Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Minimizing makespan and preemption costs on a system of uniform machines

Abstract. It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for non-preemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem. In generalized multiprocessor scheduling (GMS) wehaveajob-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS) the only feasible schedules are preemptive schedules with the smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions. For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. Our scheme for a fixed number of machines has linear running time, and can be applied also for instances where jobs have release dates, and for instances with arbitrary preemption costs. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule. Our results for MPS hold for any instance in which a job, Jj, can be processed simultaneously by ρj machines, for some ρj ≥ 1

Minimizing makespan and preemption costs on a system of uniform machines

It is well known that for preemptive scheduling on uniform machines there exist polynomial time exact algorithms, whereas for nonpreemptive scheduling there are probably no such algorithms. However, it is not clear how many preemptions (in total, or per job) suffice in order to guarantee an optimal polynomial time algorithm. In this paper we investigate exactly this hardness gap, formalized as two variants of the classic preemptive scheduling problem. In generalized multiprocessor scheduling (GMS), we have job-wise or total bound on the number of preemptions throughout a feasible schedule. We need to find a schedule that satisfies the preemption constraints, such that the maximum job completion time is minimized. In minimum preemptions scheduling (MPS), the only feasible schedules are preemptive schedules with smallest possible makespan. The goal is to find a feasible schedule that minimizes the overall number of preemptions. Both problems are NP-hard, even for two machines and zero preemptions.For GMS, we develop polynomial time approximation schemes, distinguishing between the cases where the number of machines is fixed, or given as part of the input. For MPS, we derive matching lower and upper bounds on the number of preemptions required by any optimal schedule

Інформаційна технологія оперативно-календарного планування дрібносерійного виробництва за концепцією «точно в строк»

В дисертаційній роботі розв’язано актуальне науково-практичне завдання з розроблення інформаційної технології оперативно-календарного планування дрібносерійного виробництва, яка призводить до підвищення ефективності функціонування виробничих систем за рахунок побудови оптимальних (близьких до оптимальних) за часовими критеріями календарних планів. Розглянуто існуючі моделі та методи систем планування, теорії розкладів. Розроблено методи побудови розкладів оперативно-календарного планування дрібносерійного виробництва. Обґрунтовано доцільність використання запропонованих методів. Проаналізовано ефективність запропонованих методів побудови розкладів. Розроблено інформаційну технологію оперативно-календарного планування дрібносерійного виробництва за концепцією «точно в строк». Проведені експериментальні дослідження інформаційної технології, які підтвердили адекватність запропонованих моделей та методів