Stochastic scheduling addresses several forms of uncertainty to represent better production environments in the real world. Stochastic scheduling has applications on several areas such as logistics, transportation, production, and healthcare, among others. This paper aims to evaluate the performance of various greedy functions for a GRASP-based approach, under stochastic processing times. Since simulation is used for estimating the objective function, two simulation techniques, Monte Carlo simulation and Common Random Numbers (CRN), are used to compare the performance of different greedy (utility) functions within the GRASP. In order to validate the proposed methodology, the expected total weighted tardiness minimization for a single machine problem was taken as case study. Results showed that both, CRN and Monte Carlo, are not statistically different regarding the expected weighted tardiness results. However, CRN showed a better performance in terms of simulation replications and the confidence interval size for the difference between means. Furthermore, the statistical analysis confirmed that there is a significant difference between greedy functions.

This paper studies the problem of single machine stochastic scheduling with random processing times, deterministic due dates and an independent setup time. The jobs are also deteriorated based on the position, which their processes are done. The objective function is to find a schedule of jobs, which minimizes the expected value of maximum lateness. A branch and bound scheme is presented to solve the problem analytically and a simulated annealing meta-heuristic (SA) is also provided for solving the problem in larger scales. Computational experiments demonstrate that the proposed SA is capable of finding near optimal solutions with very low gap.

During the past few years, despite tremendous contribution on deterministic flow shop problem, there are only limited number of works dedicated on stochastic cases. This paper examines stochastic scheduling problems in two-machine flow shop environment for expected makespan minimization where processing times of jobs are normally distributed. Since jobs have stochastic processing times, to minimize the expected makespan, the expected sum of the second machine’s free times is minimized. In other words, by minimization waiting times for the second machine, it is possible to reach the minimum of the objective function. A mathematical method is proposed which utilizes the properties of the normal distributions. Furthermore, this method can be used as a heuristic method for other distributions, as long as the means and variances are available. The performance of the proposed method is explored using some numerical examples.