Project scheduling under undertainty – survey and research potentials.

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;

Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments

In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing research coping with optimization problems in uncertain environment aims at finding a single sufficiently robust solution so that random noise and unpredictable circumstances would have the least possible detrimental effect on the quality of the solution. The measures of robustness are usually based on various kinds of empirically designed averaging techniques. In contrast to the previous work, our algorithm aims at finding a collection of robust schedules that allow for a more informative decision making. The notion of robustness is measured quantitatively in terms of the classical mathematical notion of a norm on a vector space. We provide a theoretical insight into the relationship between the properties of the probability distribution over the uncertain delivery times and the robustness quality of the schedules produced by the algorithm after a polynomial runtime in terms of approximation ratios

Solution and quality robust project scheduling: a methodological framework.

The vast majority of the research efforts in project scheduling over the past several years has concentrated on the development of exact and suboptimal procedures for the generation of a baseline schedule assuming complete information and a deterministic environment. During execution, however, projects may be the subject of considerable uncertainty, which may lead to numerous schedule disruptions. Predictive-reactive scheduling refers to the process where a baseline schedule is developed prior to the start of the project and updated if necessary during project execution. It is the objective of this paper to review possible procedures for the generation of proactive (robust) schedules, which are as well as possible protected against schedule disruptions, and for the deployment of reactive scheduling procedures that may be used to revise or re-optimize the baseline schedule when unexpected events occur. We also offer a methodological framework that should allow project management to identify the proper scheduling methodology for different project scheduling environments. Finally, we survey the basics of Critical Chain scheduling and indicate in which environments it is useful.Framework; Information; Management; Processes; Project management; Project scheduling; Project scheduling under uncertainty; Stability; Robust scheduling; Quality; Scheduling; Stability; Uncertainty;

Random Keys Genetic Algorithms Scheduling and Rescheduling Systems for Common Production Systems

The majority of scheduling research deals with problems in specific production environments with specific objective functions. However, in many cases, more than one problem type and/or objective function exists, resulting in the need for a more generic and flexible system to generate schedules. Furthermore, most of the published scheduling research focuses on creating an optimal or near optimal initial schedule during the planning phase. However, after production processes start, circumstances like machine breakdowns, urgent jobs, and other unplanned events may render the schedule suboptimal, obsolete or even infeasible resulting in a rescheduling problem, which is typically also addressed for a specific production environment, constraints, and objective functions. This dissertation introduces a generic framework consisting of models and algorithms based on Random Keys Genetic Algorithms (RKGA) to handle both the scheduling and rescheduling problems in the most common production environments and for various types of objective functions. The Scheduling system produces predictive (initial) schedules for environments including single machines, flow shops, job shops and parallel machine production systems to optimize regular objective functions such as the Makespan and the Total Tardiness as well as non-regular objective functions such as the Total Earliness and Tardiness. To deal with the rescheduling problem, and using as a basis the same RKGA, a reactive Rescheduling system capable of repairing initial schedules after the occurrence of unexpected events is introduced. The reactive Rescheduling system was designed not only to optimize regular and non-regular objective functions but also to minimize the instability, a very important aspect in rescheduling to avoid shop chaos due to disruptions. Minimizing both schedule inefficiency and instability, however, turns the problem into a multi-objective optimization problem, which is even more difficult to solve. The computational experiments for the predictive model show that it is able to produce optimal or near optimal schedules to benchmark problems for different production environments and objective functions. Additional computational experiments conducted to test the reactive Rescheduling system under two types of unexpected events, machine breakdowns and the arrival of a rush job, show that the proposed framework and algorithms are robust in handling various problem types and computationally reasonable

Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems

A hybrid genetic approach to solve real make-to-order job shop scheduling problems

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro TecnologicoProcedimentos de busca local (ex. busca tabu) e algoritmos genéticos têm apresentado excelentes resultados em problemas clássicos de programação da produção em ambientes job shop. No entanto, estas abordagens apresentam pobres habilidades de modelamento e poucas aplicações com restrições de ambientes reais de produção têm sido publicadas. Além disto, os espaços de busca considerados nestas aplicações são nomlalmente incompletos e as restrições reais são poucas e dependentes do problema em questão. Este trabalho apresenta uma abordagem genética híbrida para resolver problemas de programação em ambientes job shop com grande número de restrições reais, tais como produtos com vários níveis de submontagem, planos de processamento altemativos para componentes e recursos alternativos para operações, exigência de vários recursos para executar uma operação (ex., máquina, ferramentas, operadores), calendários para todos os recursos, sobreposição de operações, restrições de disponibilidade de matéria-prima e componentes comprados de terceiros, e tempo de setup dependente da sequência de operações. A abordagem também considera funções de avaliação multiobjetivas. O sistema usa algoritmos modificados de geração de programação, que incorporam várias heurísticas de apoio à decisão, para obter um conjunto de soluções iniciais. Cada solução inicial é melhorada por um algoritmo de subida de encosta. Então, um algoritmo genético híbrido com procedimentos de busca local é aplicado ao conjunto inicial de soluções localmente ótimas. Ao utilizar técnicas de programação de alta perfomlance (heurísticas construtivas, procedimentos de busca local e algoritmos genéticos) em problemas reais de programação da produção, este trabalho reduziu o abismo existente entre a teoria e a prática da programação da produção

MODELING, OPTIMISATION AND ANALYSIS OF RE-ENTRANT FLOWSHOP JOB SCHEDULING WITH FUZZY PROCESSING TIMES

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.2

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Dynamic scheduling in a multi-product manufacturing system

To remain competitive in global marketplace, manufacturing companies need to improve their operational practices. One of the methods to increase competitiveness in manufacturing is by implementing proper scheduling system. This is important to enable job orders to be completed on time, minimize waiting time and maximize utilization of equipment and machineries. The dynamics of real manufacturing system are very complex in nature. Schedules developed based on deterministic algorithms are unable to effectively deal with uncertainties in demand and capacity. Significant differences can be found between planned schedules and actual schedule implementation. This study attempted to develop a scheduling system that is able to react quickly and reliably for accommodating changes in product demand and manufacturing capacity. A case study, 6 by 6 job shop scheduling problem was adapted with uncertainty elements added to the data sets. A simulation model was designed and implemented using ARENA simulation package to generate various job shop scheduling scenarios. Their performances were evaluated using scheduling rules, namely, first-in-first-out (FIFO), earliest due date (EDD), and shortest processing time (SPT). An artificial neural network (ANN) model was developed and trained using various scheduling scenarios generated by ARENA simulation. The experimental results suggest that the ANN scheduling model can provided moderately reliable prediction results for limited scenarios when predicting the number completed jobs, maximum flowtime, average machine utilization, and average length of queue. This study has provided better understanding on the effects of changes in demand and capacity on the job shop schedules. Areas for further study includes: (i) Fine tune the proposed ANN scheduling model (ii) Consider more variety of job shop environment (iii) Incorporate an expert system for interpretation of results. The theoretical framework proposed in this study can be used as a basis for further investigation