Preemptive stochastic online scheduling on uniform machines with bounded speed ratios

One of the basic and fundamental scheduling problems is to minimize the machine completion time vector in the $$\ell _p$$ l p norm, a direct extension of the well-studied objective makespan ( $$l_{\infty }$$ l ? norm), on parallel machines. We concentrate on the on-line and preemptive version of this problem where jobs arrive one by one over a list to be allocated to two uniform machines with job preemption permitted. We present a best possible deterministic on-line scheduling algorithm for this problem along with a matching lower bound, generalizing existing results for the identical machines scheduling problem in the literature. One notable feature of this work is the highly involved technicality compared to similar analysis in the existing literature, mainly due to the intrinsic unavailability of a closed-form formula for the competitive ratio.

In this paper we address the stochastic cyclic scheduling problem in synchronous assembly and production lines. Synchronous lines are widely used in the production and assembly of various goods such as automobiles and household appliances. We consider the cycle time (or throughput rate) performance criterion as the objective of the scheduling problem with the assumption that the processing times are independent random variables.

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.

Two preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem.

The D.A.I. theorem of Gittins and Jones has proved a powerful tool in solving sequential statistical problems. A generalisation of this theorem is presented. This generalisation enables us to solve certain stochastic scheduling problems where the items or jobs to be scheduled have random times to completion, the random times having distributions dependent upon parameters to which prior distributions are allocated. Such problems are of interest in many areas where scheduling is important.

Preemptive scheduling with variable profile, precedence constraints and due dates

Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to be executed on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time.Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new input. For scheduling problems, the maximum ratio between the total size of the jobs (or parts of jobs) which may be re-scheduled upon the arrival of a new job j, and the size of j, is called migration factor.We design a strongly optimal algorithm with the migration factor \(1-\frac 1m\) for identical machines. Such algorithms avoid idle time and create solutions where the (non-increasingly) sorted vector of completion times of the machines is minimal lexicographically. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any ℓ p norm (for p > 1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines nor identical machines with restricted assignment admit an optimal algorithm with a constant migration factor. This lower bound holds both for makespan minimization and for any ℓ p norm. Finally, we analyze the case of two machines and show that in this case it is still possible to maintain an optimal schedule with a small migration factor in the cases of two uniformly related machines and two identical machines with restricted assignment.

Optimising stochastic task allocation and scheduling plans for mission workers subject to learning-forgetting, fatigue-recovery, and stress-recovery effects

No framework or classification scheme has ever been introduced for stochastic scheduling problems. It is more difficult to develop such a scheme for stochastic scheduling problems than for deterministic scheduling problems. In order to characterize a stochastic scheduling problem more information is required. For example, the distributions of the processing times have to be specified as well as the distributions of the due dates (which may be different). It has to be specified whether the processing times of the n jobs are independent or correlated (e.g., equal to the same random variable) and also which class of policies is considered. For these reasons no framework has been introduced in this book either

Evolutionary algorithm for stochastic job shop scheduling with random processing time

With the insignificant incremental cost involved in hydrogeneration, the problem of minimizing the operation cost of a hydro-thermal system essentially reduces to that of minimizing the fuel cost for thermal plants under the constraints of the water available for hydro generation in a given period of time. The problem thus belongs to the realm of dynamic optimization.In the past, many papers pertaining to optimal hydro-thermal scheduling assume water inflows to reservoirs and load demand to be deterministic. In practice, however, this is not true. To be realistic, the scheduling problem must be tackled through stochastic optimization. This paper presents a new effective approach to the optimal stochastic hydro-thermal scheduling problem. A computational algorithm based on first- order gradient technique is developed to solve the scheduling problem.

A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations

Integrated consideration of production planning and maintenance processes is a real world assumption. Specifically, by improving the monitoring equipment such as various sensors or product-embedded information devices in recent years, joint assessment of these processes is inevitable for enhancing the level of the system optimization. By means of this equipment, managers can benefit from a condition-based maintenance (CBM) for monitoring and managing their system. The chief aim of the paper is to develop a stochastic maintenance problem based on CBM activities engaged with a complex applied production problem called flexible job shop scheduling problem (FJSP). This integrated problem considers two maintenance scenarios in terms of corrective maintenance (CM) and preventive maintenance (PM). The activation of scenario is done by monitoring the degradation condition of the system and comparing the associated value by predetermined PM and CM levels. Moreover, to make it more realistic, the developed problem allows breakdown of the system between inspection intervals. The event time and duration of performing the maintenance activities are also considered stochastic. The developed methodology copes with high stochastic complexity of proposed problem through simulation-based optimization (SBO) approach, which works based on harmony search optimization algorithm. The developed items of SBO are discussed on different generated test problems and assessed through statistical methods and new visualization approach. Numerical example shows that the proposed method is practical for proposed integrated CBM and FJSP problem. It also offers a basis for any implementation of CBM on production problems.

In this paper, we investigate scenario generation methods to establish lower bounds on the optimal objective value for stochastic scheduling problems that contain random parameters with continuous distributions. In contrast to the Sample Average Approximation (SAA) approach, which yields probabilistic bound values, we use an alternative bounding method that relies on the ideas of discrete bounding and recursive stratified sampling. Theoretical support is provided for deriving exact lower bounds for both expectation and conditional value-at-risk objectives. We illustrate the use of our method on the single machine total weighted tardiness problem. The results of our numerical investigation demonstrate good properties of our bounding method, compared with the SAA method and an earlier discrete bounding method.

Maximizing the benefit gained by soft real-time jobs in many applications and embedded systems is highly needed to provide an acceptable QoS (Quality of Service). This paper considers a benefit model for on-line pre-emptive multiprocessor scheduling. The goal is to maximize the total benefit gained by the jobs that meet their deadlines. This method prioritizes the jobs using their benefit density functions and schedules them in a real-time basis. We propose an online choice of two approximation algorithms in order to partition the jobs among identical processors at the time of their arrival without using any statistics. Our analysis and experiments show that we are able to maximize the gained benefit and decrease the computational complexity (compared to existing algorithms) while minimizing make span (response time, also referred to as cost), with fewer missed deadlines and more balanced usage of processors. Our solution is applicable to a wide variety of soft real-time applications and embedded systems such as, but not limited to multimedia applications, medical monitoring systems or those with higher utilization such as bursty hosting servers.