Some topics on deterministic scheduling problems

Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case

To Develop a Knowledge-Based System for Parallel Machine Operations Scheduling

As the industrialized world develops, more and more resources are becoming critical. Machines, manpower and facilities are now commonly thought of as critical resources in production and service activities. Scheduling these resources leads to increased efficiency, utilization, and ultimately, profitability. Current operation scheduling methods require complex mathematically modeling techniques that demand the substantial and extensive knowledge. Otherwise, the simple methods may not provide good results. The project is intended to engage in the issue of parallel machine operation scheduling from the knowledge based system perspective. The deal between both fields will emerge a new development of formulation and integration in artificial intelligence at area of industrial scheduling. Eventhough there are diversity techniques in manufacturing industry, the scope of the study is only limited to identical parallel operation scheduling due to time constraint towards the completion of the project. The goal of this project is to produce a working model of knowledge system for parallel machine operation scheduling. The execution of the project will be conducted in two semesters. For the First Semester, the data gathering and carrying out the associated case studies were explicitly nurtured as to aid better understanding of the project. The case studies performed were: (1) Parallel Processing - Jobs of Equal Weight, (2) Parallel Processing - Weighted Jobs, and (3) Parallel Processing - Jobs with Due Dates. In the Second Semester, the knowledge system was effectively developed. The development of the knowledge system was done in the expert interface which consists of six parts. The first step is theory familiarization, followed by user interface development, the inference engine development, dry run or testing and verification of the system. When all the steps are taken, the knowledge system can be considered as complete

Algorithms for two scheduling problems

We describe algorithms for solving the following two scheduling problems on identical pa.rallel processors. Each job requires unit processing time, has a release date and a weight. The first problem also involves the existence of dea.dlines and consists of minimizing the weighted sum of tardy jobs. The second consists of minimizing the weighted sum of completion times. The proposed algorithms run in time 0((1 + log m)n² /m) and O((log n + n/m)n), respectively.Descrevemos algoritmos para resolver os dois problemas de escalonamento envolvendo processadores paralelos idênticos, que se seguem. Cada tarefa necessita de uma unidade de tempo de processamento, tem uma data de chegada e um peso associados. O primeiro problema também envolve a existência de prazos e consiste em minimizar o somatório ponderado das tarefas tardias. Já o segundo problema consiste em se minimizar o somatório ponderado dos tempos de término das tarefas. Os algoritmos propostos rodam em tempos O((1+log m)n² /m) e O((log n+n/m)n), respectivamente

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 of Batch Processors in Semiconductor Manufacturing – A Review

In this paper a review on scheduling of batch processors (SBP) in semiconductor manufacturing (SM) is presented. It classifies SBP in SM into 12 groups. The suggested classification scheme organizes the SBP in SM literature, summarizes the current research results for different problem types. The classification results are presented based on various distributions and various methodologies applied for SBP in SM are briefly highlighted. A comprehensive list of references is presented. It is hoped that, this review will provide a source for other researchers/readers interested in SBP in SM research and help simulate further interest.Singapore-MIT Alliance (SMA

Minimizing the number of tardy jobs with precedence constraints and agreeable due dates

AbstractMinimizing the number of precedence constrained, unit-time tardy jobs is strongly NP-hard on a single machine. We study a special case of the problem where a job is tardy if it is finished more than a fixed K time units after its earliest possible completion time under the precedence constraints. We prove that the problem remains strongly NP-hard even with these special due dates. We also present polynomial time solutions for the weighted version of the problem if the precedence constraints are out-forests or interval orders. In the process, we also present a polynomial time solution for a special case of the minimum weight hitting set problem

Multi-Period Cell Loading and Job Sequencing in a Cellular Manufacturing System

In this paper, a multi-period cell loading problem is addressed, where the objectives are to minimise the number of tardy jobs (nT) in a multi-period planning horizon and optimise the scheduling of tardy jobs. Three cell loading and job scheduling strategies are proposed and tested with two newly developed mixed integer programming models. Additionally, three types of due dates (tight, medium and loose) and three different demand levels were considered. Finally, two tardy job assignment methods were proposed to observe the impact on nT. Case problems were solved based on minimising nT, Tmax and total tardiness (TT) objectives and cost sensitivity analysis was performed. Results indicated that, the first strategy, (early start allowance and tardy job assignment after each period) performed better in terms of nT. For the secondary objectives, tradeoffs were observed among different strategies depending on the type of due date, demand level and tardy job assignment method

Innovation strategy in industry: case of the scheduling problem on parallel identical machines

In this paper, we propose an innovation strategy in the industry (case of the scheduling problem on two parallel identical machines), with the objective of minimizing the weighted sum of the end dates of jobs, this problem is NP-hard. In this frame, we suggested a novel heuristics: (H1), (H2), (H3), with two types of neighborhood (neighborhood by SWAP and neighborhood by INSERT). Next, we analyze the incorporation of three diversification times (T1), (T2), and (T3) with the aim of exploring unvisited regions of the solution space. It must be noted that job movement can be within one zone or between different zones. Computational tests are performed on 6 problems with up to 2 machines and 500 jobs