Title: A stochastic scheduling approach to minimise the number of risky jobs and total probability of tardiness

Authors: Gokhan Egilmez; Aslican Arinsoy; Gürsel A. Süer

Addresses: Department of Mechanical and Industrial Engineering, West Haven, CT, USA ' Department of Industrial and Systems Engineering, Ohio University, Athens, OH 45701, USA ' Department of Industrial and Systems Engineering, Ohio University, Athens, OH 45701, USA

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.

Keywords: stochastic scheduling; single machine; probability of tardiness; nonlinear optimisation; expected number of tardy jobs.

DOI: 10.1504/IJSOM.2018.091905

International Journal of Services and Operations Management, 2018 Vol.30 No.2, pp.186 - 202

Received: 01 Apr 2016
Accepted: 29 Jul 2016
Published online: 21 May 2018 *

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