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: In this article, the authors consider a two-agent scheduling problem in which the actual processing time of a job in a schedule is a function of the sum-of-processing-times-based learning and a control parameter of the learning function.
103 citations
TL;DR: It is shown that for a given schedule of tardy jobs, the problem of scheduling the batch deliveries is equivalent to the dynamic lot sizing problem and some special cases that are solvable in polynomial time are discussed.
102 citations
01 Oct 1998
TL;DR: An efficient pseudo-polynomial time dynamic programming algorithm is proposed that significantly improves the efficiency of the Lagrangean relaxation approach to job-shop scheduling, and makes it possible to optimize "min-max" criteria by LagRangean relaxation.
Abstract: Concerns the use of Lagrangean relaxation for complex scheduling problems. The technique has been used to obtain near-optimal solutions for single machine and parallel machine problems. It consists of relaxing capacity constraints using Lagrange multipliers. The relaxed problem can be decomposed into independent job level subproblems. Luh et al. (1990, 1991) extended the technique to general job shop scheduling by introducing additional Lagrangean multipliers to relax precedence constraints, so that each job level relaxed subproblem can be further decomposed into a set of operation level subproblems which can easily be solved by enumeration. Unfortunately, the operation level subproblems exhibit solution oscillation from iteration to iteration and, in many cases, prevent convergence. Although several methods to prevent oscillation have been proposed, none is satisfactory. We propose an efficient pseudo-polynomial time dynamic programming algorithm. We show that, by extending the technique to job shop scheduling problems, the relaxation of the precedence constraints becomes unnecessary, and thus the oscillation problem vanishes. This algorithm significantly improves the efficiency of the Lagrangean relaxation approach to job-shop scheduling, and makes it possible to optimize "min-max" criteria by Lagrangean relaxation. These criteria have been neglected in the Lagrangean relaxation literature due to their indecomposability. Computational results are given to demonstrate the improvements due to this algorithm.
102 citations
TL;DR: A fully polynomial-time approximation scheme (FPTAS) for a knapsack problem to minimize a symmetric quadratic function and it is demonstrated how the designed FPTAS can be adopted for several single machine scheduling problems to minimize the sum of the weighted completion times.
Abstract: We design a fully polynomial-time approximation scheme (FPTAS) for a knapsack problem to minimize a symmetric quadratic function. We demonstrate how the designed FPTAS can be adopted for several single machine scheduling problems to minimize the sum of the weighted completion times. The applications presented in this paper include problems with a single machine non-availability interval (for both the non-resumable and the resumable scenarios) and a problem of planning a single machine maintenance period; the latter problem is closely related to a single machine scheduling problem with two competing agents. The running time of each presented FPTAS is strongly polynomial.
99 citations
TL;DR: Heuristic methods and optimizing techniques are surveyed for both types of problems in the single-machine environment and some extensions of the TT and TWT problems are given for multi-machine environments.
98 citations