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 addresses scheduling a set of weighted jobs on a single machine in presence of release date for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of weighted flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The classical problem is NP-hard and then the extended version of the problem is NP-hard. The objective function is that of minimizing the sum of weighted flow times and delivery costs. The extended problem arises in a real supply chain network by cooperation between two layers of chain. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show the efficiency of suggested algorithm for solving instances up to 40 jobs.

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.

This paper presents a mathematical model for the problem of minimizing the maximum lateness on a single machine when the deteriorated jobs are delivered to each customer in various size batches. In reality, this issue may happen within a supply chain in which delivering goods to customers entails cost. Under such situation, keeping completed jobs to deliver in batches may result in reducing delivery costs. In literature review of batch scheduling, minimizing the maximum lateness is known as NP-Hard problem; therefore the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In order to solve the proposed model, a Simulation annealing meta-heuristic is used, where the parameters are calibrated by Taguchi approach and the results are compared to the global optimal values generated by Lingo 10 software. Furthermore, in order to check the efficiency of proposed method to solve larger scales of problem, a lower bound is generated. The results are also analyzed based on the effective factors of the problem. Computational study validates the efficiency and the accuracy of the presented model.

This paper tackles the single machine scheduling problem with dependent setup time and precedence constraints. The primary objective of this paper is minimization of total weighted tardiness. Since the complexity of the resulted problem is NP-hard we use metaheuristics method to solve the resulted model. The proposed model of this paper uses genetic algorithm to solve the problem in reasonable amount of time. Because of high sensitivity of GA to its initial values of parameters, a Taguchi approach is presented to calibrate its parameters. Computational experiments validate the effectiveness and capability of proposed method.

This paper addresses a bi-criteria scheduling problem with deteriorating jobs on a single machine. We develop a model for a single machine bi-criteria scheduling problem (SMBSP) with the aim of minimizing total tardiness and work in process (WIP) costs. WIP cost increases as a job passes through a series of stages in the production process. Due to the uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the SMBSP under the hypothesis of fuzzy L-R processing time's knowledge and fuzzy L-R due date. The effectiveness of the proposed model and the denoted methodology is demonstrated through a test problem.