The efficiency of automated container terminals primarily depends on the synchronization of automated-guided vehicles (AGVs) and automated cranes. Accordingly, we study the integrated rail-mounted yard crane and AGV scheduling problem as a multi-robot coordination and scheduling problem in this paper. Based on a discretized virtualized network, we propose a multi-commodity network flow model with two sets of flow balance constraints for cranes and AGVs. In addition, two side constraints are introduced to deal with inter-robot constraints to reflect the complex interactions among terminal agents accurately. The Alternating Direction Method of Multipliers (ADMM) method is adopted in this study as a market-driven approach to dualize the hard side constraints; therefore, the original problem is decomposed into a set of crane-specific and vehicle-specific subtasks. The cost-effective solutions can be obtained by iteratively adjusting both the primal and dual costs of each subtask. We also compare the computational performance of the proposed solution framework with that of the resource-constrained project scheduling problem (RCPSP) model using commercial solvers. Comparison results indicate that our proposed approach could efficiently find solutions within 2% optimality gaps. Illustrative and real-world instances show that the proposed approach effectively serves the accurate coordination of AGVs and cranes in automated terminals.

Yard crane and AGV scheduling in automated container terminal: A multi-robot task allocation framework

The cyclic train timetabling problem aims to synchronize limited operational resources toward a master periodic schedule of transport services. By introducing an extended time-space network construct, this paper proposes a new type of integer programming model reformulation for the cyclic train timetabling problem on a double-track railway corridor at the macroscopic level. This reformulation method also holds the promises to be applied in a broader set of routing and scheduling problems with periodic activity requirements. We also hope that this space-time network extension technique, as a special version of variable splitting methods in the dual decomposition literature, could potentially bridge the modeling gaps between cyclic and non-cyclic timetables. Specifically, the existing mathematical programming model for the periodic event scheduling problem (PESP) is transformed into a multi-commodity network flow model with two coupled schedule networks and side track capacity constraints. In addition, two dual decomposition methods including Lagrangian relaxation and Alternating Direction Method of Multipliers (ADMM), are adopted to dualize the side track capacity constraints. For each train-specific sub-problem in an iterative primal and dual optimization framework, we develop an enhanced version of forward dynamic programming to find the time-dependent least cost master schedule across the time-space network over multiple periods. ADMM-motivated heuristic methods with adjusted penalty parameters are also developed to obtain good upper bound solutions. Based on real-world instances from the Beijing-Shanghai high-speed railway corridor, we compare the numerical performance between the proposed reformulation and the PESP model that involves the standard optimization solver.

/pdf/solving-cyclic-train-timetabling-problem-through-model-5cmwwyhj7q.pdf

Solving cyclic train timetabling problem through model reformulation: Extended time-space network construct and Alternating Direction Method of Multipliers methods

Trains normally run as scheduled in a non-disrupted situation. However, due to external and/or internal factors, trains may deviate from their original timetable during daily operations. To this end, the involved dispatchers are required to reschedule disrupted trains to efficiently transport delayed passengers to their destinations as soon as possible. In this study, we focus on train rescheduling in a seriously disrupted situation where a track segment is completely blocked for a relatively long period of time, e.g., two hours. In this situation, trains cannot pass the disrupted segment, meaning that passengers will be unable to travel as scheduled. We simultaneously rescheduled trains and passenger routes from both the operator’s and passengers’ perspectives. This integrated train rescheduling and passenger rerouting problem was formulated with an Integer Linear Programming model based on a space-time network. We decomposed the integrated model into two subproblems, a train rescheduling problem and a passenger routing problem, using the alternating direction method of multipliers (ADMM) algorithm. Both subproblems could be further decomposed into a series of shortest path problems for trains or passengers, and solved by a dynamic programming algorithm. Finally, we tested our models and algorithms on both a small hypothetical railway network and a part of the Chinese high-speed railway network.

Integrated railway timetable rescheduling and dynamic passenger routing during a complete blockage

Data science and big data analytics: a systematic review of methodologies used in the supply chain and logistics research

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.

Analytics and Machine Learning in Vehicle Routing Research.

Emerging urban logistics applications need to address various challenges, including complex traffic conditions and time-sensitive requirements. In this study, in the context of urban logistics, we consider a vehicle routing problem with time-dependent travel times and time windows (VRPTW), and the goal is to minimize the total generalized costs including the transportation, waiting time, and fixed costs associated with each vehicle. We adopt a high-dimensional space–time network flow model to formulate an underlying vehicle routing problem (VRP) with a rich set of criteria and constraints. A difficult issue, when solving VRPs, is how to iteratively improve both the primal and dual solution quality in general and how to break the symmetry generated by many identical solutions, particularly with homogeneous vehicles. Along this line, many coupling constraints, such as the consensus constraints across different agents or decision makers, need to be carefully addressed to find high-quality optimal or close-to-optimal solutions under medium- or large-scale instances. Currently, the alternating direction method of multipliers (ADMM) is widely used in the field of convex optimization, as an integration of the augmented Lagrangian relaxation and block coordinate descent methods, for machine learning and large-scale continuous systems optimization and control. In this work, we introduce the use of ADMM to solve the multi-VRP, which is a special case of integer linear programming, and demonstrate a manner to reduce the quadratic penalty terms used in ADMM into simple linear functions. In a broader context, a computationally reliable decomposition framework is developed to iteratively improve both the primal and dual solution quality. Essentially, the least-cost path subproblem or other similar subproblems involving binary decisions can be embedded into a sequential solution scheme with an output of both lower bound estimates and upper bound feasible solutions. We examine the performance of the proposed approach using classical Solomon VRP benchmark instances. We also evaluate our approach on a real-world instance based on a problem-solving competition by Jingdong Logistics, a major E-commerce company.

https://par.nsf.gov/servlets/purl/10124683

ADMM-based problem decomposition scheme for vehicle routing problem with time windows

Facing uncertain and dynamic demands over different days, logistics companies need to adopt adaptive solutions for the last-mile delivery. Meanwhile, one of the major barriers for implementing vehicle routing problem (VRP) algorithms in real world dispatching systems is the stability of delivery driver’s routes and schedules. To establish a theoretically sound and practically useful solution framework, this paper aims to optimize robust and consistent space-time paths for the multi-day VRP by providing daily schedules with limited variations from the master schedule. A multi-commodity network flow-based optimization model is proposed to minimize generalized transportation costs and the daily deviation of day-dependent space-time paths among demand analysis zones. Lagrange relaxation (LR) methods and alternating direction method of multipliers (ADMM) are used to handle complex side constraints. Experiments on illustrative networks and Beijing delivery network are developed to demonstrate the effectiveness of the proposed method.

Finding robust and consistent space-time delivery paths for multi-day vehicle routing problem*

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ADMM-based problem decomposition scheme for vehicle routing problem with time windows

Finding robust and consistent space-time delivery paths for multi-day vehicle routing problem*