V-shape property for job sequences that minimize the expected completion time variance

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

In this work, the flowshop scheduling problem is considered with the objective of minimising the completion-time variance (CTV) of jobs, and an Ant Colony Optimisation (ACO) algorithm is presented. Two implementations of the Modified Ant Colony Optimisation algorithm (MACO-I and MACO-II) are proposed to solve the permutation flowshop scheduling problem. The proposed ant-colony-algorithm implementations have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed MACO implementations are compared with various algorithms and with the best CTV of jobs reported in the literature. The proposed MACO implementations are found to perform very well in minimising the chosen performance measure.

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

A single machine scheduling problem in which both the processing times and due‐dates of the jobs awaiting servicing are random variables is analyzed. It is proved that the properties of the shortest processing time rule and the due‐date rule which are known for the deterministic situation also hold in the probabilistic environment when they are suitably, and reasonably, refined for this context.

A set of n jobs is to be processed by two machines in series that are separated by an infinite waiting room; each job requires a (known) fixed amount of processing from each machine. In a classic paper, Johnson gave a simple rule for ordering of the set of jobs to minimize the time until the system becomes empty, i.e., the makespan. This paper studies a stochastic generalization of this problem in which job processing times are independent random variables. Our main result is a sufficient condition on the processing time distributions that implies that the makespan becomes stochastically smaller when two adjacent jobs in a given job sequence are interchanged. We also give an extension of the main result to job shops.

We consider the control of a single batch processing machine with random arrivals, random processing times, and compatible job families (jobs from different families may be processed together in the same batch, with the processing time distribution of the entire batch determined by the job family in the batch having the greatest expected processing time). The objective is to minimize the long-run average time that jobs spend in the system. We present properties possessed by the optimal policies and discuss the structure of these policies. We next develop a simple heuristic scheduling policy to control the machine. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances.

An Adaptive SPT Rule for Scheduling and Testing Heterogeneous Jobs

We present a decision support system (DSS) to compute performance measures of a project under uncertainty on the activities’ duration as well as four different types of precedence relationships. The DSS generates replicates of the project’s performance, in which we simulate the duration of each activity. From these replicates, the expected completion time, the variance of completion time, the service time for a given service level and the probability that each activity will be in the critical path are estimated along with their corresponding measures of accuracy. A validation of the DSS was performed by computing the empirical coverage, mean and standard deviation of halfwidths, mean square error and empirical bias for the main performance metrics of a given project. Our experimental results show that the procedures implemented in the DSS provide a good coverage and consistent half-widths. Keywords-Project Management; PERT; CPM; Project Simulation

This paper proposes a tolerance-based rule-base system for a single-crane scheduling problem in a flexible circuit board electroplating line. The objective is to minimize the completion time without a defective product. The algorithm is designed to determine the crane and job schedules in a real-time environment with dynamic change of job demand and random processing times. Two rule bases are used in the algorithm. The proposed rule base utilizes the tolerance of processing times to prevent delaying jobs’ entry times; the basic rule base which adopts only the shortest processing time (SPT) is introduced as a base to compare with the proposed one. The simulation results show the tradeoffs on the performances of the algorithm between these two rule bases and the tolerance-based rule base results in better throughput.

This paper considers two types of stochastic group scheduling problems, one involves a single machine, and the other involves an m -machine flow shop. In both problems, jobs are classified into groups. The jobs of the same group are to be processed one after another, and a sequence independent setup time is incurred between each two consecutively scheduled groups. The job processing times are independent random variables and group setup times are functions of the job processing times. The objective is to find both a group sequence and a job sequence that minimizes the expected total flow time. An optimal group sequence and an optimal job sequence are obtained by processing jobs in increasing stochastic order of their mean processing times and group setup times for a single machine problem. A precedence relationship is derived for the m -machine flow shop problem.

Greedy Randomized Adaptive Search Procedures (GRASP) are among the most popular metaheuristics for the solution of combinatorial optimization problems. While GRASP is a relatively simple and efficient framework to deal with deterministic problem settings, many real-life applications experience a high level of uncertainty concerning their input variables or even their optimization constraints. When properly combined with the right metaheuristic, simulation (in any of its variants) can be an effective way to cope with this uncertainty. In this paper, we present a simheuristic algorithm that integrates Monte Carlo simulation into a GRASP framework to solve the permutation flow shop problem (PFSP) with random processing times. The PFSP is a well-known problem in the supply chain management literature, but most of the existing work considers that processing times of tasks in machines are deterministic and known in advance, which in some real-life applications (e.g., project management) is an unrealistic assumption.

A synchronizer is a compiler that transforms a program designed to run in a synchronous network into a program that runs in an asynchronous network. The behavior of a simple synchronizer, which also represents a basic mechanism for distributed computing and for the analysis of marked graphs, was studied by S. Even and S. Rajsbaum (1990) under the assumption that message transmission delays and processing times are constant. We study the behavior of the simple synchronizer when processing times and transmission delays are random. The main performance measure is the rate of a network, i.e., the average number of computational steps executed by a processor in the network per unit time. We analyze the effect of the topology and the probability distributions of the random variables on the behavior of the network. For random variables with exponential distribution, we provide tight (i.e., attainable) bounds and study the effect of a bottleneck processor on the rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Some systems work for a job with random working and processing times, and are checked at periodic and random times. When a failure occurs, we execute the backup operation to the latest checking time. First, the expected costs with periodic and random backups are formulated, and comparisons between periodic and random policies are made. Next, we focus on the backup policies when the system is checked at the Nth interval of working times, two total expected costs are obtained and optimal numbers N* which minimize them are derived analytically. Finally, one modified backup model in which failures are detected only at checking times is proposed and two expected costs are obtained.

A stochastic scheduling algorithm for precedence constrained tasks on Grid

This paper tackles a stochastic version of single machine scheduling with random processing times, deterministic due dates, independent setup times and precedence constraints. The jobs are also deteriorated based on the position at which their processes are done. The objective function is to find a schedule of jobs which minimizes the expected value of total weighted tardiness. A branch and bound scheme is presented to solve the problem analytically. Since the problem is NP-hard, it is not possible to find global optimum values for larger scales of the problem in a reasonable run time, therefore, a simulated annealing meta-heuristic (SA) is also provided to solve the larger scale problems. Computational experiments demonstrate that the proposed SA is strongly capable of finding near optimal solutions with a very low gap.