Dario Pacciarelli

A branch and bound algorithm for scheduling trains in a railway network

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.

Scheduling Problems with Two Competing Agents

We consider the scheduling problems arising when two agents, each with a set of nonpreemptive jobs, compete to perform their respective jobs on a common processing resource. Each agent wants to minimize a certain objective function, which depends on the completion times of its jobs only. The objective functions we consider in this paper are maximum of regular functions (associated with each job), number of late jobs, and total weighted completion times. We obtain different scenarios, depending on the objective function of each agent, and on the structure of the processing system (single machine or shop). For each scenario, we address the complexity of various problems, namely, finding the optimal solution for one agent with a constraint on the other agents cost function, finding single nondominated schedules (i.e., such that a better schedule for one of the two agents necessarily results in a worse schedule for the other agent), and generating all nondominated schedules.

Job-shop scheduling with blocking and no-wait constraints

Abstract In this paper, we study the job-shop scheduling problem with blocking and/or no-wait constraints. A blocking constraint models the absence of storage capacity between machines, while a no-wait constraint occurs when two consecutive operations in a job must be processed without any interruption. We formulate the problem by means of a generalization of the disjunctive graph of Roy and Sussman, that we call an alternative graph, and investigate the applicability to the blocking and no-wait cases of some of the most effective ideas from the literature on the job shop with unlimited buffers. We show that several key properties, used to design heuristic procedures, do not hold in the blocking and no-wait cases, while some of the most effective ideas used to develop branch and bound algorithms can be easily extended. We presents several complexity results and solution procedures. Computational results for fast heuristics and exact algorithms are also reported.

Reordering and Local Rerouting Strategies to Manage Train Traffic in Real Time

Traffic controllers regulate railway traffic by sequencing train movements and setting routes with the aim of ensuring smooth train behaviour and limiting, as much as possible, train delays. In this paper, we describe the implementation of a real-time traffic management system, called ROMA (Railway traffic Optimization by Means of Alternative graphs), to support controllers in the everyday task of managing disturbances. We make use of a branch-and-bound algorithm for sequencing train movements, while a local search algorithm is developed for rerouting optimization purposes. The compound problem of routing and sequencing trains is approached iteratively, computing an optimal train sequencing for given train routes and then improving this solution by locally rerouting some trains. An extensive computational study is carried out, based on a dispatching area of the Dutch railway network. We study practical size instances, and include in the model important operational constraints, including rolling stock and passenger connections. Different types of disturbances are analysed, including train delays and blocked tracks. Comparison with common dispatching practice shows the high potential of the system as an effective support tool to improve punctuality.

Multi-agent single machine scheduling

We consider the scheduling problems arising when several agents, each owning a set of nonpreemptive jobs, compete to perform their respective jobs on one shared processing resource. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The cost functions we consider in this paper are maximum of regular functions (associated with each job), number of late jobs and total weighted completion time. The different combinations of the cost functions of each agent lead to various problems, whose computational complexity is analysed in this paper. In particular, we investigate the problem of finding schedules whose cost for each agent does not exceed a given bound for each agent.

Production scheduling in a steelmaking-continuous casting plant

In this paper we describe an optimization procedure for planning the production of steel ingots in a steelmaking-continuous casting plant. The strict requirements of the production process defeated most of the earlier approaches to steelmaking-continuous casting production scheduling, mainly due to the lack of information in the optimization models. Our formulation of the problem is based on the alternative graph, which is a generalization of the disjunctive graph of Roy and Sussman. The alternative graph formulation allow us to describe in detail all the constraints that are relevant for the scheduling problem. We then solve the problem by using a beam search procedure, and compare our results with a lower bound of the optimal solutions and with the actual performance obtained in the plant. Computational experience shows the effectiveness of this approach.

Optimally balancing assembly lines with different workstations

In this paper, we consider the problem of assigning operations to an ordered sequence of non-identical workstations, observing precedence relationships and cycle time restrictions. The objective is to minimize the cost of the workstations. We first present a dynamic programming algorithm, and introduce several fathoming rules in order to reduce the number of states in the dynamic program. A characterization of a wide class of polynomially solvable instances is given, and computational results are reported.

Optimal multi-class rescheduling of railway traffic

During real-time traffic management, the railway system suffers perturbations. The task of dispatchers is to monitor traffic flow and to compute feasible rescheduling solutions in case of perturbed operations. The main objective of the infrastructure manager is delay minimization, but the dispatchers also need to comply with the objectives of the train operating companies. This paper presents an innovative optimization framework in order to reschedule trains with different classes of priority, that can be computed statically or dynamically in order to include the needs of different stakeholders. An iterative train scheduling procedure is proposed in order to compute feasible train schedules for an ordered set of priority classes, from the highest one to the lowest one. At each step, the procedure focuses on the current priority class, preserving solution quality from the higher priority classes and neglecting lower priority classes in the optimization of train orders and times. The multi-class rescheduling problem is formulated via alternative graphs that are able to model precisely train movements at the microscopic level of block sections and block signals. Each step of the iterative train scheduling procedure is solved to optimality by a state-of-the-art branch and bound algorithm. The results show an interesting gap between single-class and multi-class rescheduling problems in terms of delay minimization. Each priority class is also evaluated in order to assess the performance of the different rescheduling solutions.

Part sequencing in three-machine no-wait robotic cells

A no-wait robotic cell is an automated flow shop in which a robot is used to move the parts from a machine to the next. Parts are not allowed to wait. We analyze the complexity of the part sequencing problem in a robotic cell with three machines, for different periodical patterns of robot moves, when the objective is productivity maximization.

Scheduling of flexible flow lines in an automobile assembly plant

This paper deals with the material flow management in a large-scale manufacturing process, namely the assembly of automobiles in a highly automated plant in Italy. After a detailed description of the plant from the viewpoint of material flow issues, the modeling process and the methodologies employed to address the problems are illustrated. The decision models were validated by means of simulations of the real plant in several different production scenarios (varying demand volume and mix, resource availability etc.).