Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization

This paper addresses the parallel machine scheduling problem with family dependent setup times and total weighted completion time minimization. In this problem, when two jobs j and k are scheduled consecutively on the same machine, a setup time is performed between the finishing time of j and the starting time of k if and only if j and k belong to different families. The problem is strongly NP-hard and is commonly addressed in the literature by heuristic approaches and by branch-and-bound algorithms. Achieving proven optimal solution is a challenging task even for small size instances. Our contribution is to introduce five novel mixed integer linear programs based on concepts derived from one-commodity, arc-flow and set covering formulations. Numerical experiments on more than 13000 benchmark instances show that one of the arc-flow models and the set covering model are quite efficient, as they provide on average better solutions than state-of-the-art approaches, with shorter computation times, and solve to proven optimality a large number of open instances from the literature

From metaheuristics to learnheuristics: Applications to logistics, finance, and computing

Un gran nombre de processos de presa de decisions en sectors estratègics com el transport i la producció representen problemes NP-difícils. Sovint, aquests processos es caracteritzen per alts nivells d'incertesa i dinamisme. Les metaheurístiques són mètodes populars per a resoldre problemes d'optimització difícils en temps de càlcul raonables. No obstant això, sovint assumeixen que els inputs, les funcions objectiu, i les restriccions són deterministes i conegudes. Aquests constitueixen supòsits forts que obliguen a treballar amb problemes simplificats. Com a conseqüència, les solucions poden conduir a resultats pobres. Les simheurístiques integren la simulació a les metaheurístiques per resoldre problemes estocàstics d'una manera natural. Anàlogament, les learnheurístiques combinen l'estadística amb les metaheurístiques per fer front a problemes en entorns dinàmics, en què els inputs poden dependre de l'estructura de la solució. En aquest context, les principals contribucions d'aquesta tesi són: el disseny de les learnheurístiques, una classificació dels treballs que combinen l'estadística / l'aprenentatge automàtic i les metaheurístiques, i diverses aplicacions en transport, producció, finances i computació.Un gran número de procesos de toma de decisiones en sectores estratégicos como el transporte y la producción representan problemas NP-difíciles. Frecuentemente, estos problemas se caracterizan por altos niveles de incertidumbre y dinamismo. Las metaheurísticas son métodos populares para resolver problemas difíciles de optimización de manera rápida. Sin embargo, suelen asumir que los inputs, las funciones objetivo y las restricciones son deterministas y se conocen de antemano. Estas fuertes suposiciones conducen a trabajar con problemas simplificados. Como consecuencia, las soluciones obtenidas pueden tener un pobre rendimiento. Las simheurísticas integran simulación en metaheurísticas para resolver problemas estocásticos de una manera natural. De manera similar, las learnheurísticas combinan aprendizaje estadístico y metaheurísticas para abordar problemas en entornos dinámicos, donde los inputs pueden depender de la estructura de la solución. En este contexto, las principales aportaciones de esta tesis son: el diseño de las learnheurísticas, una clasificación de trabajos que combinan estadística / aprendizaje automático y metaheurísticas, y varias aplicaciones en transporte, producción, finanzas y computación.A large number of decision-making processes in strategic sectors such as transport and production involve NP-hard problems, which are frequently characterized by high levels of uncertainty and dynamism. Metaheuristics have become the predominant method for solving challenging optimization problems in reasonable computing times. However, they frequently assume that inputs, objective functions and constraints are deterministic and known in advance. These strong assumptions lead to work on oversimplified problems, and the solutions may demonstrate poor performance when implemented. Simheuristics, in turn, integrate simulation into metaheuristics as a way to naturally solve stochastic problems, and, in a similar fashion, learnheuristics combine statistical learning and metaheuristics to tackle problems in dynamic environments, where inputs may depend on the structure of the solution. The main contributions of this thesis include (i) a design for learnheuristics; (ii) a classification of works that hybridize statistical and machine learning and metaheuristics; and (iii) several applications for the fields of transport, production, finance and computing

Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams

Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. In the original version of this paper, we presented a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We tested the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.Comment: 50 pages, 31 figures, published by JAIR, supplementary materials at https://github.com/IsaacRudich/ImprovedPnB. arXiv admin note: substantial text overlap with arXiv:2205.0521

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

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Integrating Dock-Door Assignment and Vehicle Routing in Cross-Docking

Cross-docking is a logistic strategy in which products arrive at terminals, are handled and then shipped to the corresponding destinations. Cross-docking consists of unloading products from inbound trucks and loading these products directly into outbound trucks with little or no storage in-between. Cross-docking aims to reduce or eliminate inventory by achieving an efficient synchronization of unloading trucks, material handling and loading trucks. This thesis introduces an integrated dock-door assignment and vehicle routing problem that consists of assigning a set of origin points to inbound doors at the cross-dock, consolidating commodities in-between inbound and outbound doors, and routing vehicles from outbound doors to destination points. The objective is to minimize the sum of the material handling cost at the cross-dock and the transportation cost for routing the commodities to their destinations. Five mixed integer programming formulations are presented and computationally compared. A column generation algorithm based on a set partitioning formulation is developed to obtain lower bounds on the optimal solution value. In addition, a heuristic algorithm is used to obtain upper bounds. Computational experiments are performed to assess the performance of the proposed MIP formulations and solution algorithms on a set of randomly generated instances