Restricted assignment scheduling with resource constraints

We consider parallel machine scheduling with job assignment restrictions, i.e., each job can only be processed on a certain subset of the machines. Moreover, each job requires a set of renewable resources. Any resource can be used by only one job at any time. The objective is to minimize the makespan. We present approximation algorithms with constant worst-case bound in the case that each job requires only a fixed number of resources. For some special cases optimal algorithms with polynomial running time are given. If any job requires at most one resource and the number of machines is fixed, we give a PTAS. On the other hand we prove that the problem is APX-hard, even when there are just three machines and the input is restricted to unit-time jobs. (C) 2018 Published by Elsevier B.V

Time-constrained project scheduling with adjacent resources

We develop a decomposition method for the Time-Constrained Project Scheduling Problem (TCPSP) with Adjacent Resources. For adjacent resources the resource units are ordered and the units assigned to a job have to be adjacent. On top of that, adjacent resources are not required by single jobs, but by job groups. As soon as a job of such a group starts, the adjacent resource units are occupied, and they are not released before all jobs of that group are completed. The developed decomposition method separates the adjacent resource assignment from the rest of the scheduling problem. Test results demonstrate the applicability of the decomposition method. The presented decomposition forms a first promising approach for the TCPSP with adjacent resources and may form a good basis to develop more elaborated methods

The Epistemology of scheduling problems

Scheduling is a knowledge-intensive task spanning over many activities in day-to-day life. It deals with the temporally-bound assignment of jobs to resources. Although scheduling has been extensively researched in the AI community for the past 30 years, efforts have primarily focused on specific applications, algorithms, or 'scheduling shells' and no comprehensive analysis exists on the nature of scheduling problems, which provides a formal account of what scheduling is, independently of the way scheduling problems can be approached. Research on KBS development by reuse makes use of ontologies, to provide knowledge-level specifications of reusable KBS components. In this paper we describe a task ontology, which formally characterises the nature of scheduling problems, independently of particular application domains and in-dependently of how the problems can be solved. Our results provide a comprehensive, domain-independent and formally specified refer-ence model for scheduling applications. This can be used as the ba-sis for further analyses of the class of scheduling problems and also as a concrete reusable resource to support knowledge acquisition and system development in scheduling applications

Local search methods for the discrete time/resource trade-off problem in project networks.

Abstract: In this paper we consider the discrete time/resource trade-off problem in project networks. Given a project network consisting of nodes (activities) and arcs (technological precedence relations specifying that an activity can only start when al of its predecessors have been completed), in which the duration of the activities is a discrete, on-increasing function of the amount of a single renewable resource committed to it, the discrete time/resource trade-off problem minimizes the project makespan subject to precedence constraints and a single renewable resource constraint. For each activity a work content is specified such that all execution modes (duration-resource pairs) for performing the activity are allowed as long as the product of the duration and the resource requirement is at least as large as the specified work content. We present a tabu search procedure which is based on subdividing the problem into a mode assignment phase and a resource-constrained project scheduling phase with fixed mode assignments. Extensive computational experience, including a comparison with other local search methods, is reported.Scheduling; Methods; Networks; Product; Assignment;

Scheduling Parallel Jobs with Linear Speedup

We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;