# Frank WernerOtto-von-Guericke-Universität Magdeburg | OvGU · Institute of Mathematical Optimization (IMO)

Frank Werner

apl. Prof. Dr. rer. nat. habil.

## About

422

Publications

95,126

Reads

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5,212

Citations

Introduction

For almost four decades, I mainly deal with the solution of different scheduling problems beginning around 1980 with the development of genetic algorithms for flow shop problems. I also investigate the complexity of scheduling problems, uncertain scheduling problems and several graph-theoretic problems. I was involved into several research projects supported by German Research Foundation (DFG), European Community (INTAS) and Belarusian Republican Foundation of Fundamantal Research.

Additional affiliations

March 2020 - present

**MBA Magdeburg**

Position

- Professor

Description

- Operations Research course (in German)

Education

September 1980 - August 1983

**Technische Hochschule Magdeburg**

Field of study

- Mathematics, Ph.D. student

September 1975 - August 1980

**Technische Hochschule Magdeburg**

Field of study

- Mathematics

September 1971 - August 1973

**EOS Geschwister Scholl Magdeburg**

Field of study

- Secondary school

## Publications

Publications (422)

One of the recently proposed strategies in health systems is providing services to patients at home and improving the service quality in addition to reducing the health system costs. In the real world, some services, such as biological tests or blood sampling, force the nurses to start or end his/her route from/at the laboratory instead of the depo...

A significant amount of hazardous waste generated from health sectors and industrial processes has posed a major threat to human health by causing environmental issues and contamination of air, soil, and water resources. This paper presents a multi-objective mixed-integer nonlinear programming (MINLP) formulation for a sustainable hazardous waste l...

One of the recently proposed strategies in health systems is providing services to patients at home, improving the service quality, besides reducing the health system costs. In the real world, some services, such as biological tests or blood sampling, force the nurses to start or end his/her route from/at the laboratory instead of the depot, changi...

This is the printed edition of the Proceedings of the 1st International Electronic Conference on Algorithms (IOCA 2021)

The problem of scheduling non-simultaneously released jobs with due dates on a single machine with the objective to minimize the maximum job lateness is known to be strongly NP-hard. Here we consider an extended model in which the compression of the job processing times is allowed. The compression is accomplished at the cost of involving additional...

One of the most critical issues in manufacturing systems is the operator management. In this paper, the operator assignment problem is studied within a cellular manufacturing system. The most important novelty of this research is the consideration of operator learning and forgetting effects simultaneously. The skill level of an operator can be incr...

This paper aims to develop a sustainable closed-loop supply chain network model with a modular single product which is specifically designed for the automotive industry. Drawing upon sustainability criteria, three objective functions are formulated for the closed-loop network design problem including maximizing total profit across the network, mini...

It is the Editorial of the special issue with the '2021 Selected Papers from Algorithms' Editorial Board members.

This Special Issue of Mathematics is dedicated to the application of Operations Research methods to a wide range of problems. […]

Forward of the edited Proceedings (ISBN: 978-989-758-528-9):
This book contains the proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), which is sponsored by the Institute for Systems and Technologies of Information, Control and Communication (INSTICC) and held i...

We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polyno...

In recent years, the management of health systems is a main concern of governments and decision-makers. Home health care is one of the newest methods of providing services to patients in developed societies that can respond to the individual lifestyle of the modern age and the increase of life expectancy. The home health care routing and scheduling...

This Special Issue of Algorithms is of a different nature than other Special Issue in the journal, which are usually dedicated to a particular subjects in the area of algorithms [...]

We consider the problem of scheduling $n$ jobs with identical processing times and given release as well as delivery times on $m$ uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a po...

Multi-criteria optimization problems naturally arise in practice when there is no single criterion for measuring the quality of a feasible solution. Since different criteria are contradictory, it is difficult and often impossible to find a single feasible solution that is good for all the criteria. Hence, some compromise is needed. As such, this bo...

In recent years, the management of health systems is a main concern of governments and decision makers. Home health care is one of the newest methods of providing services to patients in developed societies that can respond to the individual lifestyle of modern age and the increase of life expectancy. The home health care routing and scheduling pro...

This is the print version of a special issue with the same title in the journal Mathematics. The pdf can be freely downloaded from the publisher's website, the hardcover book is with payment.

Discrete optimization is an important area of applied mathematics which is at the intersectionof several disciplines and covers both theoretical and practical aspects[...]

NP-hard scheduling problems with the criterion of minimizing the maximum penalty, e.g. maximum lateness, are considered. For such problems, a metric which delivers an upper bound on the absolute error of the objective function value is introduced. Taking the given instance of some problem and using the introduced metric, the nearest instance is det...

In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound...

Scheduling in Industry 4.0 systems belongs to a class of problems that have mixed structural-temporal-logical constraints. In other words, a strong coupling is considered when product and process are created simultaneously. As a result of the proven NP-hardness of such problems, solution methods have extensively utilized different decomposition pri...

This is the printed edition of a special issue with the same title. It contains 20 chapters. The pdf is freely downloadable from the publisher's website while the print book is with payment.

Рассматривается задача теории расписаний, в которой необходимо
минимизировать суммарное взвешенное запаздывание на одном приборе
с равными продолжительностями обслуживания требований и неодно-
временным поступлением требований на обслуживание. Эта задача упо-
мянута как минимальная, статус вычислительной сложности которой не-
известен: http://www2....

In this paper, we consider the problem of minimizing total weighted tardiness for equal-length jobs with arbitrary release dates on a single machine. This problem is mentioned as a minimal open problem, see http://www2.informatik.uni-osnabrueck.de/knust/class/dateien/classes/ein_ma/ein_ma, i.e., its complexity status is still open. The latest resul...

Free Download link for full paper:
https://www.tandfonline.com/eprint/WCPCPFQFWUEQWC2BEDC7/full?target=10.1080/00207543.2019.1627439
Recently, the applications of Blockchain technology have begun to revolutionise different aspects of supply chain (SC) management. Among others, Blockchain is a platform to execute the smart contracts in the SC as tr...

This is the Printed Edition of a special issue with the sanme title in the journal Algorithms. The pdf can be freely downloaded from the publisher's website (the printed book is with fee).

Graph theory is an important area of Applied Mathematics with a broad spectrum of applications in many fields [...]

We study the problem of scheduling in manufacturing environments which are dynamically configurable for supporting highly flexible individual operation compositions of the jobs. We show that such production environments yield the simultaneous process design and operation sequencing with dynamically changing hybrid structural-logical constraints. We...

Multi-objective optimization problems are important as they arise in many practical circumstances. In such problems, there is no general notion of optimality, as there are different objective criteria which can be contradictory. In practice, often there is no unique optimality criterion for measuring the solution quality. The latter is rather deter...

New metrics for different classes of scheduling problems are introduced. We show how approximate solutions of NP-hard problems can be obtained using these metrics. To do this, we solve the optimization problem in which the introduced metric is used as the objective function, and a system of linear inequalities of (pseudo-)polynomial solvable instan...

This special issue of Algorithms is a follow-up issue of an earlier one, entitled ‘Algorithms for Scheduling Problems’. In particular, the new issue is devoted to the development of exact and heuristic scheduling algorithms. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. In the Call for...

In this paper, we consider single machine scheduling problems with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on...

The job shop scheduling problem with blocking constraints and total tardiness minimization represents a challenging combinatorial optimization problem of high relevance in production planning and logistics. Since general-purpose solution approaches struggle with finding even feasible solutions, a permutation-based heuristic method is proposed here,...

The studies on supply chain (SC) disruption management frequently assume the existence of some negative scenarios and suggest ways to proactively protect and reactively recover the SC operations and performance if such scenarios occur. Though, there is a paucity of research on how to support methodologically the detection of realistic disruption sc...

We consider N P-hard multi-machine scheduling problems with the criterion of minimizing the maximum penalty, e.g. maximum lateness. For such problems, we introduce a metric which delivers an upper bound on the absolute error of the objective function value. Taking the given instance of some problem and using the introduced metric, we determine the...

A set of jobs has to be processed on a single machine without preemptions of a job. The exact value of the job processing time (duration) is unknown until the completion of the job. Lower and upper bounds on the job duration are known before scheduling. The problem is to minimize total completion time of the given jobs. We apply a stability approac...

In this paper, we consider some special resource-constrained scheduling problems, which occur e.g. in production or in computer science. We consider the minimization of the makespan as well as total tardiness. Some complexity and approximability results are given as well as relationships to other scheduling problems.
(Full text under: https://eve...

In the manufacturing of highly customized goods and the operation of automatic logistics systems, efficient schedules constitute an everyday challenge. Therefore, the job shop problem is established as a standard model in scheduling research. While classical variants are well studied, the involvement of practically relevant conditions, such as the...

These are the slides of the talk at MIM 2019 in the open invited track 'Planning and Schedulung of Manufacturing Processes' on August 28, 2019

These are the slides of the talk at MIM'2019 on August 28, 2019.

This is the Editorial of a Special Issue in the mdpi Journal Mathematics.

A set of jobs has to be processed on parallel machines. For each job, there are given a release time and a due date and the job must be processed no later than its due date. If the job will be completed no later than the given due date, a benefit will be earned. Otherwise, this job will be rejected and the benefit will be discarded. The criterion u...

This paper presents a comprehensive and novel mathematical model to address the scheduling problem of inpatient surgeries. The interaction quality and compatibility level of surgical team members can have a significant impact on the quality and safety of a surgery. The first aim of this paper is to incorporate the decision-making styles of the surg...

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with two operations and equal processing times on each machine. This problem occurs e.g., as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present...

Множество требований необходимо обслужить на параллельных при-
борах. Для каждого требования известно время готовности к обслужива-
нию и установлен срок, не позднее которого требование должно быть об-
служено. Если обслуживание требования завершается к установленному
сроку, то начисляется определенная прибыль. Впро тивном случае требо-
вание счита...

The authors have found two errors in the paper published in Materials [...]

This paper presents a bi-objective MILP model for the vehicle routing and scheduling problem with cross-docking for perishable products. It is demonstrated that considering merely one objective sacrifices the other one and that the L1 metric method makes a suitable trade-off. Two robust models are developed when the travel time of the outbound vehi...

Highlights • We examine a scheduling problem in production of wafer fabrication. • We develop a mathematical model to describe and solve the problem. • We propose three heuristics with the worst-case performance ratio 3/2. • We compare the performance our proposed heuristics with two existing metaheuristics. • Computational results show that the pr...

In this paper, we consider some special resource-constrained scheduling problems, which occur e.g. in production or in computer science. We consider the minimization of the makespan as well as total tardiness. Some complexity and approximability results are given as well as relationships to other scheduling problems.

A set of jobs has to be processed on a single machine without preemptions of a job. The exact value of the job processing time (duration) is unknown until the completion of the job. Lower and upper bounds on the job duration are known before scheduling. The problem is to minimize total completion time of the given jobs. We apply a stability approac...

In the manufacturing of highly customized goods and the operation of automatic logistics systems, efficient schedules constitute an everyday challenge. Therefore, the job shop problem is established as a standard model in scheduling research. While classical variants are well studied, the involvement of practically relevant conditions, such as the...

Goal. The objective of this work is to propose a model that allows one to obtain velocity and direction of spherical hard-bodies after a collision, using Molecular Dynamics (MD) methods. Molecular simulations are employed to compute the properties and predict behaviors of solids, liquids and gases; the consideration of collisions between particles...

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with one equal-length operation per job on each machine. This problem occurs e.g. as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present a polyno...

In this paper, we consider the problem of minimizing total weighted tardiness for equal-length jobs with arbitrary release dates on a single machine. This problem is mentioned as a minimal open problem, see ma , i.e., its complexity status is still open. The latest results on this problem were presented in the years 2000 and 2005, namely solution a...

In this paper, we consider some special resource-constrained scheduling problems, which occur e.g. in engineering when heating an equipment or in computer science. We consider the minimization of the makespan as well as total tardiness. Some complexity and approximability results are given as well as relationships to other scheduling problems.

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro-and nanoscopic scales show that they are, as a rule, not ideal cylinders. In this paper, the channels, which have an irregular shape and a circular cross-sectio...

This is a printed book of the special issue on Algorithms for Scheduling Problems. It contains a preface and the 11 articles published under
http://www.mdpi.com/journal/algorithms/special_issues/Scheduling_Problems

We address a generalization of the classical job-shop problem which is called a hybrid job-shop problem. The criteria under consideration are the minimization of the makespan and mean flow time. In the hybrid job-shop, machines of type k are available for processing the specific subset k of the given operations. Each set k may be partitioned into s...

Scheduling in Industry 4.0 systems belongs to a class of problems that have mixed structural-temporal-logical constraints. In other words, a strong coupling is considered when product and process are created at the same time. As a result of the proven NP-hardness of such problems , solution methods have extensively utilized different decomposition...

This special issue of Algorithms is devoted to the development of scheduling algorithms based on innovative approaches for solving hard scheduling problems either exactly or approximately. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. The main topics include sequencing and scheduling wi...

In the vehicle routing problem with cross-docking (VRPCD), it is assumed that the selected suppliers and the quantity of the products purchased from each supplier are known. This paper presents an MILP model which incorporates supplier selection and order allocation into the VRPCD in a multi-cross-dock system minimising the total costs, including p...

The problem of scheduling a set of trains traveling through a given railway network consisting of single tracks, sidings and stations is considered. For every train a fixed route and travel times, an earliest departure time at the origin and a desired arrival time at the destination are given. A feasible schedule has to be determined which minimize...

The Linux operating system has been employed to execute numerous real-time applications. However, it is limited to support soft real-time systems by two scheduling policies: First-In-First-Out and Round Robin. For real-time systems with critical constraints, the soft real-time support and these scheduling policies are still insufficient. In this wo...

An uncertain single-machine scheduling problem is considered, where the processing time of a job can take any real value from a given segment. The criterion is to minimize the total weighted completion time of the n jobs, a weight being associated with each given job. We use the optimality box as a stability measure of the optimal schedule and deri...

Models and optimisation approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimisation procedure is proposed. First, the makespan value is minimised with the smallest sublots defined for the problem instance. This makes it possible to shorten the makespan signi...

The objective of this work is to reduce the machine downtime due to setup times during the electrical test in a semiconductor packaging company, whose products has high volume–high mixture characteristics. The group technology is adapted for the plant production workflow modeling. Based on the real data of the production floor, a taxonomy of setup...

The improvement of the performance of material handling tools (MHTs) and the work in process (WIP) in a discrete manufacturing system have a great importance for increasing the efficiency of the production. To this end, the static and dynamic status of MHTs are analyzed in this paper. A Markov decision process (MDP) is used to model the MHT problem...