Scheduling is a decision-making process that is concerned with the allocation of limited resources to competing tasks (operations of jobs) over a time period with the goal of optimising one or more objectives. In theory, the objective is usually to optimise some classical system performance measures such as makespan, tardiness/earliness and flowtime under deterministic and static assumptions. In practice, however, scheduling systems operate in dynamic and stochastic environments. Hence, there is a need to incorporate both uncertainty and dynamic elements into the scheduling process. In this paper, the major issues involved in scheduling decisions are discussed and the basic approaches to tackle these problems in manufacturing environments are analysed. Proactive scheduling is then focused on and several robustness and stability measures are presented. Previous research on scheduling robustness and stability is also reviewed and further research directions are suggested
This paper addresses the issue of finding robust and stable schedules with respect to random disruptions. Specifically, two surrogate measures for robustness and stability are developed. The proposed surrogate measures, which consider both busy and repair time distributions, are embedded in a tabu-search-based scheduling algorithm, which generates schedules in a single-machine environment subject to machine breakdowns. The performance of the proposed scheduling algorithm and the surrogate measures are tested under a wide range of experimental conditions. The results indicate that one of the proposed surrogate measures performs better than existing methods for the total tardiness and total flowtime criteria in a periodic scheduling environment. A comprehensive bibliography is also presented.
Abstract:The ability to cope with uncertainty in dynamic scheduling environments is becoming an increasingly important issue. In such environments, any disruption in the production schedule will translate into a disturbance of the plans for several external activities as well. Hence, from a practical point of view, deviations between the planned and realized schedules are to be avoided as much as possible. The term stability refers to this concern. We propose a proactive approach to generate efficient and stable schedules for a job shop subject to processing time variability and random machine breakdowns. In our approach, efficiency is measured by the makespan, and the stability measure is the sum of the variances of the realized completion times. Because the calculation of the original measure is mathematically intractable, we develop a surrogate stability measure. The version of the problem with the surrogate stability measure is proven to be NP-hard, even without machine breakdowns; a branch-and-bound algorithm is developed for this problem variant. A tabu search algorithm is proposed to handle larger instances of the problem with machine breakdowns. The results of extensive computational experiments indicate that the proposed algorithms are quite promising in performance.
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