Solving an integrated job-shop problem with human resource constraints

International audienceWe propose two exact methods to solve an integrated employee-timetable and job-shop-scheduling problem. The problem is to find a minimum cost employee-timetable, where employees have different competences and work during shifts, so that the production, that corresponds to a job-shop with resource availability constraints, can be achieved. We introduce two new exact procedures: (1) a decomposition and cut generation approach and (2) a hybridization of a cut generation process with a branch and bound strategy. We also propose initial cuts that strongly improve these methods as well as a standard MIP approach. The computational performances of those methods on benchmark instances are compared to that of other methods from the literature

Solving an integrated Job-Shop problem with human resource constraints

This paper investigates the integration of the employee timetabling and production scheduling problems. At the first level, we have to manage a classical employee timetabling problem. At the second level, we aim at supplying a feasible production schedule for a job-shop scheduling problem (NP-hard problem). Instead of using a hierarchical approach as in the current practice, we here integrate the two decision stages and propose two exact methods for solving the resulting problem. The former is similar to the cut generation algorithm proposed in Guyon et. al. 2010) for a problem integrating a classical employee timetabling problem and a polynomially solvable production scheduling problem. The latter is based on a Branch-And-Cut process that exploits the same feasibility cuts than the first approach. Preliminar experimental results on instances proposed in (Artigues et al. 2009) reveal a real interest for the approaches described here

Branch and Bound hybride pour un problème de job-shop soumis à des contraintes de ressources humaines

National audienceNous considérons un problème couplant ordonnancement de production et planification d'agents. On se place ainsi dans un atelier où la production à réaliser requiert divers types de machines dans des séquences variées de type job-shop. Chaque machine nécessite pour son utilisation la présence d'un employé qualifié à son pilotage. Les ressources humaines sont assujetties à des contraintes légales restreignant leur disponibilité. La production doit être entièrement ordonnancée et le critère d'optimisation retenu est la minimisation des coûts salariaux. Pour résoudre ce problème, nous avons développé une méthode exacte hybridant approche arborescente de type Procédure de Séparation et Evaluation Séquentielle et technique de génération de coupes de réalisabilité. Cette méthode exploite la décomposition naturelle du problème global en deux sous-problèmes : un problème de planification d'agents et un problème de job-shop à contraintes de disponibilité. Des méthodes de génération d'inégalités valides en pré-process (notamment du probing) ont en outre été étudiées. Notre approche s'avère particulièrement adaptée à la problématique ; ses résultats dominent en effet ceux obtenus avec l'un des meilleurs solveurs commerciaux actuels (Ilog Cplex 12.1) et ceux obtenus avec les méthodes décrites dans la littérature

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

An integrated personnel allocation and machine scheduling problem for industrial size multipurpose plants

This paper describes the development and implementation of an optimization model to solve the integrated problem of personnel allocation and machine scheduling for industrial size multipurpose plants. Although each of these problems has been extensively studied separately, works that study an integrated approach are very limited, particularly for large-scale industrial applications. We present a mathematical formulation for the integrated problem and show the results obtained from solving large size instances from an analytical services facility. The integrated formulation can improve the results up to 22.1% compared to the case where the personnel allocation and the machine scheduling problems are solved sequentially

Investigating Constraint Programming and Hybrid Methods for Real World Industrial Test Laboratory Scheduling

In this paper we deal with a complex real world scheduling problem closely related to the well-known Resource-Constrained Project Scheduling Problem (RCPSP). The problem concerns industrial test laboratories in which a large number of tests has to be performed by qualified personnel using specialised equipment, while respecting deadlines and other constraints. We present different constraint programming models and search strategies for this problem. Furthermore, we propose a Very Large Neighborhood Search approach based on our CP methods. Our models are evaluated using CP solvers and a MIP solver both on real-world test laboratory data and on a set of generated instances of different sizes based on the real-world data. Further, we compare the exact approaches with VLNS and a Simulated Annealing heuristic. We could find feasible solutions for all instances and several optimal solutions and we show that using VLNS we can improve upon the results of the other approaches

Dynamic allocation of operators in a hybrid human-machine 4.0 context

La transformation numérique et le mouvement « industrie 4.0 » reposent sur des concepts tels que l'intégration et l'interconnexion des systèmes utilisant des données en temps réel. Dans le secteur manufacturier, un nouveau paradigme d'allocation dynamique des ressources humaines devient alors possible. Plutôt qu'une allocation statique des opérateurs aux machines, nous proposons d'affecter directement les opérateurs aux différentes tâches qui nécessitent encore une intervention humaine dans une usine majoritairement automatisée. Nous montrons les avantages de ce nouveau paradigme avec des expériences réalisées à l'aide d'un modèle de simulation à événements discrets. Un modèle d'optimisation qui utilise des données industrielles en temps réel et produit une allocation optimale des tâches est également développé. Nous montrons que l'allocation dynamique des ressources humaines est plus performante qu'une allocation statique. L'allocation dynamique permet une augmentation de 30% de la quantité de pièces produites durant une semaine de production. De plus, le modèle d'optimisation utilisé dans le cadre de l'approche d'allocation dynamique mène à des plans de production horaire qui réduisent les retards de production causés par les opérateurs de 76 % par rapport à l'approche d'allocation statique. Le design d'un système pour l'implantation de ce projet de nature 4.0 utilisant des données en temps réel dans le secteur manufacturier est proposé.The Industry 4.0 movement is based on concepts such as the integration and interconnexion of systems using real-time data. In the manufacturing sector, a new dynamic allocation paradigm of human resources then becomes possible. Instead of a static allocation of operators to machines, we propose to allocate the operators directly to the different tasks that still require human intervention in a mostly automated factory. We show the benefits of this new paradigm with experiments performed on a discrete-event simulation model based on an industrial partner's system. An optimization model that uses real-time industrial data and produces an optimal task allocation plan that can be used in real time is also developed. We show that the dynamic allocation of human resources outperforms a static allocation, even with standard operator training levels. With discrete-event simulation, we show that dynamic allocation leads to a 30% increase in the quantity of parts produced. Additionally, the optimization model used under the dynamic allocation approach produces hourly production plans that decrease production delays caused by human operators by up to 76% compared to the static allocation approach. An implementation system for this 4.0 project using real-time data in the manufacturing sector is furthermore proposed

Integer linear programs and heuristic solution approaches for different planning levels in underground mining

Natürlich vorkommende Mineralien werden seit Tausenden von Jahren aus der Erde gefördert. Im Bergbau wird Operations Research (OR) hauptsächlich angewendet, um die Materialgewinnung zu vereinfachen und die Ressourcen für die Gewinnung effizienter zuzuordnen. Optimierungsprobleme im Bergbau werden üblicherweise nach ihrem Planungshorizont eingeordnet. Dabei werden Layout- und Designprobleme auf strategischer, Produktions- und Planungsprobleme auf taktischer und Ressourcenzuordnungsprobleme auf operativer Planungsebene behandelt. In dieser kumulativen Dissertation betrachten wir eine der größten deutschen Kalibergwerke und befassen uns mit drei Optimierungsproblemen auf drei verschiedenen Planungsebenen. Zunächst betrachten wir eine sogenannte „Gewinnungsprogrammplanung“ für einen Planungshorizont von einem Monat auf taktischer Planungsebene. Die betrachtete qualitätsorientierte Zielfunktion zielt auf eine gleichmäßige Kalisalzgewinnung hinsichtlich des beinhalteten Kaliums ab. Da die Menge der Gesamtförderung a priori unbekannt ist, kann die in der Gesamtförderung enthaltene Kaliummenge mithilfe nicht-linearer Nebenbedingungen in der mathematischen Formulierung bestimmt werden. Die Herausforderung besteht in der Linearisierung der entsprechenden Nebenbedingungen, damit ein gemischt ganzzahliges lineares Programm eingeführt werden kann. Darüber hinaus schlagen wir eine Heuristik vor, welche mindestens eine zulässige Lösung für realitätsnahe Probleminstanzen innerhalb eines angemessenen Zeitraums findet. Die Performanceanalyse an 100 zufällig generierten Probleminstanzen zeigt, dass eine subtile Kombination des vorgeschlagenen mathematischen Programms mit der eingeführten Heuristik nahezu optimale Lösungen für praxisrelevante Probleme findet. Als Nächstes betrachten wir eine „Grobplanung des Maschineneinsatzes“ innerhalb eines Planungshorizonts von einer Woche, welche zwischen der taktischen und der operativen Planungsebene eingeordnet werden kann und untersucht, ob die Ergebnisse der Gewinnungsprogrammplanung für die erste Woche des folgenden Monats umgesetzt werden können. Hierzu wird ein Maschinenplanungsproblem zur Minimierung des maximalen Fertigstellungszeitpunkts berücksichtigt. Wir stellen ein gemischt ganzzahliges lineares Programm vor, welches bestimmte Umstände in einem untertägigen Bergwerk wie die Wiederholung der Erstfreigabe berücksichtigt. Die größte Herausforderung besteht darin, einen Lösungsansatz zu entwickeln, der nahezu optimale Lösungen für große Probleminstanzen findet. Also wird eine Heuristik vorgeschlagen, der absichtliche Verzögerungen von Jobs vor Bearbeitungsstufen einbezieht, d. h. sogenannte aktive Pläne erzeugt. Die Performanceanalyse zeigt, dass kleine Probleminstanzen mit CPLEX optimal gelöst werden können. Bei größeren Instanzen liefert die vorgeschlagene Heuristik die besten Ergebnisse. Schließlich wird auf der operativen Planungsebene eine „Feinplanung des Maschinen- und Personaleinsatzes“ berücksichtigt. Das betrachtete Problem verfolgt einen gleichmäßigen Fortschritt im untertägigen Bergwerk innerhalb einer Arbeitsschicht. Um realistische Lösungen zu erstellen, müssen verschiedene Arten von Rüstzeiten in Betracht gezogen werden, die abhängig von der Bearbeitungsreihenfolge der Operationen an Maschinen und Arbeitern entstehen. Die größte Herausforderung besteht darin, die spezifischen Umstände einer Arbeitsschicht mathematisch darzustellen, z. B. die Berücksichtigung der Pausen der Mitarbeiter für eine eventuelle Verzögerung der Bearbeitungszeit, das Bestimmen des bearbeiteten Prozentsatzes eines Jobs während einer Arbeitsschicht, die Berechnung der Entfernungs- und Umrüstzeiten usw. Wir stellen eine Heuristik vor, die aus zwei Schritten besteht. Im ersten Schritt wird eine Relaxation des Problems unter Einhaltung einen Teil der genannten Nebenbedingungen gelöst. Die gefundene, typischerweise unzulässige Lösung wird im zweiten Schritt durch Einfügen der vernachlässigten Zeiten repariert. Die Ergebnisse zeigen, dass die vorgeschlagene Heuristik für 70 Prozent der realitätsnahen Probleminstanzen eine bessere Lösung als eine bestehende Heuristik finden kann. Anschließend formulieren wir ein neues, kompaktes, gemischt ganzzahliges lineares Programm, das mithilfe von TSP-Variablen alle Problemspezifikationen berücksichtigt. Wir zeigen, dass das vorgeschlagene gemischt ganzzahlige lineare Programm die vorgeschlagene zweistufige Heuristik erheblich übertrifft.Humans have been extracting naturally occurring minerals from the earth for thousands of years. In mining, operations research (OR) has been mainly used to help the mine planners decide how the material can be extracted and what to do with the material removed, what kind of resources to use for the extraction, and how to allocate the resources. It is very widespread to classify decision problems according to their time horizons, where 1. layout and design problems, 2. production and scheduling problems, and 3. operational equipment allocation problems are considered on strategic, tactical, and operational planning levels, respectively. In this cumulative dissertation thesis, we consider one of the biggest German potash mines and address three optimization problems on three different planning levels. First, we consider a so-called “extraction program planning” for a time horizon of one month on the tactical planning level. The related quality-oriented objective function aims at an even extraction of potash regarding the potassium content. For mathematically formulating the objective function, the amount of potassium contained in the output must be determined. Since the amount of total output is a priori unknown, the potassium amount can be determined primarily using non-linear constraints. The principal challenge is the linearization of the corresponding constraints to introduce a mixedinteger linear program with a quality-related objective function. We also propose a heuristic solution procedure that finds for realistically-sized problem instances at least one feasible solution within a reasonable amount of time. The performance analysis conducted on 100 randomly generated problem instances shows that a sophisticated combination of the proposed mixed-integer linear program and the introduced heuristic approach finds high-quality, near-optimal solutions for practice-relevant problems. Next, we deal with a “preliminary (conceptual) planning of machines” within a time horizon of one week. That problem can be classified between the tactical and operational planning levels and investigates whether the results of the extraction program planning can be implemented for the first week of the following month. For this purpose, a machine scheduling problem to minimize the makespan is taking into account. We propose a mixed-integer linear program considering particular circumstances in an underground mine, e.g., reentry. The main challenge is to provide a solution approach that can find near-optimal solutions for large-sized problem instances. For this purpose, we suggest a heuristic approach considering conscious delays of jobs in front of production stages, i.e., active scheduling is applied. The performance analysis shows that small problem instances can be optimally solved with CPLEX-solver. For larger problem instances, the best performance is achieved by the suggested advanced multi-start heuristic. Finally, a “detailed shift planning” considering a simultaneous assignment of machines and workers is taken into account on the operational planning level. That problem pursues an even progress in the underground mine within a work shift. During a work shift, in addition to a machine scheduling problem, a personnel allocation problem must be considered. Moreover, to provide realistic solutions, different kinds of setup times must be observed, depending on the processing sequence of the operations on machines and workers. The major challenge is to express the specific circumstances of a work shift mathematically, e.g., considering workers' breaks for a possible delay in the processing time of a job, determining the processed percentage of a job during a work shift, observing removal and changeover times, etc. A part of real constraints is formulated in a relaxed program as part of a heuristic solution approach. The proposed heuristic procedure consists of two steps. In the first step, a relaxed program neglecting some setup times is solved, and the typically unfeasible solution achieved is repaired in the second step by inserting the neglected times. The results show that the proposed heuristic can find for 70 percent of the realistic problem instances a better solution than an existing heuristic approach. Subsequently, we introduce a new, compact mixed-integer linear program using TSPvariables considering all the problem specifications. We show that the proposed mixed-integer linear program outperforms the proposed two-stage heuristic considerably

Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast