Gerd Finke

• Dr. rer. nat., University Kiel, Germany, 1969
• Joseph Fourier University

We consider a general model for scheduling jobs on unrelated parallel-machines with maintenance interventions. The processing times are deteriorating with their position in the production sequence and the goal of the maintenance is to help to restore good processing conditions. The maintenance duration is depending on the time elapsed since the las...

The well-known \(O(n^2)\) minmax cost algorithm of Lawler (Manag Sci 19(5):544–546, 1973) was developed to minimize the maximum cost of jobs processed by a single machine under precedence constraints. We first develop a fast updating algorithm to obtain optimal solutions for two neighboring instances. This method will be used throughout this articl...

We are presenting a general unified matrix framework for production-maintenance systems on a single machine. We have positional processing times and we propose a very general time dependent weighted maintenance system that includes most of the models from the literature. Several performance criteria are included and we show that a broad class of th...

ECCO 2010 Keywords: Service Network Design, Asset Management, Linear Relaxation of MIP. Service network design (SND) is the problem which arises in tactical planning for consolidation-based carriers [2]. A service is defined in terms of origin and destination terminals, route, capacity, and schedule. The studied problem comes from a freight transp...

ECCO 2009 The classical transportation problem is a special case of a minimum cost flow problem with the property that the nodes of the network are either supply nodes or demand nodes. The sum of all supplies and the sum of all demands are equal, and a shipment between a supply node and a demand node induces a linear cost. The aim is to determine...

R ́esum ́e : Nous consid ́erons l’ordonnancement de n taˆches sur une machine. Taˆche j, j = 1,...,n, est caract ́eris ́ee par le temps d’ex ́ecution pj ≥ 0 et par une fonction croissante Φj(t) qui indique le couˆt a` paier si taˆche j termine a` l’instant t. Il y a des contraintes de pr ́ec ́edence d ́ecrites par un graphe orient ́e acyclique G =...

Coupled tasks are two-operation tasks, where the two operations are separated by a time interval of fixed duration. Coupled task scheduling problems refer then to the scheduling of a set of coupled tasks on a single machine. Applications of these problems, reported in the literature, arise in connection with radar systems, robotic cells, and in man...

The well-known \(O(n^2)\) minmax cost algorithm of Lawler (MANAGE SCI 19(5):544–546, 1973) was developed to minimize the maximum cost of jobs processed by a single machine under precedence constraints. We propose two results related to Lawler’s algorithm. Lawler’s algorithm delivers one specific optimal schedule while there can exist other optimal...

In classical scheduling problems, the processing times are assumed to be constant. However, in a real manufacturing system, the durations of jobs may be varied due to deteriorating (aging) effects. For example, the production may slow down with the deterioration of the tools used in the production. To counteract the effect of deteriorating, the mac...

Two extensions are given to Lawler's well-known min-max cost algorithm. Lawler's algorithm provides a Two extensions are given to Lawler's well-known min-max cost algorithm. Lawler's algorithm provides a single very particular optimal solution. The first aim is to give necessary and sufficient conditions of optimality. The second problem is a speci...

The problem of scheduling tasks on a radar system can be modeled using coupled-tasks. We consider the case where all tasks are identical. This case raises original complexity questions and belongs to so-called high multiplicity scheduling problems. We present some complexity issues and results regarding the problem. We also describe a series of cou...

For an industrial application in the chemical industry, we were confronted with the planning of experiments, where human intervention of a chemist is required to handle the starting and termination of each of the experiments. This gives rise to a new type of scheduling problem, namely problems of finding schedules with time periods when the tasks c...

The purpose of this note is two-fold. First, it answers an open prob-lem about a single-machine scheduling problem with exponential position-dependent processing times defined in [V. S. Gordon, C. N. Potts, V. A. Strusevich, J. D. Whitehead, Single machine scheduling models with dete-rioration and learning: Handling precedence constraints via prior...

We analyze degeneracy characterizations for two classical problems: the transportation paradox in linear transportation problems and the pure constant fixed charge transportation problem. Solving the pure constant fixed charge problem is equivalent to finding a basic tree solution with maximum degree of degeneracy. Problems possess degenerate solut...

We consider the complexity of the maximum (maximum weight) independent set problem within triangle graphs, i.e., graphs G satisfying the following triangle condition: for every maximal independent set I in G and every edge uv in G−I, there is a vertex w∈I such that {u,v,w} is a triangle in G. We also introduce a new graph parameter (the upper indep...

Several studies have been made concerning the control and the flow optimisation in car assembly plants in order to satisfy the expectations and customer needs. But investigations of the same nature were not observed so far in component manufacturing plants. That is why we propose in this paper to study the production management problem in an engine...

2011 Optimization Days, Montreal, Canada TITLE: The identical coupled-task scheduling problem AUTHORS: - Finke, Gerd, Laboratoire G-SCOP - Brauner, Nadia, Laboratoire G-SCOP - Lehoux-Lebacque, Vassilissa, Laboratoire G-SCOP Abstract: --------- General coupled-task problems originate in radar systems. Their complexity status is known with except...

Coupled tasks belong to the class of multi-operation tasks, where two consecutive operations are separated by a certain time interval of fixed duration. The objective is to schedule the tasks on one machine in order to minimize the makespan. Such problems occur especially in the case of the management of radar systems. The complexity status of thi...

In this paper, we introduce the concept of a distance-(k, l) matching of a graph, which is a subset of edges of this graph such that the number of intermediate edges in the shortest path between any two edges of this set lies between k and l. We prove that the problem MAXIMUM DISTANCE-(k, l) MATCHING, which asks whether a graph contains a distance-...

Fundamental concepts Software Indivisible units Modeling with integer variables Conclusion Bibliography

Mots-Clés : Ordonnancement cyclique, high-multiplicity, tâches couplées Le problème des tâches couplées a été introduit par Shapiro en 1980 pour l'ordonnancement des opérations d'un radar [10]. Le radar émet un signal qui est transmis à une cible puis renvoyé au radar qui doit le réceptionner. Ainsi, le radar doit exécuter deux opérations par tâche...

4.1 Introduction 4.2 Hierarchical planning 4.3 Strategic planning and productive system design 4.3.1 Group technology 4.3.2 Locating equipment 4.4 Tactical planning and inventory management 4.4.1 A linear programming model for medium-term planning 4.4.2 Inventory management 4.4.3 Wagner and Whitin model 4.4.4 The economic order quantity model (E...

The aim of this chapter is to highlight a few specific models in production planning and management, which to seem interesting from the combinatorial optimization point of view. It structured according to the hierarchical planning approach, which the chapter sets out briefly and presents three main themes: strategic planning and productive system d...

A subset of vertices in a graph is called a dissociation set if it induces a subgraph with vertex degree at most 1. A dissociation set D is maximal if no other dissociation set contains D. The complexity of finding a dissociation set of maximum size in line graphs and finding a maximal dissociation set of minimum size in general graphs is considere...

In this paper, we present a new objective function for scheduling on parallel machines: minimizing the number of machines for schedules of minimum length. We study its complexity and we prove the NP-completeness of this problem, even if there is no precedences or for unitary execution times. We propose several polynomial algorithms for various part...

In the scheduling literature, the notion of machine non-availability periods is well known, for instance for maintenance. In our case of planning chemical experiments, we have special periods (the week-ends, holidays, vacations) where the chemists are not available. However, human intervention by the chemists is required to handle the starting and...

A subset of vertices in a graph is called a dissociation set if it induces a subgraph with a vertex degree of at most 1. The maximum dissociation set problem, i.e., the problem of finding a dissociation set of maximum size in a given graph is known to be NP-hard for bipartite graphs. We show that the maximum dissociation set problem is NP-hard for...

This paper deals with the problem of task scheduling in a flowshop with two (discrete and batching) machines. Each task has to be processed by both machines. All tasks visit the machines in the same order. The first machine is a discrete machine that can process no more than one task at a time, and the second machine is a batching machine that can...

Coupled task scheduling problems have been known for more than 25 years. Several complexity results have been established in the meantime, but the status of the identical task case remains still unsettled. We describe a new class of equivalent one-machine no-wait robotic cell problems. It turns out that scheduling of identical coupled tasks corresp...

Coupled task problems arise in connection with radar systems. For the transmission and reception of an electromagnetic pulse the radar (the processor) has to execute two tasks that are separated by some fixed time interval. Most of the complexity issues for scheduling a set of such pairs of two-operation tasks have been settled. However, the comple...

An induced matchingM of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M. The Minimum Maximal Induced Matching problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complet...

We analyze batch-scheduling problems that arise in connection with certain industrial applications. The models concern processing on a single max-batch machine with the additional feature that the tasks of the same batch have to be compatible. Compatibility is a symmetric binary relation—the compatible pairs are described with an undirected “compat...

This book presents the principal concepts of operations research (OR) as tools for the planning, support, and management of various types of networks, including both physical and logical networks. It analyzes real problems, and offers a collection of models for many application areas, together with the corresponding solution techniques. Following t...

This paper deals with two-machine flowshop problems with deteriorating tasks, i.e. tasks whose processing times are a nondecreasing function that depend on the length of the waiting periods. We consider the so-called Restricted Problem. This problem can be defined as follows: for a given permutation of tasks, find an optimal placement on two machin...

We analyze batch-scheduling problems that arise in connection with certain industrial applica-tions. The models concern processing on a single max-batch machine with the additional feature that the tasks of the same batch have to be compatible. Compatibility is a symmetric binary relation – the compatible pairs are described with an undirected "com...

A scheduling problem is described that was proposed by the Institut Français du Pétrole (IFP) and was analyzed in the laboratory G-SCOP in Grenoble. The aim is to schedule experiments to find the best conditions for the synthesis of certain chemicals. For a given chemical, one has two phases of experiments. Starting with a given heating exposure, P...

In general, distributed scheduling problem focuses on simultaneously solving two issues: (i) allocation of jobs to suitable factories and (ii) determination of the corresponding production scheduling in each factory. The objective of this approach is to maximize the system efficiency by finding an optimal planning for a better collaboration among v...

This paper extends the previous work on multibin packing problems and gives a deeper insight into these models and their complexity, so as to provide a strong framework for future application-oriented studies. In a multibin problem, an object requires several bins to be packed. New models are represented, including the maximum cardinality multibin...

Conditions imposed on the matrices of the Quadratic Assignment Problem (QAP) are derived such that an optimum of the QAP is attained on a given permutation. These conditions describe four new sets of matrices, which, in the general case, are not anti-Monge and Toeplitz matrices that were used for most of the known well solvable special cases of the...

In the past, various different solution methods have been proposed for certain modifications of the classical transportation problem, such as reshipment, over-shipment and post-optimization problems. It will be shown in this article that the three preceding problems may be solved by a modified version of the primal transportation algorithm. This un...

Ce chapitre est structuré selon l'approche de planification hiérarchique et présente trois thèmes principaux: -planification stratégique et conception du système productif ; -planification tactique de la production et gestion des stocks ; -planification opérationnelle de la production et ordonnancement. Nous conclurons en mentionnant brièvement que...

We study the problem of scheduling n jobs in a no-wait flow shop consisting of m batching machines. Each job has to be processed by all the machines. All jobs visit the machines in the same order. A job completed on an upstream machine should be immediately transferred to the downstream machine. Batching machines can process several jobs simultaneo...

An important property of strategies used to solve goals in functional logic programming (FLP) languages is the complete exploration of the solution space. Integrating constraints into FLP proved to be useful in many cases, as the resulting constraint functional logic programming (CFLP) offers more facilities and more efficient operational semantics...

Robotic cells consist of a flow-shop with a circular layout and a single transporter, a robot, for the material handling. A single part is to be produced and the objective is to minimize the production rate. Different cell configurations have been studied, depending on the travel times of the empty robot: additive, constant or just triangular. A k-...

In this paper, we deal with multibin packing problems. These problems are linked to multiprocessor-task scheduling as well as to bin packing problems: they consist of n objects to be packed into m bins, with each object requiring space in several bins. We propose an intuitive greedy approach (the best-fit rule), which extends the well-known list a...

Robotic cells consists of a flow-shop with a circular layout and a single transporter, a robot, for the material handling. A single part is to be produced and the objective is to minimize the production rate. Different cell configurations have been studied, depending on the travel times of the empty robot: additive, constant or just triangular. A k...

Dans ce chapitre, nous décrivons l'ordonnancement intégrant l'affectation des opérateurs. Nous présentons un cadre général de modélisation du problème. Nous examinons ensuite des modèles de calcul de productivité pour des cellules de production avec déplacement de l'opérateur entre les machines, par analogie avec les cellules robotisées. Enfin, nou...

Cellular network design is a very large and complex combinatorial optimization problem. It consists of antenna location and parameters settings. Until now, the design is done using radio quality criteria. Radio coverage, traffic capacity and field overlap are the main factors considered within optimization process to make decisions about network so...

An important property of answer generation strategies for functional logic programming (FLP) languages is the complete explo- ration of the solution space. Integrating constraints into FLP proves to be useful in many cases, as the resulting constraint functional logic pro- gramming (CFLP) oers more facilities and more ecien t operational semantics....

CHAPTER 23 SCHEDULING WITH DISCRETE RESOURCE CONSTRAINTS J. Błażewicz, N. Brauner, G. Finke 23.1 Introduction In this chapter we will consider the problem of scheduling tasks on processors (machines) under resource constraints. The additional resources may stand for memory, channels, reentrant procedures in case of computer systems or for tools, f...

In this paper, a graph partitioning problem that arises in the design of SONET/SDH networks is defined and formalized. Approximation algorithms with performance guarantees are presented. To solve this problem efficiently in practice, fast greedy algorithms and a tabu-search method are proposed and analyzed by means of an experimental study.

We study the computational complexity of finding the shortest route the robot should take when moving parts between machines in a flow-shop. Though this complexity has already been addressed in the literature, the existing attempts made crucial assumptions which were not part of the original problem. Therefore, they cannot be deemed satisfactory. W...