Minimising variance of job completion times in a single machine
01 Jan 2012-International Journal of Operational Research (Inderscience Publishers Ltd)-Vol. 13, Iss: 1, pp 110-127
TL;DR: In this article, the authors considered a deterministic n-job, single-machine sequencing problem with the objective of minimising the variance of job completion times and provided an exact algorithm to solve the single machine CTV minimization problem based on implicit enumeration.
Abstract: In this paper, we consider a deterministic n-job, single-machine sequencing problem with the objective of minimising the variance of job completion times. Completion time variance (CTV) is relevant in situations where uniformity in service is needed. CTV is a non-regular performance measure that can decrease when one or more completion times increases. It penalises jobs that are completed early as well as late. Minimising CTV in a single machine is a ‘hard’ problem. The objective of this paper is to provide an exact algorithm to solve the single-machine CTV minimisation problem based on implicit enumeration. We develop a lower bound for a given partial sequence and present a branch and bound algorithm to solve the problem. Computational results show that optimal solutions for problems up to 80 jobs can be obtained with less computational time when compared to an existing pseudo-polynomial algorithm.
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TL;DR: In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered and a good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel- machine scheduling problem.
Abstract: This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.
8 citations
TL;DR: An incident-based mixed-integer rescheduling model is proposed which is solved using CPLEX software which automatically generates optimal solutions, and an innovative method which decomposes the main problem to five smaller sub-problems, each of which is solve by branch-and-bound algorithm.
Abstract: This paper studies a double-track train rescheduling problem, when an un-foreseen incident over a specific time horizon occurs. We solve the problem by utilising a rescheduling technique named bi-operational approach. An incident-based mixed-integer rescheduling model is proposed which is solved using CPLEX software which automatically generates optimal solutions. To reduce the computation time, an innovative method is proposed which decomposes the main problem to five smaller sub-problems, each of which is solved by branch-and-bound algorithm. Moreover, a novel heuristic is proposed which divides the available computation time between sub-problems proportionately depending on their sizes. An experimental analysis, on two double-track railways of Iranian network, indicates that the decomposition method provides near-optimal solutions with much shorter computation times compared with CPLEX. The analysis also provides evidence for effectiveness of the proposed heuristic in tackling large-scale problems; so that good feasible solutions are achievable in limited times compatible with real-time use.
5 citations
TL;DR: The analysis of the development and analysis of hybrid genetic algorithms for flow shop scheduling problems with sequence dependent setup time reveals the superior performance of hybrid Genetic algorithms for all the problem groups.
Abstract: This paper deals with the development and analysis of hybrid genetic algorithms for flow shop scheduling problems with sequence dependent setup time. A constructive heuristic called setup ranking algorithm is used for generating the initial population for genetic algorithm. Different variations of genetic algorithm are developed by using combinations of types of initial populations and types of crossover operators. For the purpose of experimentation, 27 group problems are generated with ten instances in each group for flow shop scheduling problems with sequence dependent setup time. An existing constructive algorithm is used for comparing the performance of the algorithms. A full factorial experiment is carried out on the problem instances developed. The best settings of genetic algorithm parameters are identified for each of the groups of problems. The analysis reveals the superior performance of hybrid genetic algorithms for all the problem groups.
4 citations
TL;DR: A lower bound on CTV is developed for a known partial schedule and a branch and bound algorithm is proposed to solve the problem and results are reported.
1 citations