282 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Serial-batch scheduling – the special case of laser-cutting machines
The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning
LP-based approximation algorithms for partial-ordered scheduling and matroid augmentation
In this thesis, we study two NP-hard problems from Combinatorial Optimization, from the perspective of approximation algorithms. The first problem we study is called Partial-Order Scheduling on Parallel Machines, which we abbreviate to PO Scheduling. Here, we are given a partially ordered set of jobs which we want to schedule to a set of machines. Each job has some weight and some processing time associated to it. On each machine, the order of the jobs scheduled to it must agree with the given partial order, i.e., a job can only be started once all its predecessors scheduled to the same machine have been completed. However, two jobs scheduled to different machines are not constrained in any way. Thus, PO Scheduling deviates from the well-studied problem of precedence-constrained scheduling in this regard. The goal of PO Scheduling is to find a feasible schedule which minimizes the sum of weighted completion times of the jobs. PO Scheduling generalizes an already NP-hard version of scheduling introduced by Bosman, Frascaria, Olver, Sitters and Stougie [3], where they ask the same question as in PO Scheduling for the case where the jobs are totally ordered. The authors above present a constant-factor approximation algorithm for their problem. We conjecture that there is a constant-factor approximation algorithm for PO Scheduling as well. While we do not solve the problem, we give approximation algorithms for the special case that the partial order consists of disjoint totally ordered chains of linearly bounded length. Additionally, we give a structural result for optimal schedules in the case that the partial order consists of disjoint, backwardly ordered (with regard to the Smith-ratio) chains. We point towards some potential research directions. For the Weighted Tree Augmentation Problem, we are given a graph with a distinguished spanning tree. Each non tree-edge has a cost associated to it. The goal is to find a cost-minimal set of edges such that when we add them to the tree-edges, the resulting graph is 2-edge-connected. Weighted tree augmentation is NP-hard. There has been recent progress in decreasing the best-known approximation factor for the problem by Traub and Zenklusen to (1.5 + ε) [51, 52]. We study a generalization of weighted tree augmentation, called the Weighted Matroid Augmentation Problem, which we abbreviate to WMAP. In WMAP, we consider a matroid with a distinguished basis and a cost function on the non-basis elements. The goal is to find a cost-minimal set such that the union of the fundamental circuits of the elements in the set with regard to the distinguished basis cover that basis. We conjecture that there is a 2-approximation algorithm for the problem in the case that the matroid is regular. While we do not solve the problem, we give an approximation algorithm for the special case of the cographic matroid and show that there is no constant-factor approximation algorithm for WMAP for representable matroids unless P = NP
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Operational Research: methods and applications
This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
Operational research:methods and applications
Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order
Scheduling with a Limited Testing Budget
Scheduling with testing falls under the umbrella of the research on
optimization with explorable uncertainty. In this model, each job has an upper
limit on its processing time that can be decreased to a lower limit (possibly
unknown) by some preliminary action (testing). Recently, D{\"{u}}rr et al.
\cite{DBLP:journals/algorithmica/DurrEMM20} has studied a setting where testing
a job takes a unit time, and the goal is to minimize total completion time or
makespan on a single machine. In this paper, we extend their problem to the
budget setting in which each test consumes a job-specific cost, and we require
that the total testing cost cannot exceed a given budget. We consider the
offline variant (the lower processing time is known) and the oblivious variant
(the lower processing time is unknown) and aim to minimize the total completion
time or makespan on a single machine.
For the total completion time objective, we show NP-hardness and derive a
PTAS for the offline variant based on a novel LP rounding scheme. We give a
-competitive algorithm for the oblivious variant based on a
framework inspired by the worst-case lower-bound instance. For the makespan
objective, we give an FPTAS for the offline variant and a
-competitive algorithm for the oblivious variant. Our algorithms
for the oblivious variants under both objectives run in time
. Lastly, we show that our results are essentially optimal
by providing matching lower bounds.Comment: To appear in ESA 202
Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines
We study the classic weighted maximum throughput problem on unrelated machines. We give a (1-1/e-?)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ?-approximation algorithm for the single-machine problem to obtain an approximation factor of (1-1/e)? -? for the corresponding unrelated-machines problem, for any ? > 0. On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1-1/e) -? for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine
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