Grammar-Based Decomposition Methods for Multi-Activity Tour Scheduling

RÉSUMÉ : Les problèmes de planification d'horaires du personnel consistent à sélectionner un ensemble de quarts de travail en respectant certaines règles, et à assigner un certain nombre d'employés à chaque quart de travail, de sorte à satisfaire la demande de personnel. Ces problèmes sont généralement classés en trois catégories: planification des quarts de travail, planification des jours de repos et planification des patrons de travail. La première catégorie a pour but d'assigner les périodes de travail et de repos aux quarts de travail, et à sélectionner un ensemble de ces quarts de travail pour satisfaire les besoins en personnel. En planification des quarts de travail, l'horizon de planification est en général d'une journée, divisée en périodes de longueurs égales. La deuxième catégorie vise à sélectionner les jours de repos de chaque employé sur un horizon de planification d'au moins une semaine. Cette sélection est généralement contrainte par les préférences des employés ou par des conventions collectives. La dernière catégorie comprend les problèmes qui découlent de l'intégration des problèmes de planification des quarts de travail et de planification des jours de repos. Dans la version continue du problème de planification des patrons de travail, les quarts de travail peuvent s'étendre sur deux jours. Par contre, dans la version discontinue les quarts de travail doivent couvrir une seule journée. Différentes extensions du problème de planification d'horaires du personnel apparaissent lorsque des applications réelles sont considérées. Par exemple, dans les problèmes de planification des quarts multi-activités (MASSP) ou planification des patrons de travail multi-activités (MATSP), en plus de la définition des périodes de travail et de repos, des activités de travail différentes doivent être attribuées aux quarts de travail. Dans un contexte de multi-activités, les caractéristiques spécifiques liées aux règles de travail, aux conventions collectives, aux compétences des employés et à leurs préférences définissent un ensemble de règles à respecter pour construire les horaires des employés. D'autre part, le MASSP et le MATSP peuvent être soit personnalisés soit anonymes. Dans le premier cas, les employés ont des compétences et des préférences différentes, alors qu'elles sont identiques dans le second. Le problème peut également être stochastique, dans ce cas les besoins en employés (la demande) est incertaine. Dans cette thèse, nous aborderons trois catégories de MATSP : 1) MATSP discontinu, personnalisé, avec demande déterministe; 2) MATSP discontinu, anonyme avec demande déterministe; 3) MATSP discontinu, anonyme, avec demande stochastique. Pour résoudre ces problèmes, nous proposons différentes techniques de modélisation et de résolution qui sont principalement basées sur les méthodes de décomposition et les langages formels. Notre première contribution réside dans la conception de deux méthodes de type branch-and-price (B&P) pour aborder l'intégration de deux problèmes : le MASSP personnalisé et le problème de planification des patrons de travail discontinu. Chaque algorithme B\&P repose sur une formulation mathématique différente. La première formulation (formulation basée sur les jours) est une extension naturelle du MASSP personnalisé, ou les colonnes correspondent aux quarts de travail multi-activités, et les patrons de travail sont assemblés dans le problème maitre en utilisant des contraintes supplémentaires. Dans la seconde formulation (formulation basée sur les patrons de travail), le sous problèmes consistent à construire les quarts de travail multi-activités ainsi qu'à choisir les jours de repos. Par conséquent, dans cette formulation, les colonnes correspondent aux patrons de travail multi-activités. Dans les deux formulations, l'utilisation de grammaires nous permet de modéliser toutes les règles de travail pour la composition des quarts de travail, et de déduire des structures de graphes spéciales permettant de trouver les quarts de travail avec un coût réduit négatif. Une comparaison expérimentale et théorique de la qualité des bornes obtenues par la relaxation linéaire de chacune des formulations est réalisée. Les résultats montrent que la formulation basée sur les patrons de travail est meilleure (relativement aux bornes obtenues par la relaxation linéaire) que la formulation basée sur les jours. De plus, nos expériences montrent d'une part que les approches de modélisation proposées peuvent traiter une grande variété de règles sur les quarts de travail et sur les patrons de travail, et d'autre part que les méthodes implémentées peuvent résoudre efficacement des versions réalistes du problème. Les approches proposées sont clairement pertinentes en pratique, cependant des problèmes liés à la taille du modèle apparaissent lorsque le nombre d'activités et d'employés augmentent. La seconde contribution est une approche qui combine la décomposition de Benders et la génération de colonnes pour résoudre le problème intégrant le MASSP anonyme et la planification des patrons de travail discontinue. Afin de résoudre les problèmes de croissance des modèles et de symétrie associés aux nombres d'activités et d'employés, une autre façon de modéliser le MATSP est présentée. Les quarts de travail multi-activités sont implicitement générés par un modèle de programmation en nombres entiers basé sur une grammaire, alors que les patrons de travail sont explicitement composés via la génération de colonnes. Comme les sous-problèmes de l'approche de Benders sont des MIP qui n'ont pas la propriété d'intégralité, nous présentons une stratégie qui combine la génération de coupes de Benders classiques avec des coupes de Benders entières afin de garantir la convergence de la méthode. Les résultats expérimentaux montrent : 1) la capacité de notre approche à résoudre des cas pratiques impliquant un grand nombre d'employés et d'activités de travail; 2) que l'approche combinant la décomposition de Benders et la génération de colonnes à de meilleures performances que la méthode B&P pour le MATSP discontinu anonyme. Notre dernière contribution présente une approche de programmation stochastique en deux étapes pour résoudre le MATSP stochastique, discontinu, et anonyme. Les décisions de la première étape correspondent à l'affectation des employés aux patrons de travail. Les décisions de la deuxième étape (actions de recours) sont associées à la répartition des activités de travail et des pauses dans les quarts de travail. Une heuristique de type multi-cut L-shaped est présentée. Les expériences montrent que les performances de la méthode dépendent du profil de la demande, et que l'utilisation du modèle stochastique permet de réduire les coûts, en comparaison avec l'espérance de la solution moyenne.----------ABSTRACT : Personnel scheduling problems consist in constructing a set of feasible shift schedules and assigning them to the company staff to satisfy a given demand for staff requirements. These problems are typically classified into three main categories: shift scheduling, days-off scheduling and tour scheduling. The first category deals with the specification of work and rest periods to assign to shifts, as well as the selection of a set of those shifts to satisfy the demand for staff requirements. In shift scheduling, the planning horizon is usually one day divided into time periods of equal length. The second category involves the selection of days-off over a planning horizon of at least one week. Such selection is usually restricted by employee preferences or workplace agreements. The last category includes problems that arise from the integration of shift scheduling and days-off scheduling. The continuous version of the tour scheduling problem appears when shifts are allowed to span from one day to another. The discontinuous version arises when shifts span only one working day. Different extensions of classical personnel scheduling problems appear when real applications are considered. For instance, when more than one work activity has to be scheduled, the multi-activity shift scheduling (MASSP) and the multi-activity tour scheduling (MATSP) problems appear. In both extensions not only the specification of work and rest periods is necessary, but also the assignment of work activities to the shifts. In a multi-activity context, specific characteristics related to work rules, workplace agreements, and employee skills and preferences define the rules to build the schedule of employees. The MASSP and the MATSP can further be distinguished as personalized and anonymous problems. In the former, employee skills and preferences are different. In the latter, employee skills and preferences are identical. Additionally, if employee requirements (demand) is uncertain, the stochastic version of the problems appears. In this thesis we address three categories of the MATSP: 1) the discontinuous MATSP when employees have different skills and demand is deterministic; 2) the discontinuous MATSP when employees are identical and demand is deterministic; 3) the discontinuous MATSP when employees are identical and demand is stochastic. To address these problems we propose different modeling approaches and solution techniques which are mainly based on decomposition methods and formal languages. Our first contribution lies in the proposal of two branch-and-price (B&P) methods to address the integration of two problems: the personalized MASSP and the discontinuous tour scheduling problem. Each B&P algorithm is based on a different mathematical formulation. The first formulation (daily-based formulation) arises as a natural extension of the personalized MASSP, where columns correspond to multi-activity shifts and tours are assembled into the master problem by means of extra constraints. The second formulation (tour-based formulation) aims to include, in the subproblem level, the construction of multi-activity shifts and the assembling of days-off. Therefore, in this formulation the set of columns correspond to multi-activity tours. In both formulations, the use of grammars allows us to model all the work rules for the composition of shifts and to derive specialized graph structures used to find the shifts with negative reduced cost. An experimental and theoretical comparison on the quality of the LP relaxation bounds achieved by each formulation is made. The results show that the tour-based formulation is strong in terms of its LP relaxation bound, when compared with the daily-based formulation. Additionally, computational experiments suggest that the modeling approaches proposed can handle a wide variety of rules over shifts and tours and that the solution methods implemented efficiently solve realistic versions of the problem. However, while the practical relevance of the approaches is clear, convergence and scalability issues arise when the number of work activities and employees increases. As a second contribution we present an approach that combines Benders decomposition and column generation to solve the integration of the anonymous MASSP and the discontinuous tour scheduling problem. The aim of the approach is to present an alternative way to model the MATSP in order to solve the scalability and symmetry issues associated with the number of work activities and employees. While multi-activity daily shifts are implicitly generated with a grammar-based integer programming model, tour patterns are explicitly composed via column generation. Because Benders subproblems are MIP programs that do not possess the integrality property, we present an alternative algorithmic strategy that combines the generation of classical Benders cuts with integer Benders cuts to guarantee the convergence of the method. Experimental results show: 1) the capability of our approach to solve practical instances involving a large number of employees and work activities; 2) the combined Benders decomposition and column generation approach outperforms a B&P method that solves the anonymous discontinuous MATSP. Our last contribution consists in the introduction of a two-stage stochastic programming approach to solve the discontinuous stochastic MATSP for employees with identical skills. The problem is formulated as a two-stage stochastic programming model. First-stage decisions correspond to the assignment of employees to weekly tours. Second-stage decisions (recourse actions) are related to the allocation of work activities and breaks to daily shifts. A heuristic multi-cut L-shaped method is presented as a solution approach. Computational results show that the performance of the method depends on the demand profile used and that the use of the stochastic model helps to prevent additional costs, when compared with the expected-value problem solutions

Solving the Multi-activity Shift Scheduling Problem using Variable Neighbourhood Search

This paper presents a set of benchmarks instances for the multi-activity shift scheduling problem and the results produced using a variable neighbourhood search method. The data set is intended as a resource to generate and verify novel research on an important and practical but challenging problem. The variable neighbourhood search uses four different neighbourhood operators and can produce feasible solutions within short computation times

Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

In practice, vehicle scheduling is planned on a variable timetable so that the departure times of trips can be shifted in tolerable ranges, rather than on a fixed timetable, to decrease the required fleet size. This paper investigates the vehicle scheduling problem on a variable timetable with the constraint that each vehicle can perform limited trips. Since the connection-based model is difficult to solve by optimization software for a medium-scale or large-scale instance, a designed path-based model is developed. A Benders-and-Price algorithm by combining the Benders decomposition and column generation is proposed to solve the LP-relaxation of the path-based model, and a bespoke Branch-and-Price is used to obtain the integer solution. Numerical experiments indicate that a variable timetable approach can reduce the required fleet size with a tolerable timetable deviation in comparison with a fixed timetable approach. Moreover, the proposed algorithm is greatly superior to GUROBI in terms of computational efficiency and guarantees the quality of the solution. Document type: Articl

Simultaneous column-and-row generation for solving large-scale linear programs with column-dependent-rows

In this thesis, we handle a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints, which are either too many to be included in the formulation directly, or the full set of linking constraints can only be identified, if all variables are generated explicitly. Due to this dependence between columns and rows, we refer to this class of linear programs as problems with column-dependent-rows. To solve these problems, we need to be able to generate both columns and rows on-the-fly within a new solution method. The proposed approach in this thesis is called simultaneous column-and-row generation. We first characterize the underlying assumptions for the proposed column-and-row generation algorithm. These assumptions are general enough and cover all problems with column-dependent-rows studied in the literature up until now. We then introduce, in detail, a set of pricing subproblems, which are used within the proposed column-and-row generation algorithm. This is followed by a formal discussion on the optimality of the algorithm. Additionally, this generic algorithm is combined with Lagrangian relaxation approach, which provides a different angle to deal with simultaneous column-and-row generation. This observation then leads to another method to solve problems with column-dependent-rows. Throughout the thesis, the proposed solution methods are applied to solve different problems, namely, the multi-stage cutting stock problem, the time-constrained routing problem and the quadratic set covering problem. We also conduct computational experiments to evaluate the performance of the proposed approaches

드론을 활용한 통합 물류의 네트워크 설계 및 경로 계획

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 문일경.Along with the new trend called the Fourth Industrial Revolution, structural changes are continuously taking place throughout society, and new driving forces, encompassing science, technology, and industry, are drawing attention. In particular, the economic and social changes brought by the rapidly emerging drone technology are the key elements underpinning the Fourth Industrial Revolution. Academia and industry already extensively conduct technical research for the commercial use of drones and achievements in the public service sector. On the other hand, operations research related to drone application is relatively insufficient. To maximize the utility value of drones, an operational plan that takes into account the physical limitations of the drone while fully revealing its strengths should be laid out. Therefore, it is necessary to propose the optimization problem from a new point of view because only limited application is possible for existing problems. In this dissertation, we carry out research on advanced logistics system with drone operations. Specifically, a new methodology is proposed for the network design and route planning of the logistics system in association with drones. For a logistics network design, the facility location plan must be first preceded. In order to do so, the inherent uncertainty of drone operations is addressed through a stochastic approach. Based on this modelling framework, the locations of facilities and the deployment of drones stationed in each facility are determined. Subsequently, we present an integrated model that simultaneously determines the facility location of the strategic-level decision and the delivery schedules of operational-level decisions. Lastly, we propose a system in which drones work with trucks to perform delivery missions together. Swifter and cost-efficient delivery can be achieved by incorporating the complementary characteristics of two types of vehicles. In summary, the new variants of the optimization problems are proposed for stunning applications of drone technology. Practical solving techniques for the developed models are provided together. We believe that the results obtained from this dissertation will alleviate the burden of operating drones and serve as the basis for further drone application. This research will be the one of starting points for drones to play a key role in contributing to new paradigm in logistics, not only limited to the delivery service.4차 산업혁명이라 불리는 새로운 흐름에 따라, 사회 전반에서 구조적인 변화가 지속적으로 일어나고 있으며 과학기술 및 산업분야를 아우르는 신성장동력들이 주목 받고 있다. 특히, 빠른 속도로 발전 중인 드론 기술이 가져오는 경제, 사회적 변화는 4차 산업혁명의 핵심요소이다. 학계 및 산업계는 이미 드론의 상업적 활용과 공공 서비스 영역에서의 성과를 위한 기술적 연구를 활발히 수행 중이다. 반면에 드론 활용과 관련된 운영과학적 연구는 상대적으로 미흡하다. 드론의 활용 가치를 최대화하기 위해서는 드론이 가진 장점을 충분히 활용하면서도 드론의 물리적 한계를 고려한 운영 계획이 필요하다. 따라서 기존의 정의된 문제로는 제한적인 적용만이 가능하기 때문에 새로운 관점에서의 문제 정의가 필요하다. 본 논문에서는 드론 운용이 고려된 선진 물류 체계에 대한 연구를 수행한다. 구체적으로는, 드론을 고려한 통합 물류 체계의 네트워크 설계와 경로 계획을 위한 새로운 방법론을 제안한다. 물류 네트워크를 구성하기 위해서는 시설의 위치를 결정하는 계획이 선행적으로 수립되어야 한다. 시설의 위치를 합리적으로 결정하기 위해서 드론 운용의 내재된 불확실성들을 추계학적으로 대응한다. 이를 기반으로 시설의 위치와 드론의 배치를 동시에 결정한다. 그 다음으로, 전략적 수준의 계획인 시설위치결정과 운영적 수준의 계획인 배송 스케줄링을 동시에 의사 결정하는 통합모형을 제시한다. 마지막으로 드론이 트럭과 협력하여 배송 임무를 함께 수행하는 시스템에 대해서 연구한다. 두 운송수단의 상호보완적 특성을 활용하여 더 빠르고, 비용 효율적인 배송을 추구한다. 요약하면, 드론의 성공적인 활용을 위해 전통적인 최적화 문제의 새로운 확장 문제들을 제안하였다. 새롭게 개발된 모든 모형들의 실용적인 풀이 기법들도 함께 제시된다. 본 연구의 결과는 드론 운용의 부담을 완화시키며 드론의 활용 분야를 더욱 확대하는 기반을 조성할 것이다. 환언하면 본 연구는 드론이 물류 분야에서 단순한 배송 영역이 아닌 패러다임 자체를 변화시키는 역할을 수행하는 출발점이 될 것이다.Chapter 1. Introduction 1 1.1 Facility location problems 3 1.2 Vehicle routing problem 6 1.3 Research motivations and contributions 9 1.4 Outline of the dissertation 12 Chapter 2. Facility Location Problem with Drones 13 2.1 Introduction 13 2.2 Problem description and mathematical model 16 2.2.1 Chance constraints 18 2.2.2 Mathematical formulation 21 2.2.3 Discussion of the FLP-D 23 2.3 Solution techniques using Benders decomposition and linear programming relaxation 25 2.3.1 Master problem and slave problem 26 2.3.2 Generating Benders cuts 27 2.3.3 Heuristic algorithm for the FLP-D 29 2.3.4 Discussion of the heuristic algorithm 31 2.4 Computational experiments 32 2.4.1 Description of experiments 32 2.4.2 Sensitivity analysis on different parameter 34 2.4.3 Comparison between deterministic approach and stochastic approach 35 2.4.4 Comparison between the FLP-D and heuristic algorithm 38 2.5 Summary 39 Chapter 3. Scheduling-location Problem with Drones 42 3.1 Introduction 42 3.2 Problem description and mathematical model 46 3.2.1 Mathematical model 47 3.2.2 Discussion of the ScheLoc-D 50 3.3 Pattern-based approach for the ScheLoc-D 51 3.3.1 Set-covering reformulation 51 3.3.2 Generating attractive patterns (columns) 55 3.3.3 Restricted master heuristic 60 3.4 Computational experiments 62 3.4.1 Description of experiments 62 3.4.2 Comparing the RMH to the MILP formulation 64 3.5 Summary 66 Chapter 4. Vehicle Routing Problem with Time Windows and Drones 68 4.1 Introduction 68 4.2 Problem description and mathematical model 74 4.2.1 Mathematical formulation 77 4.2.2 Discussion of VRPTW-D 82 4.3 Solution approach for the VRPTW-D 85 4.3.1 Finding an initial VRPTW tour 86 4.3.2 Drone assignment algorithm 87 4.3.3 Route combination algorithm 88 4.3.4 Remarks for the TSH 90 4.4 Computational experiments 92 4.4.1 Description of experiments 92 4.4.2 Comparing the TSH to the mathematical model 93 4.4.3 Comparing a coordinated delivery system to truck-only delivery 96 4.4.4 Sensitivity Analysis with the drone features 101 4.5 Summary 103 Chapter 5. Conclusions 105Docto

Short-term rail rolling stock rostering and maintenance scheduling

This paper describes an optimization framework for railway rolling stock rostering and maintenance scheduling. A key problem in railway rostering planning requires covering a given set of services and maintenance works with limited rolling stock units. The problem is solved via a two-step approach that combines the scheduling tasks related to train services, short-term maintenance operations and empty runs. A commercial MIP solver is used for the development of a real-time decision support tool. A campaign of experiments on real world scenarios from Trenitalia (Italian train operating company) illustrates the improvement achievable by the approach when compared to the practical solution