Evaluation model for the stochastic flowshop cyclic scheduling problem

Converging to periodic schedules for cyclic scheduling problems with resources and deadlines

A two-stage assignment strategy for the robust scheduling of dual-resource constrained stochastic job shop scheduling problems

Two efficient cyclic scheduling heuristics for re-entrant job shop environments were developed. Each heuristic generated an efficient and feasible cyclic production schedule for a job shop in which a single product was produced repetitively on a set of machines was to determine an efficient and feasible cyclic schedule which simultaneously minimized flow time and cycle time. The first heuristic considered a repetitive production re-entrant job shop with a predetermined sequence of operations on a single product with known processing times, set-up and material handling times. The second heuristic was a specialization of the first heuristic where the set-up for an operation could commence even while the preceding operation was in progress. These heuristics have been extensively tested and computational results are provided. Also, extensive analysis of worst-case and trade-offs between cycle time and flow time are provided. The results indicate that the proposed heuristics are robust and yield efficient and superior cyclic schedules with modest computational effort.

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.

Modern scheduling techniques must take into account incomplete information and/or potential changes in the environment, i.e. uncertainty. The central issue is to design robust scheduling techniques, aimed at guaranteeing the feasibility and the quality of the executed schedule. Several ways to get a more robust schedule have already been investigated. One way among others is to keep one and only one fixed schedule to execute, but reschedule when it appears the quality of the currently executing schedule degrades. This approach is relevant as far as rescheduling is fast enough w.r.t. the scheduling execution, i.e. when the dynamics of the system are low. The problem we tackle is on-line rescheduling with temporal uncertainty: activity durations are uncertain and activity end times must be observed during execution. In this paper we assume we have a representation of the uncertainty on each activity duration in the form of probability distributions which are used in the simulation of schedule execution. We use the simulations to monitor the execution of the schedule and in particular to estimate the quality of the schedule and the end times of the activities. Given an initial schedule, execution starts and we must decide when to reschedule. We propose and explore a non-monotonic technique where each time we reschedule we can completely change the existing schedule except for those activities that have already started or finished execution. This paper addresses the basis on which the decision to reschedule is made by investigating three simple measures of the data provided by simulation that are called the rescheduling criteria. We have chosen to use constraint programming for scheduling the initial problem and rescheduling when necessary. We illustrate our approach on job-shop problems with uncertain durations. The first experimental results are promising since on-line rescheduling improves schedule quality with a little additional computational effort whatever the rescheduling criterion used. In addition, these techniques can easily be extended to solve more complex problems and simulation permits us to quickly obtain good approximations whatever type of uncertainties and probability distributions are considered. Future work will focus on developing these scheduling methods to better tune the different parameters and implementing a monotonic approach where a partial schedule is built until some horizon and never questioned.

A hybrid differential evolution(DE) algorithm,namely OHTDE,is proposed to solve the stochastic flow shop scheduling problem(FSSP) with limited buffers between consecutive machines.Two different criteria are considered.The first is to minimize a general earliness/tardiness cost function and the second is to minimize the total completion time.The proposed algorithm is a hybrid of DE and two techniques:the optimal computing budget allocation(OCBA) technique and hypothesis test(HT) .DE is used to execute both global and local search.OCBA is utilized to reasonably allocate a limited sampling budget for every solution,assigning more for better individuals to improve the confidence level of getting good solutions under noise environment.HT is adopted to perform a statistical comparison on solutions performances so that the repeated search on the similar region of the solution space can be avoided to some extent.Moreover,a special crossover,which is performed on some good solutions identified by OCBA and HT,is designed to enhance the capability of local search.Furthermore,the stochastic convergence property of OHTDE is analyzed by using the theory of finite Markov chain.Experimental results and comparison show the effectiveness and robustness of the proposed OHTDE.

The current work contributes to stochastic hybrid flow shop scheduling. After a thorough literature analysis, it is firstly evident that works on stochastic flow shop scheduling are still limited in number; moreover, they often rely on simplifying assumptions; eventually, they may lack in a full viability for industrial application of the proposed models or algorithms. Considering these limitations, the present work proposes a scheduling framework based on Discrete Event Simulation and on Genetic Algorithms. The work stems from a previously published work, therefore, contributes by identifying some inconsistencies in the original algorithm in the so called “limit cases”. Overall, the paper proposes an alternative fitness function to avoid the generation of such inconsistencies; besides, it considers a realistic probability distribution to describe the stochastic processing times for robust scheduling of a hybrid flow shop. The end purpose is to move towards a viable application of optimization algorithms in industrial environments.

Introduction Robust scheduling is one of the approaches adopted to deal with uncertainties in stochastic scheduling. Since these uncertainties, arising as they do from variability in the scheduling parameters, significantly affect the performance of a system, a viable approach has been to determine a robust schedule that is least susceptible to disturbances or variations in the input parameters and that has minimum variability in its output performance measure. For instance, when processing times are uncertain, a robust schedule would have the least variance of the output performance measure, although it might not necessarily have the least expected value. As also mentioned in Chapter 1, of the various parameters involved in scheduling, we intend to focus on the uncertainty factor associated with job processing times. The following sections detail different robust scheduling methodologies that are available to model certain scheduling environments and the underlying principles behind those various approaches. Our primary focus is to elicit and delve in detail on the modeling approaches and not to expostulate the solution methodologies. However, we do briefly discuss the various solution approaches that are used to solve these robust scheduling problems and also state relevant results (as propositions) that are used in developing these solution methodologies. We intend to capture the core techniques that have been used in modeling robustness in scheduling and would advise interested readers to refer to the appropriate literature for a detailed and complete exposition.

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.

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance

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

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.

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

Train Scheduling Networks under Time Duration Uncertainty

We study the preemptive stochastic online scheduling problem on uniformly related machines where jobs are arriving over time. The objective is to minimize total weighted expected completion time. We consider the class of machines sets where the speed ratios have a lower bound. For each set of machines in this class, we design an algorithm with competitive is 2. More specially, we show that the competitive of our algorithm can't be improved. This generalizes the currently best known result for identical machines and includes the result for two uniform machines obtained by Gu et al.