, there exist a different service rate for each customer-server pairs which creates Markovian models with enormous number of states and makes these approaches difficult to apply on even medium sized problems. Because of demand uncertainty, the nearest servers to a customer might not be available to intervene and this can significantly increase the service times. In this paper, we propose two new aggregate models and an approximate solution method with a dynamic programming heuristic. Results are compared with existing location models on hypothetical and real cases

Hypercube queueing models for emergency response systems

Spatial queueing systems (SQS) can be defined as a type of queue that mobile servers are assigned to travel to the customer and provide on-scene service or the customers travel to service facilities to have service. It has a lot of application areas in literature from emergency response to vehicle repair services, dial-a-ride to paratransit. In this research, our aim is to find a rapid approach to calculate performance measures of SQS. Our ultimate aim is to utilize this rapid approach as an instance solver inside some optimization algorithms such as simulated annealing (SA) and variable neighborhood search (VNS) to find better location for systems such as ambulances, fire brigades. For this purpose, we have developed two methods to calculate performance measures of an instance of SQS. To check accuracy and efficiency, the approach is compared with simulation results on some instances. Then the two methods are used with SA and VNS to improve server locations. Results show that the approach is promising and can be applied as a tool inside some optimization algorithms

Extended Hypercube Models for Large Scale Spatial Queueing Systems

Different than the conventional queueing systems, in spatial queues, servers travel to the customers and provide service on the scene. This property makes them applicable to emergency response (e.g. ambulances, police, fire brigades) and on-demand transportation systems (e.g. shuttle bus services, paratransit, taxis). The difference between the spatial queues and conventional queueing systems is various types of customers and servers and different service rates for different customer-server pairs. For the Markovian arrival and service characteristics, one of the methods to find system performance measures is to model and calculate steady state probability of the Markov chain for the hypercube queueing model. One of the obstacles on the way to apply hypercube queueing models to real life problems is the size of the problem; it grows exponentially with the number of servers and a linear system with exponential number of variables should be solved for each instance. In this research, in order to increase scalability of the problem, we propose two new models. In addition to that, we modeled the problem by using Monte Carlo simulation and tested the convergence and stability properties of the simulation results and compare them with stationary distributions. In the final part, a mixed integer linear programming formulation is given for optimal server configuration with different objectives improving different performance measures. As a future work, we are planning to use the optimal solutions of this formulation to evaluate different dispatching policies

An Optimisation Framework for Airline Fleet Maintenance Scheduling with Tail Assignment Considerations

Fierce competition between airlines has led to the need of minimising the operating costs while also ensuring quality of service. Given the large proportion of operating costs dedicated to aircraft maintenance, cooperation between airlines and their respective maintenance provider is paramount. In this research, we propose a framework to develop commercially viable and maintenance feasible flight and maintenance schedules. Such framework involves two multi-objective mixed integer linear programming (MMILP) formulations and an iterative algorithm. The first formulation, the airline fleet maintenance scheduling (AMS) with violations, minimises the number of maintenance regulation violations and the number of not airworthy aircraft; subject to limited workshop resources and current maintenance regulations on individual aircraft flying hours. The second formulation, the AMS with tail assignment (TA) allows aircraft to be assigned to different flights. In this case, subject to similar constraints as the first formulation, six lexicographically ordered objective functions are minimised. Namely, the number of violations, maximum resource level, number of tail reassignments, number of maintenance interventions, overall resource usage, and the amount of maintenance required by each aircraft at the end of the planning horizon. The iterative algorithm ensures fast computational times while providing good quality solutions. Additionally, by tracking aircraft and using precise flying hours between maintenance opportunities, we ensure that the aircraft are airworthy at all times. Computational tests on real flight schedules over a 30-day planning horizon show that even with multiple airlines and workshops (16000 flights, 529 aircraft, 8 maintenance workshops) our solution approach can construct near-optimal maintenance schedules within minutes

Facility location problem for emergency and on-demand transportation systems

Although they have different objectives, emergency response systems and on-demand transportation systems are two similar systems in the sense that both deal with stochastic demand and service time which create congestions for moderate level of demand. Emergency response system location problems are one of the early problems immensely dealt in the literature. These problems are modeled by either set covering or transportation models which do not give much attention to the stochastic nature of the problem. On-demand transportation is a newly developing type of transportation system and literature is not broad enough but has similarities with emergency response systems. In this research, our aim is to solve facility location problem with stochastic demand and service time. Specifically we are dealing with temporal and spatial stochasticity which emerge because of the uncertainty in demand and service time. Recently we have developed a mixed aggregate hypercube model which are extensions to Larson (1974) and Boyacı and Geroliminis (2012). Results are promising and applicable to real life instances

Considering spatial and temporal flexibility in optimizing one-way electric carsharing systems

Carsharing is a shared-use vehicle model that allows users to rent cars for short periods of times. There are different types of systems according to their operational properties. In round-trip carsharing systems users are expected to return vehicles to their pickup locations. One-way systems relax this restriction and allows users to return cars to different drop-off locations. In station-based systems, there are designated parking locations to which vehicles should be returned. Free-floating systems relax this restriction and allow users to park vehicles to any legal parking locations within a designated area. In this research we are dealing with operational planning decisions in station-based one-way electric carsharing systems with dynamic relocations. Different than the previous work in literature, we introduce spatial and temporal flexibility to the system by considering multiple pick-up and drop-off times and locations at different prices to increase total profit of the system

Investigating the effect of temporal and spatial flexibility on the performance of one-way electric carsharing systems

One-way electric carsharing systems provide an environmentally friendly option for facilitating urban mobility needs. However, the management of one-way electric carsharing systems presents operational challenges stemming from the need to relocate cars in order to strike an optimum balance between demand and supply. As a result, the cost associated with vehicle relocation operations represents a significant proportion of the total operating cost. In the context of electric carsharing systems, the problem of vehicle relocation is further exacerbated by the car battery charging requirements. The introduction of temporal and spatial flexibility regarding the pick-up and drop-off of vehicles provides the means of improving the efficiency of one-way electric carsharing systems. However, the literature currently lacks models that can be used to investigate the effect of temporal and spatial flexibility on the performance of one-way electric carsharing systems. In this paper, we are introducing an integrated modeling and solution framework for investigating the effect of temporal and/or spatial flexibility, and different options for processing trip requests to the profitability and utilization of one-way electric carsharing systems. The application of the proposed framework to a realistic size system suggests that spatial flexibility has a stronger effect on the system performance than temporal flexibility. Furthermore, both spatial and temporal flexibility can increase the profitability of the system by serving more customers with fewer vehicle relocation needs

An event-based simulation for optimizing one-way car-sharing systems

Car-sharing systems allow registered users to use cars spread throughout an urban area: vehicles are at their disposal anytime they need one against some amount of money per minute rental. The customer avoids some issues linked to the ownership of a car such as insurance fees, maintenance or parking. Such a system is beneficial for the society in terms of environmental, energetic impacts and congestion. It completes the urban transportation service by allying the efficiency of public transportation and the flexibility of owning a vehicle. Car-sharing systems can be classified in different families depending on the rental conditions. For instance, free-floating systems allow people to park the vehicles anywhere in city area whereas non-free floating impose to users to park them inside stations with limited number of allowed spots. In this last family, another differentiating feature is the "one-way/two-way" characteristic: two-way systems force the user to return the car to the location where it was picked-up whereas one-way systems allow drop-off at any station. We focus in this research mainly on non-free-floating one-way electric systems. The system operations naturally induce imbalances in the distribution of vehicles that need to be corrected by performing relocations. Our aim is to model and simulate those operations to first analyze the way the system evolves with time and then to test different management policies for operations and especially relocations in order to both maximize customers' satisfaction and make the operation of the system sustainable for the operator