The thesis deals with planning and scheduling of production in the food industry. The theoretical part is concerned with the formulation and structure of the task scheduling and analyses the flow shop in the detail, for which a real application for an unnamed company has been created. It also briefly describes the technical specifications of production, which are crucial for the practical part. The practical part deals with the formulation of a mathematical model. The optimal solution is obtained using the optimization program MPL for Windows. Mathematical model includes variables that solves serial and parallel processors and try to capture as most exact as possible manufacturing processes with the technical specifications for a particular enterprise. The criterion for optimization is to minimize the cost in terms of the selected technology of production.

The classic flow shop problem assumes that jobs make only single passes through the processing machines and that the processing times are not affected by the length of the delay before jobs are processed. These assumptions are being relaxed in recent papers that consider reentrance problems and those with schedule deterioration. In this study, these two assumptions are both relaxed, and a model of a reentrant flowshop with a deteriorating schedule is considered. A linear programming formulation of the problem is first presented. Three solution heuristics are considered under different deterioration scenarios. It was observed that both Nawaz Enscor and Ham (NEH) algorithm and Genetic Algorithm (GA) performed much better than the Campbell Dudek and Smith (CDS) algorithm. Overall, when considering both the quality of solution and computational time together, the NEH algorithm seems to have performed much better than the others as the size of problems increases. This model would find useful applications in some metallurgical and manufacturing processes where such problems are usually encountered. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2021. / Industrial and Systems Engineering / MEng (Industrial Engineering) / Unrestricted

The main aim of this thesis is flow shop and job shop scheduling problem in logistics warehouses. Managing and scheduling works is currently often problem. There is no simple solution due to complexity of this problem. This problem must be resolved because of a lack efficiency of work with a higher load such as during the christmas holidays. This paper describes the methods used to solve this problem focusing mainly on the use of search algorithms, evolutionary algorithms, specifically grammar guided genetic programming. This paper describes the problem of job shop scheduling on a simple theoretical example. The implemented algorithm for solving this problem was subjected to tests inspired on data from real warehouse, as well as synthetically created tests with more jobs and a greater number of workers. Synthetic tests were generated randomly. All tests were therefore run several times and the results were averaged. In conclusion of this work are presented the results of the algorithm and the optimum parameter settings for different sizes of problems and requirements for the solution. Genetic algorithm has been extended to calculate fitness of individuals with regard to number of collisions, extended to use priority rules during run of evolution, and some parts of algorithm was parallelized.

The sponsor of the thesis is the Composite Unit of AIRBUS Nantes plant, which manufactures aircraft composite. The basic process to manufacture composite parts is to lay-up raw composite material on a tool and involves very costly means and raw material. This process can be modeled as a two-stage hybrid flow shop problem with specific constraints, particularly prescription constraints on the jobs. This thesis restates the practical problem as a scheduling problem by doing hypotheses and restrictions. Then, it designs a mathematical model based on time-indexed variables. This model has been implemented in an IP solver to solve real based scenarios. A heuristic algorithm is developed for obtaining good solutions quickly. Finally, the heuristic is used to increase the execution speed of the IP solver. This thesis concludes by a discussion on the advantages and disadvantages of each option (IP solver vs. heuristic software) for the sponsor. / Master of Science

O problema do sequenciamento da produção diz respeito à alocação das tarefas nas máquinas em um ambiente de fabricação, o qual vem sendo amplamente estudado. O sequenciamento pode variar em tamanho e complexidade dependendo do tipo de ambiente onde ele é aplicado, do número e tipos de restrições tecnológicas e da função objetivo do problema. A utilização de métodos de decisão para a solução de problemas de sequenciamento na indústria depende de modelos que sejam capazes de oferecer soluções para os problemas reais, que geralmente envolvem diversas restrições, os quais devem ser considerados simultaneamente. No presente trabalho o problema de sequenciamento da produção em ambientes flow shop permutacionais, com bloqueio com buffer zero, e com tempos de setup dependente da sequência e da máquina, com o objetivo de minimização do makespan é estudado, sendo este considerado um problema NP-Completo. O problema é pouco explorado na literatura. No presente trabalho é apresentado um procedimento de cálculo para o makespan e três métodos de solução para o problema: quatro limitantes inferiores para o procedimento Branch-and-Bound; quatro modelos MILP, sendo dois deles adaptados; e 28 modelos heurísticos construtivos adaptados para o problema. Os métodos desenvolvidos baseiam-se em propriedades matemáticas do problema que são apresentadas neste trabalho como limitante inferior e limitante superior. Dentre todos os modelos MILP, o modelo adaptado RBZBS1 obteve os melhores resultados para os problemas menores e o modelo desenvolvido TNZBS1 obteve os melhores desvios relativos médios do makespan para os problemas maiores, que não foram resolvidos dentro do limite de tempo computacional estipulado. O limitante inferior para o Branch-and-Bound LBTN2 foi melhor que os demais tanto no tempo computacional e no número de nós explorados como também no número de problemas não resolvidos e no desvio relativo médio do makespan. Foi realizado uma comparação entre o melhor modelo MILP e o melhor limitante inferior para o Branch-and-Bound, sendo que o último obteve melhores resultados para os problemas testados. Entre os métodos heurísticos adaptados, o PF foi o que obteve, de uma forma geral, os melhores resultados em todas as fases. / Production scheduling is defined as a problem of allocating jobs in machines in a production environment and it has been largely studied. The scheduling can vary in difficulty and complexity depending on the environment, the variety and types of technological restraints and the objective function of the problem. The use of decision making methods to solve scheduling problems in the industry needs models that are capable to solve real problems, that usually involve a big variety of restraints that have to be simultaneously studied. At the present work the scheduling problem in a permutational flow shop environment, considering blocking with zero buffer, and sequence and machine dependent setup times, with the objective of minimizing makespan is studied, which is considered a NP-Complete problem and little explored in literature. The work presents a calculation procedure for the makespan and three solution methods for the problem: four lower bounds for the Branch-and-Bound procedure; four MILP models, two of which are adapted; and 28 constructive heuristic methods adapted to the problem. The methods developed are based on mathematical properties of the problem that are presented in this work as a lower bound and an upper bound. Among all the MILP models, the adapted model RBZBS1 was the one to obtain the best results for the smaller problems, and the developed model TNZBS1 obtained the smallest mean relative deviation of the makespan for the bigger problems that were not solved within the specified computational time limit. The lower bound for the Branch-and-Bound LBTN2 obtained smaller computational times and number of explored nodes as well as the number of unsolved problems and the mean relative deviation for the makespan than all other lower bounds. Also, a comparison among the best MILP model and the best lower bound for the Branch-and-Bound was performed, being that the last obtained better results for the tested problems. Among the adapted heuristic methods, the PF heuristic was the one that obtained, in general, the better results in all phases.

Au sein d’un établissement hospitalier, le bloc opératoire représente un des secteurs les plus emblématiques et les plus coûteux. Le fonctionnement du bloc opératoire est orchestré par un programme opératoire qui consiste à construire un planning prévisionnel des interventions chirurgicales à réaliser pendant un horizon donné. La littérature abondante sur le sujet est unanime sur le fait que la construction du programme opératoire est une tâche complexe, car il s’agit non seulement de planifier et d’ordonnancer les interventions, mais aussi de satisfaire des exigences souvent antagonistes. Ce projet est le fruit d’une collaboration entre la Communauté d’Agglomération de Sarreguemines Confluences et la Région Lorraine, des membres du secteur hospitalier (Hôpital Robert Pax de Sarreguemines) et l’équipe Gestion Industrielle et Logistique (GIL) du Laboratoire de Génie Industriel, de Production et de Maintenance (LGIPM). L’objectif de cette recherche est d’apporter une aide aux gestionnaires du bloc opératoire, qui ont besoin de plus en plus des méthodes et des outils d’aide à la décision en vue d’optimiser leur fonctionnement. Pour répondre à ce besoin nous nous intéressons dans la première partie de cette thèse à la gestion des opérations électives en prenant en compte différentes contraintes et en particulier la disponibilité des chirurgiens. Nous nous plaçons dans le contexte d’une stratégie « open scheduling » et nous proposons deux modèles mathématiques permettant d’élaborer le programme opératoire. La complexité des modèles mathématiques et leur explosion combinatoire rendent difficile la recherche de l’optimum pour des tailles réalistes. Ceci nous a donc amené à proposer une heuristique constructive utilisant le modèle proposé et permettant d’obtenir des solutions là où la méthode exacte ne nous le permettait pas. Dans la seconde partie de cette thèse, nous considérons l’intégralité du processus opératoire (brancardage vers le bloc opératoire, préparation et anesthésie, acte chirurgicale et réveil). Nous modélisons ce processus comme un flow shop hybride à 4 étages avec contrainte de blocage de type RSb, et nous le résolvons à l’aide d’un algorithme génétique dont l’objectif est de synchroniser toutes les ressources nécessaires, en respectant au mieux le programme opératoire prévisionnel. Outre les opérations électives, nous nous intéressons dans la dernière partie aux opérations urgentes. Nous proposons un outil d’aide à la décision pour la gestion des opérations urgentes. En prenant en considération la pathologie et la gravité de l’état du patient, nous distinguons principalement 3 degrés d’urgences et proposons pour chacune un algorithme permettant d’intégrer en temps réel ces opérations dans le programme prévisionnel, tout en minimisant différents critères (temps d’attente avant affectation, heures supplémentaires, décalage par rapport aux anciennes dates de débuts) / The operating theater is one of the most critical and expensive hospital resources. Indeed, a high percentage of hospital admissions are due to surgical interventions. Rising expenditures spur health care organizations to organize their processes more efficiently and effectively. This thesis is supported by the urban community of Sarreguemines-France and the region of Lorraine-France, and is carried out in collaboration with the Centre Hospitalier de Sarreguemines - Hôpital Robert Pax. In the first part of this work, we propose two mathematical programming models to help operating theater managers in developing an optimal operating rooms scheduling. We also propose a constructive heuristic to obtain near optimal results for realistic sizes of the problem. In the second part of our work, the whole scheduling process is modeled as a hybrid four-stage flow shop problem with RSb blocking constraint, and is solved by a genetic algorithm. The objective is to synchronize all the needed resources around the optimal daily schedule obtained with the proposed mathematical model. The last part of our work is dedicated to non-elective surgeries. We propose a decision support tool, guiding the operating room manager, to handle this unpredictable flow of patients. Non-elective patients are classified according to their medical priority. The main contribution of the proposed decision support tool is to provide online assignment strategies to treat each non elective patient category. Proposed assignments are riskless on patient’s health. According to non-elective surgery classes, the proposed adjusted schedule minimizes different criteria such as patient’s waiting time, deviation from the firstly scheduled starting time of a surgery and the amount of resulting overtime

O problema do sequenciamento da produção diz respeito à alocação das tarefas nas máquinas em um ambiente de fabricação, o qual vem sendo amplamente estudado. O sequenciamento pode variar em tamanho e complexidade dependendo do tipo de ambiente onde ele é aplicado, do número e tipos de restrições tecnológicas e da função objetivo do problema. A utilização de métodos de decisão para a solução de problemas de sequenciamento na indústria depende de modelos que sejam capazes de oferecer soluções para os problemas reais, que geralmente envolvem diversas restrições, os quais devem ser considerados simultaneamente. No presente trabalho o problema de sequenciamento da produção em ambientes flow shop permutacionais, com bloqueio com buffer zero, e com tempos de setup dependente da sequência e da máquina, com o objetivo de minimização do makespan é estudado, sendo este considerado um problema NP-Completo. O problema é pouco explorado na literatura. No presente trabalho é apresentado um procedimento de cálculo para o makespan e três métodos de solução para o problema: quatro limitantes inferiores para o procedimento Branch-and-Bound; quatro modelos MILP, sendo dois deles adaptados; e 28 modelos heurísticos construtivos adaptados para o problema. Os métodos desenvolvidos baseiam-se em propriedades matemáticas do problema que são apresentadas neste trabalho como limitante inferior e limitante superior. Dentre todos os modelos MILP, o modelo adaptado RBZBS1 obteve os melhores resultados para os problemas menores e o modelo desenvolvido TNZBS1 obteve os melhores desvios relativos médios do makespan para os problemas maiores, que não foram resolvidos dentro do limite de tempo computacional estipulado. O limitante inferior para o Branch-and-Bound LBTN2 foi melhor que os demais tanto no tempo computacional e no número de nós explorados como também no número de problemas não resolvidos e no desvio relativo médio do makespan. Foi realizado uma comparação entre o melhor modelo MILP e o melhor limitante inferior para o Branch-and-Bound, sendo que o último obteve melhores resultados para os problemas testados. Entre os métodos heurísticos adaptados, o PF foi o que obteve, de uma forma geral, os melhores resultados em todas as fases. / Production scheduling is defined as a problem of allocating jobs in machines in a production environment and it has been largely studied. The scheduling can vary in difficulty and complexity depending on the environment, the variety and types of technological restraints and the objective function of the problem. The use of decision making methods to solve scheduling problems in the industry needs models that are capable to solve real problems, that usually involve a big variety of restraints that have to be simultaneously studied. At the present work the scheduling problem in a permutational flow shop environment, considering blocking with zero buffer, and sequence and machine dependent setup times, with the objective of minimizing makespan is studied, which is considered a NP-Complete problem and little explored in literature. The work presents a calculation procedure for the makespan and three solution methods for the problem: four lower bounds for the Branch-and-Bound procedure; four MILP models, two of which are adapted; and 28 constructive heuristic methods adapted to the problem. The methods developed are based on mathematical properties of the problem that are presented in this work as a lower bound and an upper bound. Among all the MILP models, the adapted model RBZBS1 was the one to obtain the best results for the smaller problems, and the developed model TNZBS1 obtained the smallest mean relative deviation of the makespan for the bigger problems that were not solved within the specified computational time limit. The lower bound for the Branch-and-Bound LBTN2 obtained smaller computational times and number of explored nodes as well as the number of unsolved problems and the mean relative deviation for the makespan than all other lower bounds. Also, a comparison among the best MILP model and the best lower bound for the Branch-and-Bound was performed, being that the last obtained better results for the tested problems. Among the adapted heuristic methods, the PF heuristic was the one that obtained, in general, the better results in all phases.

Nous considérons dans cette thèse un problème d’ordonnancement de flow-shop de permutation où un ensemble de travaux doit être ordonnancé sur un ensemble de machines. Les travaux doivent être ordonnancés sur les machines dans le même ordre. L’objectif est de minimiser le retard total. Nous proposons des algorithmes heuristiques et des nouvelles matheuristiques pour ce problème. Les matheuristiques sont un nouveau type d’algorithmes approchés qui ont été proposés pour résoudre des problèmes d’optimisation combinatoire. Les méthodes importent de la résolution exacte au sein des approches (méta) heuristiques. Ce type de méthode de résolution a reçu un grand intérêt en raison de leurs très bonnes performances pour résoudre des problèmes difficiles. Nous présentons d’abord les concepts de base d’un problème d’ordonnancement. Nous donnons aussi une brève introduction à la théorie de l’ordonnancement et nous présentons un panel de méthodes de résolution. Enfin, nous considérons un problème où un flow shop de permutation à m-machine et un problème de tournées de véhicules sont intégrés, avec pour objectif la minimisation de la somme des retards. Nous proposons un codage direct d’une solution et une méthode de voisinage. Les résultats montrent que l’algorithme Tabou améliore grandement la solution initiale donnée par EDD et où chaque voyage ne délivre qu’un travail. / We consider in this thesis a permutation flow shop scheduling problem where a set of jobs have to be scheduled on a set of machines. The jobs have to be processed on the machines in the same order. The objective is to minimize the total tardiness. We propose heuristic algorithms and many new matheuristic algorithms for this problem. The matheuristic methods are a new type of approximated algorithms that have been proposed for solving combinatorial optimization problems. These methods embed exact resolution into (meta)heuristic approaches. This type of resolution method has received a great interest because of their very good performances for solving some difficult problems. We present the basic concepts and components of a scheduling problem and the aspects related to these components. We also give a brief introduction to the theory of scheduling and present an overview of resolution methods. Finally, we consider a problem where m-machine permutation flow shop scheduling problem and a vehicle routing problem are integrated and the objective is to minimize the total tardiness. We introduce a direct coding for a complete solution and a Tabu search for finding a sequence and trips. The results show that the TS greatly improves the initial solution given by EDD heuristic where each trip serves only one job at a time.

Balancing trade-offs between production cost and holding cost is critical for production and operations management. Utilization of an operating room affects production cost, which relates to makespan, and patient flowtime affects holding cost. There are trade-offs between two objectives, to minimize makespan and to minimize flowtime. However, most existing constructive heuristics focus only on single-objective optimization. In the current literature, NEH is the best constructive heuristic to minimize makespan, and LR heuristic is the best to minimize flowtime. In this thesis, we propose a current and future deviation (CFD) heuristic to balance trade-offs between makespan and flowtime minimizations. Based on 5400 randomly generated instances and 120 instances in Taillard’s benchmarks, our CFD heuristic outperforms NEH and LR heuristics on trade-off balancing, and achieves the most stable performances from the perspective of statistical process control.

La gestion des blocs opératoires est actuellement l'objet de multiples questionnements, aussi bien sur le court terme que sur le long terme. Elle se heurte en effets aux problèmes aigus d'emploi des ressources aussi bien humaines que matérielles, qui sont aujourd'hui toutes deux disponibles en capacité finie. Dans l'investigation de cette problématique, nos travaux de recherche ont été effectués selon trois axes principaux. En premier lieu, dans une perspective initiale descriptive, nous avons analysé les différentes activités, ressources et flux du processus opératoire. Cette analyse nous a permis d'identifier les forces et faiblesses d'un existant et de modéliser ses différentes entités de gestion. Ensuite, nous avons proposé les différentes étapes d'une organisation de gestion d'un processus opératoire. Nous nous sommes limités dans notre étude aux périodes pré- (avant l'intervention) et per-opératoire (pendant l'intervention). Enfin, nous avons proposé des outils de résolution et expérimenté la capacité de ceux-ci à répondre aux différents problèmes de gestion. Quatre problèmes de gestion ont été identifiés : la programmation des interventions, la définition des plages horaires d'ouverture des salles d'opérations, la planification du bloc opératoire et enfin l'ordonnancement des salles d'opérations. Nous avons conçu une extension de la méthode Hongroise pour la résolution des problèmes de programmation et de planification opératoire. La définition des plages horaires d'ouverture des salles d'opérations a été définie comme un problème linéaire. L'ordonnancement des salles d'opérations a été identifié comme un problème de type Flow-Shop Hybride à trois étages sans temps d'attente avec contraintes de précédences. Il a été résolu à l'aide des règles connues d'ordonnancement et d'affectation.<br />Ces travaux nous ont permis de démontrer que des méthodes d'analyse et outils de résolution issus du manufacturier peuvent être appliqués au domaine hospitalier.