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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: In this paper, the authors considered a single machine scheduling problem with release dates and proposed a branch-and-bound algorithm that can solve the problem in O(n 2 ) and O( n ln n ) time.
22 citations
22 citations
Proceedings Article•
16 Jan 2012TL;DR: This work enhances the map of known order constraints by proving an extended version of a constraint that has been conjectured by Mondal and Sen more than a decade ago by proving the inuence of different kinds order constraints on the performance of exact algorithms is systematically evaluated.
Abstract: We consider the problem of scheduling jobs on a single machine. Given a quadratic cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each job is defined as the cost function value at the job's completion time. Throughout the past decades, great effort has been made to develop fast exact algorithms for the case of quadratic costs. The efficiency of these methods heavily depends on the utilization of structural properties of optimal schedules such as order constraints, i.e., sufficient conditions for pairs of jobs to appear in a certain order. A considerable number of different kinds of such constraints have been proposed. In this work we enhance the map of known order constraints by proving an extended version of a constraint that has been conjectured by Mondal and Sen more than a decade ago.
Besides proving this conjecture, our main contribution is an extensive experimental study where the inuence of different kinds order constraints on the performance of exact algorithms is systematically evaluated. In addition to a best-first graph search algorithm, we test a Quadratic Integer Programming formulation that admits to add order constraints as additional linear constraints. We also evaluate the optimality gap of well known Smith's rule for different monomial cost functions. Our experiments are based on sets of problem instances that have been generated using a new method which allows us to adjust a certain degree of difficulty of the instances.
22 citations
TL;DR: An error is pointed out in an algorithm given to solve the single-machine common due-window problem considering convex resource allocation and aging effect with a deteriorating rate-modifying activity and this algorithm remains valid when all the modifying rates are 1.
22 citations
TL;DR: In this paper, the authors considered a single-machine scheduling problem with deteriorating jobs in which the due dates are determined by the equal slack (SLK) method. And they proved that two special cases of the problem remain polynomially solvable.
Abstract: We consider a single-machine scheduling problem with deteriorating jobs in which the due dates are determined by the equal slack (SLK) method. By a deteriorating job, we mean that the job’s processing time is an increasing function of its starting time. We model job deterioration as a function that is proportional to a linear function of time. The objective is to minimize the total weighted earliness penalty subject to no tardy jobs. We prove that two special cases of the problem remain polynomially solvable. The first case is the problem with equally weighted monotonous penalty objective function and the other case is the problem with weighted linear penalty objective function.
22 citations