Minimizing The Number of Tardy Jobs in Hybrid Flow Shops with Non-Identical Multiple Processors

Two-stage hybrid flow shops (a.k.a., flow shops with multiple processors (FSMPs)) are studied wherein the multiple processors at a stage are non-identical, but related (a.k.a., uniform) in their processing speeds.   The impact of ten different dispatching procedures on a due-date based criterion (specifically, the number of tardy jobs) is analyzed over a set of 1,800 problems of varying configurations wherein the number of jobs per problem is between 20 and 100 and their due dates are randomly assigned.  Results indicate that the modified due date (MDD), earliest due date (EDD), slack (SLK), shortest processing time (SPT), and least work remaining (LWR) rules are statistically inseparable but yield superior performance to the other rules included in this study.  The longest processing time (LPT) and most work remaining (MWR) rules provide the poorest performance

Scheduling independent jobs on uniform parallel machines to minimize tardiness criteria

International audienceThe problem of scheduling N jobs on M uniform parallel machines is studied. The objective is to minimize the mean tardiness or the weighted sum of tardiness with weights based on jobs, on periods or both. For the mean tardiness criteria in the preemptive case, this problem is NP-hard but good solutions can be calculated with a transportation problem algorithm. In the nonpreemptive case the problem is therefore NP-hard, except for the cases with equal job processing times or with job due dates equal to job processing times. No dominant heuristic is known in the general nonpreemptive case. The author has developed a heuristic to solve the nonpreemptive scheduling problem with unrelated job processing times. Initially, the algorithm calculates a basic solution. Next, it considers the interchanges of job subsets to equal processing time sum interchanging resources (i.e. a machine for a given period). This paper models the scheduling problem. It presents the heuristic and its result quality, solving 576 problems for 18 problem sizes. An application of school timetable scheduling illustrates the use of this heuristic

A Framework for Approximate Optimization of BoT Application Deployment in Hybrid Cloud Environment

We adopt a systematic approach to investigate the efficiency of near-optimal deployment of large-scale CPU-intensive Bag-of-Task applications running on cloud resources with the non-proportional cost to performance ratios. Our analytical solutions perform in both known and unknown running time of the given application. It tries to optimize users' utility by choosing the most desirable tradeoff between the make-span and the total incurred expense. We propose a schema to provide a near-optimal deployment of BoT application regarding users' preferences. Our approach is to provide user with a set of Pareto-optimal solutions, and then she may select one of the possible scheduling points based on her internal utility function. Our framework can cope with uncertainty in the tasks' execution time using two methods, too. First, an estimation method based on a Monte Carlo sampling called AA algorithm is presented. It uses the minimum possible number of sampling to predict the average task running time. Second, assuming that we have access to some code analyzer, code profiling or estimation tools, a hybrid method to evaluate the accuracy of each estimation tool in certain interval times for improving resource allocation decision has been presented. We propose approximate deployment strategies that run on hybrid cloud. In essence, proposed strategies first determine either an estimated or an exact optimal schema based on the information provided from users' side and environmental parameters. Then, we exploit dynamic methods to assign tasks to resources to reach an optimal schema as close as possible by using two methods. A fast yet simple method based on First Fit Decreasing algorithm, and a more complex approach based on the approximation solution of the transformed problem into a subset sum problem. Extensive experiment results conducted on a hybrid cloud platform confirm that our framework can deliver a near optimal solution respecting user's utility function

GRASP and Tabu Search applied to scheduling problems in parallel machines

Orientador: Vinicius Amaral ArmentanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho é dedicado à programação de tarefas em máquinas paralelas. Dois ambientes são considerados. No primeiro, as máquinas são idênticas e o objetivo é a minimização da soma ponderada de custos de atraso. Todas as tarefas estão disponíveis para processamento no início do horizonte de programação e a cada uma são associadas uma data de entrega e uma penalização por atraso específicas. No segundo, as máquinas são não relacionadas e o objetivo é a minimização da soma ponderada de custos de avanço e de atraso. Instantes de liberação, datas de entrega, penalizações por avanço e por atraso são específicos para cada tarefa. Em ambos, as transições entre tarefas requerem tempos de preparação dependentes da seqüência de processamento. Os problemas são resolvidos por meio de GRASP e Busca Tabu. Memória de longo prazo é empregada para melhorar o desempenho das duas metaheurísticas. No GRASP, soluções de elite influenciam a fase construtiva. Na Busca Tabu, estratégias de diversificação e de intensificação fazem uso direto das soluções de elite e também de freqüências de residência. Como pós-otimização, nas duas metaheurísticas, realizam-se religações de caminhos entre as soluções de eliteAbstract: This work is dedicated to the scheduling of a set of jobs in parallel machines. Two scenarios are considered. In the first one, the machines are identical and the objective is the minimization of the weighted sum of tardiness costs. All jobs are ready for processing at the beginning of the scheduling horizon and to each one is associated a due date and a tardiness penalty. In the second scenario, the machines are non-related and the objective is the minimization of the weighted sum of earliness and tardiness costs. Ready times, due dates, earliness and tardiness penalties are specifics to each job. In both problems, the transitions between jobs require sequence dependent setup times. The problems are solved using GRASP and Tabu Search. Long term memory is applied to improve the performance of the metaheuristics. A set of elite solutions are used to influence the constructive phase in GRASP. In Tabu Search, diversification and intensification strategies make direct use of the elite solutions, as well of residence frequences. Path relinking between the elite solutions is used as a post-optimization approachDoutoradoAutomaçãoDoutor em Engenharia Elétric

A methodology for scheduling jobs in a flexible flowshop with sequence dependent setup times and machine skipping

A flexible flowshop, comprised of one or more stages having unrelated parallel machines, is investigated in this research. Unrelated parallel machines can perform the same function but have different capacity or capability. Since this problem is motivated by industry research, dynamic job release times and dynamic machine availability times have been considered. Each job considered in this research can have different weight and due date. Sequence-dependent setup times of jobs further add to the complexity of the research. Machine skipping is yet another innate feature of this research that allows jobs to skip one or more stages depending upon customer's demand or budgetary constraints. The objective of this research is to minimize the sum of the weighted tardiness of all jobs released within the planning horizon. The research problem is modeled as a mixed (binary) integer-linear programming model and is shown to be strictly NP-hard. Being strongly NP-hard, industry size problems cannot be solved using an implicit enumeration technique within a reasonable computation time. Cognizant of the challenges in solving industry-size problems, we use the tabu-search-based heuristic solution algorithm to find optimal/near optimal solutions. Five different initial solution finding mechanisms, based on dispatching rules, have been developed, to initiate the search. The five initial solution finding mechanisms (IS1-IS5) have been used in conjunction with the six tabu-search-based heuristics (TS1-TS6) to solve the problems in an effective and efficient manner. The applicability of the search algorithm on an example problem has been demonstrated. The tabu-search based heuristics are tested on seven small problems and the quality of their solutions is compared to the optimal solutions obtained by the branch-and-bound technique. The evaluations show that the tabu-search based heuristics are capable of obtaining solutions of good quality within a much shorter computation time. The best performer among these heuristics recorded a percentage deviation of only 2.19%. The performance of the tabu-search based heuristics is compared by conducting a statistical experiment that is based on a randomized complete block design. Three sizes of problem structures ranging from 9 jobs to 55 jobs are used in the experiment. The results of the experiment suggest that no IS finding mechanism or TS algorithm contributed to identifying a better quality solution (i.e a lower TWT) for all three problem instances (i.e. small, medium and large). In other words, no IS finding mechanism or TS algorithm could statistically outperform others. In absence of a distinct outperformer, TS1 with short-term memory and fixed TLS are recommended for all problem instances. When comparing the efficiency of the search algorithm, the results of the experiment show that IS1, which refers to the EDD (earliest due date) method, is recommended as the initial solution generation method for small problem sizes. The EDD method is capable of obtaining an initial solution that helps the tabu-search based heuristic to get to the final solution within a short time. TS1 is recommended as the tabu-search based heuristic for large problems, in order to save on time. TS1 is also recommended to solve small and medium problem structures in absence of a statistically proven outperformer