Topic
Single-machine scheduling
About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.
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TL;DR: A new procedure that considers the use of inserted idle time to optimally solve the single machine scheduling problem where the objective is to minimize the sum of squares lateness is proposed.
24 citations
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TL;DR: This paper proves APX-hardness of the problem when the number of resources is part of the input, and new polynomial time approximation schemes are devised for some variants.
Abstract: The paper presents new approximability results for single machine scheduling problems with jobs requiring some non-renewable resources (like raw materials, energy, or money) beside the machine. Each resource has an initial stock and additional supplies over time. A feasible schedule specifies a starting time for each job such that no two jobs overlap in time, and when a job is started, enough resources are available to cover its requirements. The goal is to find a feasible schedule of minimum makespan. This problem is strongly NP-hard. Recently, the authors of this paper have proposed a PTAS for the special case with a single non-renewable resource and with a constant number of supply dates, as well as an FPTAS for the special case with two supply dates and one resource only. In this paper we prove APX-hardness of the problem when the number of resources is part of the input, and new polynomial time approximation schemes are devised for some variants, including (1) job release dates, and more than one, but constant number of resources and resource supply dates, and (2) only one resource, arbitrary number of supply dates and job release dates, but with resource requirements proportional to job processing times. © 2015 Springer Science+Business Media New York
24 citations
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25 Jun 2007TL;DR: This paper extends previous results by presenting a framework for obtaining (2 i¾? 2/d)-approximation algorithms provided that the set of precedence constraints has fractional dimension d, and provides the first results for bounded degree and interval dimension 2 orders.
Abstract: We consider the single machine scheduling problem to minimize the average weighted completion time under precedence constrains. Improving on the various 2-approximation algorithms is considered one of the ten most prominent open problems in scheduling theory. Recently, research has focused on special cases of the problem, mostly by restricting the set of precedence constraints to special classes such as convex bipartite, two-dimensional, and interval orders.
In this paper we extend our previous results by presenting a framework for obtaining (2 i¾? 2/d)-approximation algorithms provided that the set of precedence constraints has fractional dimension d. Our generalized approach yields the best known approximation ratios for all previously considered classes of precedence constraints, and it provides the first results for bounded degree and interval dimension 2 orders.
As a negative result we show that the addressed problem remains NP-hard even when restricted to the special case of interval orders.
24 citations
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TL;DR: Computer results indicate that the performance of the heuristic is robust and significantly outperforms the modified TADC solution in the literature, and the efficiency of the mixed binary integer programming model and the impact of the dirt accumulation as well as cleaning time are explored in detail.
24 citations
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TL;DR: This study addresses an NP-Hard problem of minimizing the total tardiness on a single machine with sequence-dependent setup times and a position-based learning effect on processing times and develops a branch and bound algorithm for solving the problem.
24 citations