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 agent's 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

A bilevel rescheduling framework for optimal inter-area train coordination

Railway dispatchers reschedule trains in real-time in order to limit the propagation of disturbances and to regulate traffic in their respective dispatching areas by minimizing the deviation from the off-line timetable. However, the decisions taken in one area may influence the quality and even the feasibility of train schedules in the other areas. Regional control centers coordinate the dispatchers\u27 work for multiple areas in order to regulate traffic at the global level and to avoid situations of global infeasibility. Differently from the dispatcher problem, the coordination activity of regional control centers is still underinvestigated, even if this activity is a key factor for effective traffic management. This paper studies the problem of coordinating several dispatchers with the objective of driving their behavior towards globally optimal solutions. With our model, a coordinator may impose constraints at the border of each dispatching area. Each dispatcher must then schedule trains in its area by producing a locally feasible solution compliant with the border constraints imposed by the coordinator. The problem faced by the coordinator is therefore a bilevel programming problem in which the variables controlled by the coordinator are the border constraints. We demonstrate that the coordinator problem can be solved to optimality with a branch and bound procedure. The coordination algorithm has been tested on a large real railway network in the Netherlands with busy traffic conditions. Our experimental results show that a proven optimal solution is frequently found for various network divisions within computation times compatible with real-time operations

Part sequencing in three-machine no-wait robotic cells

Abstract A no-wait robotic cell is an automated ow 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 di erent periodical patterns of robot moves, when the objective is productivity maximization

Susceptibility of optimal train schedules to stochastic disturbances of process times

This work focuses on the stochastic evaluation of train schedules computed by a microscopic scheduler of railway operations based on deterministic information. The research question is to assess the degree of sensitivity of various rescheduling algorithms to variations in process times (running and dwell times). In fact, the objective of railway traffic management is to reduce delay propagation and to increase disturbance robustness of train schedules at a network scale. We present a quantitative study of traffic disturbances and their effects on the schedules computed by simple and advanced rescheduling algorithms. Computational results are based on a complex and densely occupied Dutch railway area; train delays are computed based on accepted statistical distributions, and dwell and running times of trains are subject to additional stochastic variations. From the results obtained on a real case study, an advanced branch and bound algorithm, on average, outperforms a First In First Out scheduling rule both in deterministic and stochastic traffic scenarios. However, the characteristic of the stochastic processes and the way a stochastic instance is handled turn out to have a serious impact on the scheduler performance

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