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: The relation of time indexed formulations of nonpreemptive single machine scheduling problems to the node packing problem is established and then used to provide simple and intuitive alternate proofs of validity and maximality for previously known results on the facial structure of the scheduling problem.
Abstract: The relation of time indexed formulations of nonpreemptive single machine scheduling problems to the node packing problem is established and then used to provide simple and intuitive alternate proofs of validity and maximality for previously known results on the facial structure of the scheduling problem. Previous work on the facial structure has focused on describing the convex hull of the set of feasible partial schedules, schedules in which not all jobs have to be started. The equivalence between the characteristic vectors of this set and those of the set of feasible node packings in a graph whose structure is determined by the parameters of the scheduling problem is established. The main contribution of this paper is to show that the facet inducing inequalities for the convex hull of the set of feasible partial schedules that have integral coefficients and right hand side 1 or 2 are the maximal clique inequalities and the maximally and sequentially lifted 5-hole inequalities of the convex hull of the set of feasible node packings in this graph respectively.
23 citations
TL;DR: Results of extensive computational tests are reported, showing that the heavy computational burden of testing potential solutions renders the local search algorithms uncompetitive in comparison to the construction algorithms.
Abstract: In this paper, we study a strongly NP-hard single machine scheduling problem in which each job consists of two operations that are separated by a time delay which lies within a specified range. The objective is to minimize the makespan. Determining the feasibility and, if applicable, makespan of any proposed permutation of the operations is non-trivial, requiring a longest path algorithm with O(n2) complexity for each permutation. Several heuristic algorithms are proposed: a deterministic and randomized construction algorithm, three descent algorithms and two reactive tabu search algorithms. The local search algorithms use a first improvement neighbourhood and mainly visit only feasible solutions within the search space. Results of extensive computational tests are reported, showing that the heavy computational burden of testing potential solutions renders the local search algorithms uncompetitive in comparison to the construction algorithms. The iterated descent algorithm performs least well.
22 citations
TL;DR: In this study, machine conditions are evaluated by machine reliability and the relationship between reliability and processing energy consumption was developed and modified Emmons rules were proposed and embedded into an ant colony algorithm to solve real-world problems from a rotor production workshop.
22 citations
TL;DR: In this article, the authors consider the problem of scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline.
Abstract: We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP‐hard even if all the jobs have a unit weight, (ii) the problem is binary NP‐hard and admits a pseudo‐polynomial‐time algorithm and a fully polynomial‐time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.
22 citations
TL;DR: This paper presents heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound.
22 citations