A hybrid optimization-simulation approach for robust weekly aircraft routing and retiming

We address the robust weekly aircraft routing and retiming problem, which requires determining weekly schedules for a heterogeneous fleet that maximizes the aircraft on-time performance, minimizes the total delay, and minimizes the number of delayed passengers. The fleet is required to serve a set of flights having known departure time windows while satisfying maintenance constraints. All flights are subject to random delays that may propagate through the network. We propose to solve this problem using a hybrid optimization-simulation approach based on a novel mixed-integer nonlinear programming model for the robust weekly aircraft maintenance routing problem. For this model, we provide an equivalent mixed-integer linear programming formulation that can be solved using a commercial solver. Furthermore, we describe a Monte-Carlo-based procedure for sequentially adjusting the flight departure times. We perform an extensive computational study using instances obtained from a major international airline, having up to 3387 flights and 164 aircraft, which demonstrates the efficacy of the proposed approach. Using the simulation software SimAir to assess the robustness of the solutions produced by our approach in comparison with that for the original solutions implemented by the airline, we found that on-time performance was improved by 9.8–16.0%, cumulative delay was reduced by 25.4–33.1%, and the number of delayed passengers was reduced by 8.2–51.6%.     

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.     

A distributed VNS algorithm for optimizing dial-a-ride problems in large-scale scenarios

These days, transportation and logistic problems in large cities are demanding smarter transportation services that provide flexibility and adaptability. A possible solution to this arising problem is to compute the best routes for each new scenario. In this problem, known in the literature as the dial-a-ride problem, a number of passengers are transported between pickup and delivery locations trying to minimize the routing costs while respecting a set of prespecified constraints. This problem has been solved in the literature with several approaches from small to medium sized problems. However, few efforts have dealt with large scale problems very common in massive scenarios (big cities or highly-populated regions). In this study, a new distributed algorithm based on the partition of the requests space and the combination of the routes is presented and tested on a set of 24 different scenarios of a large-scale problem (up to 16,000 requests or 32,000 locations) in the city of San Francisco. The results show that, not only the distributed algorithm is able to solve large problem instances that the corresponding sequential algorithm is unable to solve in a reasonable time, but also to have an average improvement of 9% in the smaller problems. The results have been validated by means of statistical procedures proving that the distributed algorithm can be an effective way to solve high dimensional dial-a-ride problems.     

Design and development of a hybrid ant colony-variable neighbourhood search algorithm for a multi-depot green vehicle routing problem

The traditional distribution planning problem in a supply chain has often been studied mainly with a focus on economic benefits. The growing concern about the effects of anthropogenic pollutions has forced researchers and supply chain practitioners to address the socio-environmental concerns. This research study focuses on incorporating the environmental impact on route design problem. In this work, the aim is to integrate both the objectives, namely economic cost and emission cost reduction for a capacitated multi-depot green vehicle routing problem. The proposed models are a significant contribution to the field of research in green vehicle routing problem at the operational level. The formulated integer linear programming model is solved for a set of small scale instances using LINGO solver. A computationally efficient Ant Colony Optimization (ACO) based meta-heuristic is developed for solving both small scale and large scale problem instances in reasonable amount of time. For solving large scale instances, the performance of the proposed ACO based meta-heuristic is improved by integrating it with a variable neighbourhood search.     

Application specific instance generator and a memetic algorithm for capacitated arc routing problems

Capacitated arc routing problem (CARP) is a well known combinatorial problem that requires identifying minimum total distance traveled by a fleet of vehicles in order to serve a set of roads without violating the vehicles’ capacity constraints. A number of optimization algorithms have been proposed over the years to solve basic CARPs and their performance have been analyzed using selected benchmark suites available in literature. From an application point of view, there is a need to assess the performance of algorithms on specific class of instances that resemble realistic applications, e.g., inspection of electric power lines, garbage collection, winter gritting etc. In this paper we introduce a benchmark generator that controls the size and complexity of the underlying road network resembling a target application. It allows generation of road networks with multiple lanes, one-way/two-way roads and varying degree of connectedness. Furthermore, an algorithm capable of solving real life CARP instances efficiently within a fixed computational budget of evaluations is introduced. The proposed algorithm, referred to as MA-CARP, is a memetic algorithm embedded with a similarity based parent selection scheme inspired by multiple sequence alignment, hybrid crossovers and a modified neighborhood search to improve its rate of convergence. The mechanism of test instance generation is presented for three typical scenarios, namely, inspection of electric power lines, garbage collection and winter gritting. The code for the generator is available from http://seit.unsw.adfa.edu.au/research/sites/mdo/Research-Data/InstanceGenerator.rar. The performance of the algorithm is compared with a state-of-the-art algorithm for three generated benchmarks. The results obtained using the proposed algorithm are better for all the above instances clearly highlighting its potential for solving CARP problems.     

Optimal planning of liquefied natural gas deliveries

We investigate the problem of designing an optimal annual delivery plan for Liquefied Natural Gas (LNG). This problem requires determining the long-term cargo delivery dates and the assignment of vessels to the cargoes while accommodating several constraints, including berth availability, liquefaction terminal inventory, planned maintenance, and bunkering requirements. We describe a novel mixed-integer programming formulation that captures important industry requirements and constraints with the objective of minimizing the vessel fleet size. A peculiar property of the proposed formulation is that it includes a polynomial number of variables and constraints and is, in our experience, computationally tractable for large problem instances using a commercial solver. Extensive computational runs demonstrate the efficacy of the proposed model for real instances provided by a major energy company that involve up to 118 cargoes and a 373-day planning horizon.     

Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots

Dial-a-ride problems are concerned with the design of efficient vehicle routes for transporting individual persons from specific origin to specific destination locations. In real-life this operational planning problem is often complicated by several factors. Users may have special requirements (e.g. to be transported in a wheelchair) while service providers operate a heterogeneous fleet of vehicles from multiple depots in their service area. In this paper, a general dial-a-ride problem in which these three real-life aspects may simultaneously be taken into account is introduced: the Multi-Depot Heterogeneous Dial-A-Ride Problem (MD-H-DARP). Both a three- and two-index formulation are discussed. A branch-and-cut algorithm for the standard dial-a-ride problem is adapted to exactly solve small problem instances of the MD-H-DARP. To be able to solve larger problem instances, a new deterministic annealing meta-heuristic is proposed. Extensive numerical experiments are presented on different sets of benchmark instances for the homogeneous and the heterogeneous single depot dial-a-ride problem. Instances for the MD-H-DARP are introduced as well. The branch-and-cut algorithm provides considerably better results than an existing algorithm which uses a less compact formulation. All seven previously unsolved benchmark instances for the heterogeneous dial-a-ride problem could be solved to optimality within a matter of seconds. While computation times of the exact algorithm increase drastically with problem size, the proposed meta-heuristic algorithm provides near-optimal solutions within limited computation time for all instances. Several best known solutions for unsolved instances are improved and the algorithm clearly outperforms current state-of-the-art heuristics for the homogeneous and heterogeneous dial-a-ride problem, both in terms of solution quality and computation time.     

Reasonable scheduling for arrival–departure track operations in railway stations

We analyze the train types handled at a section station and the factors affecting the scheduling of the arrival–departure track operation, using the following conditions as our optimization goals: operating the arrival–departure tracks in accordance with a fixed operation scheme, and reducing the influence which the departing–receiving operations impose on shunting operations. We establish a 0–1 integer programming model for formulating a track operation plan. By applying modern sequencing theory, this is transformed into a fixed sequencing model of special parallel machines. We then design a heuristic algorithm to solve the model. Finally, the example of Yiyang railway station is used to verify the advantages of the model and the algorithm. A better operation plan is obtained using MATLAB 7.0 by applying the model and the algorithm provided in the paper, indicating the superiority of our study’s approach.     

A semi-analytical approach for solving the bottleneck model with general user heterogeneity

This paper proposes a novel semi-analytical approach for solving the dynamic user equilibrium (DUE) of a bottleneck model with general heterogeneous users. The proposed approach makes use of the analytical solutions from the bottleneck analysis to create an equivalent assignment problem that admits closed-form commute cost functions. The equivalent problem is a static and asymmetric traffic assignment problem, which can be formulated as a variational inequality problem (VIP). This approach provides a new tool to analyze the properties of the bottleneck model with general heterogeneity, and to design efficient solution methods. In particular, the existence and uniqueness of the DUE solution can be established using the P-property of the Jacobian matrix. Our numerical experiments show that a simple decomposition algorithm is able to quickly solve the equivalent VIP to high precision. The proposed VIP formation is also extended to address simultaneous departure time and route choice in a single O–D origin-destination network with multiple parallel routes.     

A disjunctive convex programming approach to the pollution-routing problem

The pollution-routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of values. In this paper, we keep speed as a continuous decision variable within an interval and propose new formulations for the PRP. In particular, we build two mixed-integer convex optimization models for the PRP, by employing tools from disjunctive convex programming. These are the first arc-based formulations for the PRP with continuous speed. We also derive several families of valid inequalities to further strengthen both models. We test the proposed formulations on benchmark instances. Some instances are solved to optimality for the first time.     

Designing an integrated distribution system for catering services for high-speed railways: A three-echelon location routing model with tight time windows and time deadlines

An emerging task in catering services for high-speed railways (CSHR) is to design a distribution system for the delivery of high-quality perishable food products to trains in need. This paper proposes a novel model for integrating location decision making with daily rail catering operations, which are affected by various aspects of rail planning, to meet time-sensitive passenger demands. A three-echelon location routing problem with time windows and time budget constraints (3E-LRPTWTBC) is thus proposed toward formulating this integrated distribution system design problem. This model attempts to determine the capacities/locations of distribution centers and to optimize the number of meals delivered to stations. The model also attempts to generate a schedule for refrigerated cars traveling from distribution centers to rail stations for train loading whereby meals can be catered to trains within tight time windows and sold before a specified time deadline. By relaxing the time-window constraints, a relaxation model that can be solved using an off-the-shelf mixed integer programming (MIP) solver is obtained to provide a lower bound on the 3E-LRPTWTBC. A hybrid cross entropy algorithm (HCEA) is proposed to solve the 3E-LRPTWTBC. A small-scale case study is implemented, which reveals a 9.3% gap between the solution obtained using the HCEA and that obtained using the relaxation model (RM). A comparative analysis of the HCEA and an exhaustive enumeration algorithm indicates that the HCEA shows good performance in terms of computation time. Finally, a case study considering 156 trains on the Beijing-Shanghai high-speed corridor and a large-scale case study considering 1130 trains on the Chinese railway network are addressed in a comprehensive study to demonstrate the applicability of the proposed models and algorithm.     

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.     

Short-term planning of liquefied natural gas deliveries

The ability of a supplier of liquefied natural gas (LNG) to deliver cargoes at desired times, while effectively managing a fleet of cryogenic vessels can significantly impact its profits. We investigate in this paper an LNG short-term delivery planning problem by considering mandatory cargoes as well as optional cargoes to select, along with the scheduling of a heterogeneous vessel fleet with controllable cruising speeds. Several technical constraints are accommodated including time windows, berth availability, bunkering restrictions, inventory, liquefaction terminal storage capacity, maximum waiting time, and planned maintenance restrictions. The objective is to maximize the net profit.We propose a mixed-integer programming formulation that includes a polynomial number of variables and constraints and accommodates all of the problem features. Also, we describe an optimization-based variable neighborhood search procedure that embeds the proposed compact formulation. To assess the quality of the generated solutions, we propose a second valid formulation with an exponential number of decision variables and we solve its linear programming relaxation using column generation. We provide the results of extensive computational results that were carried out on a set of large-scale set of realistic instances, with up to 62 vessels and 160 cargoes, provided by a major LNG producer. These results provide evidence that the proposed improvement procedure yields high-quality solutions.     

Integrated scheduling of m-truck,m-drone,and m-depot constrained by time-window,drop-pickup,and m-visit using constraint programming

The idea of deploying unmanned aerial vehicles, also known as drones, for final-mile delivery in logistics operations has vitalized this new research stream. One conceivable scenario of using a drone in conjunction with a traditional delivery truck to distribute parcels is discussed in earlier literature and termed the parallel drone scheduling traveling salesman problem (PDSTSP). This study extends the problem by considering two different types of drone tasks: drop and pickup. After a drone completes a drop, the drone can either fly back to depot to deliver the next parcels or fly directly to another customer for pickup. Integrated scheduling of multiple depots hosting a fleet of trucks and a fleet of drones is further studied to achieve an operational excellence. A vehicle that travels near the boundary of the coverage area might be more effective to serve customers that belong to the neighboring depot. This problem is uniquely modeled as an unrelated parallel machine scheduling with sequence dependent setup, precedence-relationship, and reentrant, which gives us a framework to effectively consider those operational challenges. A constraint programming approach is proposed and tested with problem instances of m-truck, m-drone, m-depot, and hundred-customer distributed across an 8-mile square region.     

A column generation algorithm for the bus driver scheduling problem

Bus driver scheduling aims to find the minimum number of bus drivers to cover a published timetable of a bus company. When scheduling bus drivers, contractual working rules must be enforced, thus complicating the problem. In this research, we develop a column generation algorithm that decomposes this complicated problem into a master problem and a series of pricing subproblems. The master problem selects optimal duties from a set of known feasible duties, and the pricing subproblem augments the feasible duty set to improve the solution obtained in the master problem. The proposed algorithm is empirically applied to the realistic problems of several bus companies. The numerical results show that the proposed column generation algorithm can solve real‐world problems and obtain bus driver schedules that are better than those developed and used by the bus companies. Copyright © 2016 John Wiley & Sons, Ltd.     

A math-heuristic algorithm for the integrated air service recovery

A sophisticated flight schedule might be easily disrupted due to adverse weather, aircraft mechanical failures, crew absences, etc. Airlines incur huge costs stemming from such flight schedule disruptions in addition to the serious inconveniences experienced by passengers. Therefore, an efficient recovery solution that simultaneously decreases an airline's recovery cost while simultaneously mitigating passenger dissatisfaction is of great importance to the airline industry. In this paper, we study the integrated airline service recovery problem in which the aircraft and passenger schedule recovery problems are simultaneously addressed, with the objective of minimizing aircraft recovery and operating costs, passenger itinerary delay cost, and passenger itinerary cancellation cost.Recognizing the inherent difficulty in modeling the integrated airline service recovery problem within a single formulation (due to its huge solution space and quick response requirement), we propose a three-stage sequential math-heuristic framework to efficiently solve this problem, wherein the flight schedules and aircraft rotations are recovered in the first stage, Then, a flight rescheduling problem and passenger schedule recovery problems are iteratively solved in the next two stages. Time-space network flow representations, along with mixed-integer programming formulations, and algorithms that take advantages of the underlying problem structures, are proposed for each of three stages. This algorithm was tested on realistic data provided by the ROADEF 2009 challenge and the computational results reveal that our algorithm generated the best solution in nearly 72% of the test instances, and a near-optimal solution was achieved in the remaining instances within an acceptable timeframe. Furthermore, we also ran additional computational runs to explore the underlying characteristics of the proposed algorithm, and the recorded insights can serve as a useful guide during practical implementations of this algorithm.     

Spatial allocation on a network with congestion

This article formalizes the land use design problem as a discrete-convex programming problem integrating within a quadratic assignment framework a realistic representation of transportation behavior (automobile congestion and variable demand for travel) as modelled by a combined trip distribution trip assignment model. Hill-climbing algorithms are proposed to solve the resulting optimization problem. Their performance is compared and evaluated on a set of test problems.     

带时间窗的混和车辆路径问题的优化算法研究

文章针对带时间窗约束的混合车辆路径问题的特点,建立了带时间窗的混合车辆路径问题的数学模型,并设计了变邻域禁忌搜索算法对该问题进行求解。通过标准算例测试及与现有文献计算结果的比较,验证了该算法的有效性。     

Transportation service procurement problem with transit time

In this work, we investigate transit time in transportation service procurement, which is conducted by shippers using auctions to purchase transportation service from carriers in the planning stage. Besides cost, we find that many shippers are most concerned with transit time in practice; shorter transit time indicates better transportation service. To minimize both the total cost and transit time, the problem faced by shippers is the biobjective transportation service procurement problem with transit time. To solve the problem, we introduce a biobjective integer programming model that can also accommodate some important business constraints. A biobjective branch-and-bound algorithm that finds all extreme supported nondominated solutions is developed. To speed up the algorithm, two fast feasibility checks, a network flow model for particular subproblems, and lower bounds from relaxation are proposed. In addition, a sophisticated heuristic is introduced to meet shipper’s requirements in some situations. Computational experiments on evaluating the performance of the algorithms are conducted on a set of test instances that are generated from practical data.     

Multi-scenario optimization approach for assessing the impacts of advanced traffic information under realistic stochastic capacity distributions

In this study, to incorporate realistic discrete stochastic capacity distribution over a large number of sampling days or scenarios (say 30–100 days), we propose a multi-scenario based optimization model with different types of traveler knowledge in an advanced traveler information provision environment. The proposed method categorizes commuters into two classes: (1) those with access to perfect traffic information every day, and (2) those with knowledge of the expected traffic conditions (and related reliability measure) across a large number of different sampling days. Using a gap function framework or describing the mixed user equilibrium under different information availability over a long-term steady state, a nonlinear programming model is formulated to describe the route choice behavior of the perfect information (PI) and expected travel time (ETT) user classes under stochastic day-dependent travel time. Driven by a computationally efficient algorithm suitable for large-scale networks, the model was implemented in a standard optimization solver and an open-source simulation package and further applied to medium-scale networks to examine the effectiveness of dynamic traveler information under realistic stochastic capacity conditions.