A stochastic scheduling approach to minimise the number of risky jobs and total probability of tardiness Online publication date: Mon, 21-May-2018
by Gokhan Egilmez; Aslican Arinsoy; Gürsel A. Süer
International Journal of Services and Operations Management (IJSOM), Vol. 30, No. 2, 2018
Abstract: In this paper, single machine stochastic scheduling problem is addressed where jobs have probabilistic processing times and deterministic due dates. In classical scheduling literature, a job is called 'tardy' if it is completed after its due date; otherwise it's called 'early'. However, in probabilistic concept, a job can have a non-zero probability of tardiness. To capture this situation, a stochastic nonlinear mathematical model is developed. The objective is to minimise the expected number of tardy jobs and the total probability of tardiness. Experimentation is performed with datasets having varying number of jobs from 10 to 100. Results are compared with deterministic model. The proposed approach resulted in a significant decrease in the number of risky jobs and the total probability of tardiness. In addition, as the variance of processing times increased, the proposed stochastic approach provided safer schedules in terms of the total probability of tardiness.
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