Time-space Network Research Articles

Solving a Large-Scale Multi-Depot Vehicle Scheduling Problem in Urban Bus Systems

This study proposes an improved model and algorithm for the large-scale multi-depot vehicle scheduling problem (MDVSP) with departure-duration restrictions. In this study, the time-space network is applied to model the large-scale MDVSP. Considering that crews usually change shifts in the depot, departure-duration restrictions are added to the classic set-partitioning model to ensure that buses return to the depot when crews reach their working time limits. By embedding a preliminary exploring tactic to the shortest path faster algorithm (SPFA), researchers developed an improved large neighborhood search (LNS) algorithm to solve large-scale instances of MDVSP with departure-duration restrictions. The proposed methodology is applied to a real-life case in China and several test instances. The results show that the improved LNS algorithm can achieve very good performance in computational efficiency without deteriorating solution quality, which is important for large-scale systems. More specifically, the total cost of the improved LNS algorithm is approximately equal to branch-and-price, but the computational time is much shorter in the case study. For test instances with different number of timetabled trips (500, 1000, 1500, and 2000), the Quality Gap (QG) is very small, approximately 0.35%, 0.38%, 0.63%, and 0.93%, while the Efficiency Ratio (ER) reaches up to 2.89, 2.98, 3.65, and 3.79, respectively.

Optimal scheduling of a taxi fleet with mixed electric and gasoline vehicles to service advance reservations

This study addresses the problem of scheduling a fleet of taxis that are appointed to solely service customers with advance reservations. In contrast to previous studies that have dealt with the planning and operations of a taxi fleet with only electric vehicles (EVs), we consider that most taxi companies may have to operate with fleets comprised of both gasoline vehicles (GVs) and plug-in EVs during the transition from GV to (complete) EV taxi fleets. This paper presents an innovative multi-layer taxi-flow time-space network which effectively describes the movements of the taxis in the dimensions of space and time. An optimization model is then developed based on the time-space network to determine an optimal schedule for the taxi fleet. The objective is to minimize the total operating cost of the fleet, with a set of operating constraints for the EVs and GVs included in the model. Given that the model is formulated as an integer multi-commodity network flow problem, which is characterized as NP-hard, we propose two simple but effective decomposition-based heuristics to efficiently solve the problem with practical sizes. Test instances generated based on the data provided by a Taiwan taxi company are solved to evaluate the solution algorithms. The results show that the gaps between the objective values of the heuristic solutions and those of the optimal solutions are less than 3%, and the heuristics require much less time to obtain the good quality solutions. As a result, it is shown that the model, coupled with the algorithms, can be an effective planning tool to assist the company in routing and scheduling its fleet to service reservation customers.

Capturing correlation with a mixed recursive logit model for activity-travel scheduling

Representing activity-travel scheduling decisions as path choices in a time–space network is an emerging approach in the literature. In this paper, we model choices of activity, location, timing and transport mode using such an approach and seek to estimate utility parameters of recursive logit models. Relaxing the independence from irrelevant alternatives (IIA) property of the logit model in this setting raises a number of challenges. First, overlap in the network may not fully characterize perceptual correlation between paths, due to their interpretation as activity schedules. Second, the large number of states that are needed to represent all possible locations, times and activity combinations imposes major computational challenges to estimate the model. We combine recent methodological developments to build on previous work by Blom Västberg et al. (2016) and allow to model complex and realistic correlation patterns in this type of network. We use sampled choices sets in order to estimate a mixed recursive logit model in reasonable time for large-scale, dense time-space networks. Importantly, the model retains the advantage of fast predictions without sampling choice sets. In addition to estimation results, we present an extensive empirical analysis which highlights the different substitution patterns when the IIA property is relaxed, and a cross-validation study which confirms improved out-of-sample fit.

Real-time multi-depot vehicle type rescheduling problem

The multiple-depot vehicle type rescheduling problem (MDVTRSP) is a dynamic extension of the classic multiple-depot vehicle scheduling problem (MDVSP), where a heterogeneous fleet is considered. The MDVTRSP consists of finding a new schedule given that a severe disruption occurred in previously scheduled trips very quickly, simultaneously minimizing the transportation costs and the deviations from the original plan. Although several mathematical formulations and solution methods have been developed for the robust MDVTRSP, the real time MDVTRSP is still unexplored. In this paper, we introduce a formulation of the problem and develop a heuristic solution method, employing time-space network, truncated column generation, and preprocessing procedures. The solution method has been implemented in several algorithm variants, combining different developed preprocessing methods. Computational experiments on randomly generated instances were performed to evaluate the performance of the developed algorithms. The best solutions concerning efficiency and efficacy were obtained by the variants considering state space reductions to accelerate the convergence process of the column generation. Solutions were obtained very quickly (in less than 150 seconds for large instances, considering up to 2500 trips, eight depots, and one breakdown. The developed heuristics also presented a good behavior for several simultaneous disruptions, solving the problem with a little increase (less than 8.5%, on average) in the required CPU time. A case study using data from a real-life small instance in Brazil also demonstrated the efficiency and efficacy of the approach when compared with manual planning strategies.

Resolução integrada de problemas do planejamento do transporte público: foco na tabela de horários e no escalonamento de veículos com frota heterogênea

In this paper, we propose a new Integer Linear Programming model, based on a time-space network that integrates the timetable generation problem and the vehicle scheduling problem with heterogeneous fleet. A difference of this approach consists in considering the demand for the timetable redefinition and the vehicle scheduling, factor rarely applied in optimization models of the transportation system. We applied real and large random instances. The results indicate that the model may contribute to optimizing the public transport planning leading to significant savings in terms of scheduled vehicles. Moreover, as the timetable changes are fairly short, it is slightly modified, minimally modifying the passengers routine, which enables the application of these approaches to real context.

A real-time conflict solution algorithm for the train rescheduling problem

We consider the real-time resolution of conflicts arising in real-world train management applications. In particular, given a nominal timetable for a set of trains and a set of modifications due to delays or other resources unavailability, we are aiming at defining a set of actions which must be implemented to grant safety, e.g., to avoid potential conflicts such as train collisions or headway violations, and restore quality by reducing the delays. To be compatible with real-time management, the required actions must be determined in a few seconds, hence specialized fast heuristics must be used.We propose a fast and effective parallel algorithm that is based on an iterated greedy scheduling of trains on a time-space network. The algorithm uses several sortings to define the initial train dispatching rule and different shaking methods between iterations. The performance is further enhanced by using various sparsification methods for the time-space network. The best algorithm configuration is determined through extensive experiments, conducted on a set of instances derived from real-world networks and instances from the literature. The resulting heuristic proved able to consistently resolve the existing conflicts and obtaining excellent solution quality within just two seconds of computing time on a standard personal computer, for instances involving up to 151 trains and two hours of planning time horizon.

Heuristic algorithm for ready-mixed concrete plant scheduling with multiple mixers

Abstract In this study, the problem of integration of ready-mixed concrete (RMC) production scheduling and truck and pump dispatching in an RMC plant with multiple mixers is focused upon. A time-space network model, which combines RMC production and vehicle dispatching, is proposed. A heuristic algorithm with eight sets of conjoint priority rules for production scheduling, truck and pump dispatching, and mixer scheduling is developed to solve the problem. Computational experiments are conducted on actual cases collected from an RMC company; these cases are classified into four types based on the quantity of orders from construction sites and the discrete degree of construction sites. The advantages and disadvantages of adopting various conjoint-rules in the various types of cases are determined. The experimental results demonstrate that this heuristic solution is capable of enabling managers of RMC plants to develop more suitable schedules in various types of practical cases.

Stochastic fleet deployment models for public bicycle rental systems

ABSTRACTThis paper presents two stochastic bike deployment (SBD) models that determine the optimal number of bicycles allocated to each station in a leisure-oriented public bicycle rental system with stochastic demands. The SBD models represent the stochastic demands using a set of scenarios with given probabilities. A multilayer bike-flow time-space network is constructed for developing the models, where each layer corresponds to a given demand scenario and effectively describes bicycle flows in the spatial and temporal dimensions. As a result, the models are formulated as the integer multi-commodity network flow problem, which is characterized as NP-hard. We propose a heuristic to efficiently obtain good quality solutions for large-size model instances. Test instances are generated using real data from a bicycle rental system in Taiwan to evaluate the performance of the models and the solution algorithm. The test results show that the models can help the system operator of a public bicycle system make effective fleet deployment decisions.

Integrated optimization on train scheduling and preventive maintenance time slots planning

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.

Logistics planning for hospital pharmacy trusteeship under a hybrid of uncertainties

This paper presents two medicine logistics planning models by using a time-space network approach, one with deterministic variables and the other with stochastic variables. Flow dependent variable costs, random demand and random service time are featured in our models in addressing economies of scale and uncertainties in a real-world medical logistics problem. Effective computational schemes are designed, and an evaluation method is proposed to derive and assess a solution to the models. Numerical tests are conducted and show promising results for applications to a real-world problem.

Optimal Truck Dispatching For Construction Waste Conveyance

Abstract—Waste from the construction industry has to be conveyed to and disposed at specific waste-treatment plants. Decision makers, who work in environmental protection companies, usually schedule and dispatch the trucks used for conveying construction waste to plants manually, which is neither efficient nor effective. In practice, there are space and capacity limitations in every construction site and waste-treatment plant, meaning that the amount of the construction waste for transporting and disposing at a specific time and position is restricted. Moreover, when the number of trucks is insufficient, the responsible environmental protection companies could also hire vehicles from car rental companies. Given these considerations, coupled with the related operational constraints and objective of construction waste conveyance in practice, in this study we employ a time-space network flow technique to develop an optimal scheduling model that can assist decision makers in dispatching both their own and rented trucks for conveying construction waste efficiently. The model is formulated as an integer network flow problem with side constraints. Finally, a case study using the real data from an environmental protection company in Taiwan is performed and the results indicate that the model could be useful for dispatching trucks efficiently and thus decreasing the conveyance cost.

Novel time-space network flow formulation and approximate dynamic programming approach for the crane scheduling in a coil warehouse

This article proposes an efficient event-based time-space network flow model with side constraints for the crane scheduling problem in a coil warehouse where the crane should carry out a set of coil storage, retrieval and shuffling requests, and determine the sequence of handling these requests as well as the positions to which the coils are moved. The model is formulated based on a graph such that each node represents a location in the warehouse at the end of a specific scheduling stage, and each edge indicates a crane's move between two locations in a stage. Variables reduction strategies are presented to accelerate solving the model. In order to solve large-sized instances of the problem, an exact dynamic programming approach based on optimal assignments between coils and positions in a bipartite network with cuts is designed by exploiting the problem structure. Then an approximate dynamic programming (ADP) approach is developed, in which an affine value function approximation is defined as the estimation of crane's traveling time for handling each coil, and updated via iterations by collecting information from the solutions of separate subproblems. Computational results show that the proposed model is tighter and can be solved much more quickly than a traditional model for a reduced crane scheduling problem in the literature and the standard time-space network flow model. Besides, the proposed algorithm can obtain high quality solutions for large-sized instances in a few minutes and is more efficient in solving the problem than a commercial software package.

Rental bike location and allocation under stochastic demands

In this research, we develop four planning models for leisure-oriented public bicycle rental systems under deterministic and stochastic demands, respectively. Time-space network models are employed to determine the locations of bike rental stations, bike fleet allocation and bike routing. These models are formulated as mixed integer programs that are characterized as NP-hard. While the two deterministic models can be solved directly using CPLEX, a threshold-accepting-based heuristic is developed to efficiently solve the stochastic models. Finally, numerical tests using operating data from the New Taipei City Public Bike program are performed to evaluate the models and the solution algorithm. The test results show that the proposed models and solution algorithm are useful for practices.

Real-time management of transportation disruptions in forestry

In this paper, we present a mathematical programming model based on a time-space network representation for solving real-time transportation problems in forestry. We cover a wide range of unforeseen events that may disrupt the planned transportation operations (e.g., delays, changes in the demand and changes in the topology of the transportation network). Although each of these events has different impacts on the initial transportation plan, one key characteristic of the proposed model is that it remains valid for dealing with all the unforeseen events, regardless of their nature. Indeed, the impacts of such events are reflected in a time-space network and in the input parameters rather than in the model itself. The empirical evaluation of the proposed approach is based on data provided by Canadian forestry companies and tested under generated disruption scenarios. The test sets have been successfully solved to optimality in short computational times and demonstrate the potential improvement of transportation operations incurred by this approach.

A novel constraint propagation approach for airline schedule design problem

In this paper, we propose a novel finite domain constraint programming formulation using constraint propagation (CP) approach with variable and value ordering for solving flight scheduling problem. We subsequently model the same problem using time-space network representation and integer linear programming (ILP) technique. The performance of the CP and ILP models are evaluated on simulated and a real life case. The ILP and CP models are solved using CPLEX 12.2 solver and CP optimiser 12.2, respectively. We observe that the ILP model generates better first feasible solutions, while the CP model produces faster feasible solutions. In few cases, the CP model takes longer time compared to the ILP model. For the case data with 600 aircrafts and 1,000 markets, the CP model generates feasible solution rather faster, while the ILP model could not find feasible solution in a day for defined time-space network flow problem with some additional constraints.

Vulnerability Analysis of Railway Networks in Case of Multi-Link Blockage

Abstract: In this paper, we propose a methodology to analyze the most critical links of a railway network based on flow interdiction. Our strategy for network interdiction is to maximize network disruption by removing the links with the greatest impact to the system. For this purpose, we first introduce our primary model to determine vulnerable links based on routing costs, which are based on the minimum cost model. Next, we propose a heuristic approach to solve this model with partial enumeration of network components to assess the most vulnerable parts. Since an important factor in system vulnerability is flow, we introduce the time-space network flow model as the second model to simulate train flow in the network. After interdicting critical links in the railway network, the trains are scheduled in the residual network with considerations of various factors including customer demand, track and station capacities, and time planning horizon. The paper includes a computational instance which has been analyzed by the proposed models under various disruption scenarios, and the results are compared with full enumeration of network components using a network scan method. The accuracy of obtained results indicates the effectiveness of the proposed method in addition to fast computational time compared to the enumeration method.

Use of the Time-Space Network Technique for Modeling Gradual Flooding and Congestion Delays during Short-Notice Bus-Based Evacuations

Use of the Time-Space Network Technique for Modeling Gradual Flooding and Congestion Delays during Short-Notice Bus-Based Evacuations

A time-space network flow approach to dynamic repositioning in bicycle sharing systems

Faced with increasing population density, rising traffic congestion, and the resulting upsurge in carbon emissions, several urban metropolitan areas have instituted public bicycle sharing system as a viable alternative mode of transportation to complement existing long-distance bus- and metro- transit systems. A pressing issue that needs to be addressed in bike sharing systems is the accrued imbalance of bicycles between commuter demands and inventory levels at stations. To overcome this issue, a commonly employed strategy is to reposition bicycles during off-peak periods (typically at night) when no new user arrivals are expected. However, when such an imbalance occurs during day-time peak hours, such a passive strategy would result in lower resource utilization rates. To overcome this drawback, in this study, we propose a dynamic bicycle repositioning methodology that considers inventory level forecasting, user arrivals forecasting, bicycle repositioning, and vehicle routing in a unified manner. A multi-commodity time-space network flow model is presented, which results in an underlying complex nonlinear optimization problem. This problem is then reformulated into an equivalent mixed-integer problem using a model transformation approach and a novel heuristic algorithm is proposed to efficiently solve this model. Specifically, the first stage involves solving the linear relaxation of the MIP model, and a set covering problem is subsequently solved in the second stage to assign routes to the repositioning vehicles. The proposed methodology is evaluated using standard test-bed instances from the literature, and our numerical results reveal that the heuristic algorithm can achieve a significant reduction in rejected user requests when compared to existing methods, while yet expending only minimal computational effort.

Scheduling for yard cranes based on two-stage hybrid dynamic programming

Making operational plans for Yard Cranes (YCs) to enhance port efficiency has become vital issues for the container terminals. This paper discusses the load-scheduling problem of multiple YCs. The problem is to schedule two YCs at different container blocks, which serve the loading operations of one quay crane so as to minimize the total distance of visiting paths and the make-span at stack area. We consider the container handling time, the YC visiting time, and the waiting time of each YC when evaluating the make-span of the loading operation by YCs. Both the container bay visiting sequences and the number of containers picked up at each visit of the two YCs are determined simultaneously. A mathematical model, which considers interference between adjacent YCs, is provided by means of time-space network to formulate the problem and a two-stage hybrid algorithm composed of greedy algorithm and dynamic programming is developed to solve the proposed model. Numerical experiments were conducted to compare performances of the algorithm in this study with actual scheduling rules.

A Two-Stage Optimization Framework for Optimizing Large-Scale Vehicular Evacuation Routing and Scheduling Operation with Uninterrupted Traffic Flow

In many emergency management operations, an efficient evacuation strategy is of great importance because if it is successful, it has the ability to significantly reduce the loss of property and human life. This paper develops a routing and scheduling optimization framework for large-scale vehicular evacuation. To guarantee high optimization efficiency, we consider the routing and scheduling optimization as a two- stage problem instead of optimizing them as a whole (i.e. using time-space network). In the first phase, a multiple-objective mixed integer programming (MIP) model, with the objectives of minimizing the total in-network time and network clearance time is proposed to find an optimal routing plan. In the second phase, a simulation-based scheduling Heuristic is proposed to dynamically generate the time-dependent departure rates. A real-world evacuation scenario in Eastern Shore of Maryland is studied by using the proposed optimization model. The calculation results indicate a good optimization capability and flexibility of the proposed model. Keywords: Vehicular Evacuation, Routing, Scheduling, Optimization, Heuristic Copyright c 2016 SERSC Language: en