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.

An approximation algorithm for scheduling aircraft with holding time

Abstract: We consider the problem of scheduling arrival air traffic in the vicinity of large airports. The problem is posed as a single queue problem, from which aircraft can be pulled out and put "on hold", in holding loops, each loop taking a fixed amount of time to traverse before they join the queue again. The difficulty of deriving efficient solutions to this problem (which is currently controlled non optimally by human air traffic controllers) is the minimization of "idle time" generated by traversing an integer number of loops. We formulate this problem as a single machine scheduling problem where we are given N jobs characterized by release times and deadlines. We are given a processing time and and a holding time. In a feasible schedule, each job is assigned a starting time within a constraint set corresponding to an integer number of processing times and holding times. Our goal is to find feasible schedules to alternatively minimize two objectives: the sum of the starting times of all jobs and the makespan (the time at which all jobs are finished). We present approximation algorithms which can alternatively approximate two objectives with factors of 5 and 3. respectively. Our main algorithm consists of solving two subproblems one of which is solved optimally using dynamic programming, while the other is solved approximately using linear programming relaxation and rounding.

A modified particle swarm optimization algorithm for a single-machine scheduling problem with periodic maintenance

Abstract: In this paper, a particle swarm optimization (PSO) algorithm is presented to solve the single-machine scheduling problem with periodic maintenance activities. The most important issue for applying PSO algorithm successfully to the addressed scheduling problem is how to develop an effective 'problem mapping' and 'construction of a particle sequence' mechanism. For the problem mapping aspect, we apply the ''job-to-position'' representation for the particles. For the construction of a particle sequence aspect, we use the largest position value (LPV) rule. Besides, to enhance the effective of the proposed PSO algorithm, we embedded a restarting strategy and three stopping criteria. The objective is to find a schedule that minimizes the makespan. The addressed problem is shown to be NP-hard in the strong sense by transforming to the 3-partition problem. Computational results show that the proposed PSO-M algorithm is quite satisfactory on both solution accuracy and efficiency to solve the addressed problem.

A note on the single-machine scheduling problem with minimum weighted completion time and maximum allowable tardiness

Abstract: This paper analyzes the Smith-heuristic for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith-heuristic is guaranteed to lead to optimal solutions. We also provide a worst-case analysis of the Smith-heuristic; the analysis shows that the fractional increase in the objective function value for the Smith-heuristic from the optimal solution is unbounded in the worst case.