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.
Papers published on a yearly basis
Papers
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TL;DR: A heuristic algorithm with time complexity O( n 3 ) and a branch and bound algorithm to solve a single machine scheduling problem with dual criteria, i.e., the minimization of the total weighted earliness subject to minimum number of tardy jobs is developed.
37 citations
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TL;DR: This work suggests an original due date assignment method in which all jobs within a family are restricted to be assigned the same due date, while each family can be assigned a due date without any restriction.
37 citations
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TL;DR: A new algorithm that can output optimal solutions even when available memory is limited is presented and it has been found to run faster than dynamic programming and depth-first branch-and-bound formulations and can solve much larger instances of the problem in reasonable time.
37 citations
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16 Apr 2012TL;DR: A tight analysis of the approximation factor of Smith's rule under any particular convex or concave cost function is considered, which turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial.
Abstract: We consider the problem of scheduling jobs on a single machine. Given some continuous cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each individual job is determined by the cost function value at the job's completion time. This problem is closely related to scheduling a single machine with nonuniform processing speed. We show that for piecewise linear cost functions it is strongly NP-hard.
The main contribution of this article is a tight analysis of the approximation factor of Smith's rule under any particular convex or concave cost function. More specifically, for these wide classes of cost functions we reduce the task of determining a worst case problem instance to a continuous optimization problem, which can be solved by standard algebraic or numerical methods. For polynomial cost functions with positive coefficients it turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial. To overcome unrealistic worst case instances, we also give tight bounds that are parameterized by the minimum, maximum, and total processing time.
37 citations
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TL;DR: This paper considers single machine scheduling problem in which job processing times are controllable variables with linear costs, and presents an O(n log n) algorithm to obtain the optimal solution.
37 citations