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"Agnetis, Alessandro"
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Multiagent Scheduling : Models and Algorithms
Scheduling theory has received a growing interest since its origins in the second half of the 20th century. Developed initially for the study of scheduling problems with a single objective, the theory has been recently extended to problems involving multiple criteria. However, this extension has still left a gap between the classical multi-criteria approaches and some real-life problems in which not all jobs contribute to the evaluation of each criterion. In this book, we close this gap by presenting and developing multi-agent scheduling models in which subsets of jobs sharing the same resources are evaluated by different criteria. Several scenarios are introduced, depending on the definition and the intersection structure of the job subsets. Complexity results, approximation schemes, heuristics and exact algorithms are discussed for single-machine and parallel-machine scheduling environments. Definitions and algorithms are illustrated with the help of examples and figures.
Book
Scheduling Jobs on Unreliable Machines Subject to Linear Risk
Background: This paper addresses a new class of scheduling problems in the context of machines subject to (unrecoverable) interruptions; i.e., when a machine fails, the current and subsequently scheduled work on that machine is lost. Each job has a certain processing time and a reward that is attained if the job is successfully completed. Methods: For the failure process, we considered the linear risk model, according to which the probability of machine failure is uniform across a certain time horizon. Results: We analyzed both the situation in which the set of jobs is given, and that in which jobs must be selected from a pool of jobs, at a certain selection cost. Conclusions: We characterized the complexity of various problems, showing both hardness results and polynomial algorithms, and pointed out some open problems.
Journal Article
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. [PUBLICATION ABSTRACT]
Journal Article
Some Results on Shop Scheduling with S-Precedence Constraints among Job Tasks
We address some special cases of job shop and flow shop scheduling problems with s-precedence constraints. Unlike the classical setting, in which precedence constraints among the tasks of a job are finish–start, here the task of a job cannot start before the task preceding it has started. We give polynomial exact algorithms for the following problems: a two-machine job shop with two jobs when recirculation is allowed (i.e., jobs can visit the same machine many times), a two-machine flow shop, and an m-machine flow shop with two jobs. We also point out some special cases whose complexity status is open.
Journal Article
Price of anarchy and price of stability in multi-agent project scheduling
We consider a project scheduling environment in which the activities are partitioned among a set of agents. The owner of each activity can decide its length, which is linearly related to its cost within a minimum (crash) and a maximum (normal) length. For each day the project makespan is reduced with respect to its normal value, a reward is offered to the agents, and each agent receives a given ratio of the reward. As in classical game theory, we assume that the agents’ parameters are common knowledge. We study the Nash equilibria of the corresponding non-cooperative game as a desired state where no agent is motivated to change his/her decision. Regarding project makespan as an overall measure of efficiency, here we consider the worst and the best Nash equilibria (i.e., for which makespan is maximum and, respectively, minimum among Nash equilibria). We show that the problem of finding the worst Nash equilibrium is NP-hard (finding the best Nash equilibrium is already known to be strongly NP-hard), and propose an ILP formulation for its computation. We then investigate the values of the price of anarchy and the price of stability in a large sample of realistic size problems and get useful insights for the project owner.
Journal Article
A decomposition approach for the combined master surgical schedule and surgical case assignment problems
This research aims at supporting hospital management in making prompt Operating Room (OR) planning decisions, when either unpredicted events occur or alternative scenarios or configurations need to be rapidly evaluated. We design and test a planning tool enabling managers to efficiently analyse several alternatives to the current OR planning and scheduling. To this aim, we propose a decomposition approach. More specifically, we first focus on determining the Master Surgical Schedule (MSS) on a weekly basis, by assigning the different surgical disciplines to the available sessions. Next, we allocate surgeries to each session, focusing on elective patients only. Patients are selected from the waiting lists according to several parameters, including surgery duration, waiting time and priority class of the operations. We performed computational experiments to compare the performance of our decomposition approach with an (exact) integrated approach. The case study selected for our simulations is based on the characteristics of the operating theatre (OT) of a medium-size public Italian hospital. Scalability of the method is tested for different OT sizes. A pilot example is also proposed to highlight the usefulness of our approach for decision support. The proposed decomposition approach finds satisfactory solutions with significant savings in computation time.
Journal Article
A Lagrangian approach to single-machine scheduling problems with two competing agents
In this paper, we develop branch-and-bound algorithms for several hard, two-agent scheduling problems, i.e., problems in which each agent has an objective function which depends on the completion times of its jobs only. Our bounding approach is based on the fact that, for all problems considered, the Lagrangian dual gives a good bound and can be solved exactly in strongly polynomial time. The problems addressed here consist in minimizing the total weighted completion time of the jobs of agent A, subject to a bound on the cost function of agent B, which may be: (i) total weighted completion time, (ii) maximum lateness, (iii) maximum completion time. An extensive computational experience shows the effectiveness of the approach.
Journal Article
Complexity results and algorithms for an integrated single machine scheduling and outbound delivery problem with fixed sequence
In this paper, we consider an integrated production and outbound delivery scheduling problem. In particular, we address the situation in which the scheduling sequence and the delivery sequence are the same and predefined. A set of jobs are processed on a single machine and finished jobs are delivered to the customers by a single capacitated vehicle. Each job has a processing time and transportation times between customers are taken into account. Since the sequence is given, the problem consists to form batches of jobs and our objective is to minimize the sum of the delivery times or general functions of the delivery times. The NP-hardness of the general problem is established and a pseudopolynomial time dynamic programming algorithm is given. Some particular cases are treated, for which NP-hardness proofs and polynomial time algorithms are given. Finally, a fixed-parameter tractability result is given.
Journal Article