The Minimum Backlog Problem

We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP. The discrete MBP is a 2-person game played on a graph $G=(V,E)$. The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time. The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog. We show that the competitive ratio of any algorithm for the MBP has a lower bound of $\Omega(D)$, where $D$ is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog. For the absolute value of the backlog there is a trivial lower bound of $\Omega(D)$, and the deamortization analysis of Dietz and Sleator gives an upper bound of $O(D\log N)$ for $N$ cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of $O(D)$, independently of the number of cups.Comment: 1+16 pages, 3 figure

Shop-floor scheduling as a competitive advantage:A study on the relevance of cyber-physical systems in different manufacturing contexts

The aim of this paper is to analyse the relevance of cyber-physical systems (CPS) in different manufacturing contexts and to study whether CPS could provide companies with competitive advantage by carrying out a better scheduling task. This paper is developed under the umbrella of contingency theory which states that certain technologies and practices are not universally applicable or relevant in every context; thus, only certain companies will benefit from using particular technologies or practices. The conclusion of this paper, developed through deductive reasoning and supported by preliminary simulation experiments and statistical tests, is that factories with an uncertain and demanding market environment as well as a complex production process could benefit the most from implementing a CPS at shop-floor level since a cyber-physical shop-floor will provide all the capabilities needed to carry out the complex scheduling task associated with this type of context. On the other hand, an increase in scheduling performance due to a CPS implementation in factories with simple production flows and stable demand could not be substantial enough to overcome the high cost of installing a fully operational CPS

Lot Streaming in Different Types of Production Processes: A PRISMA Systematic Review

At present, any industry that wanted to be considered a vanguard must be willing to improve itself, developing innovative techniques to generate a competitive advantage against its direct competitors. Hence, many methods are employed to optimize production processes, such as Lot Streaming, which consists of partitioning the productive lots into overlapping small batches to reduce the overall operating times known as Makespan, reducing the delivery time to the final customer. This work proposes carrying out a systematic review following the PRISMA methodology to the existing literature in indexed databases that demonstrates the application of Lot Streaming in the different production systems, giving the scientific community a strong consultation tool, useful to validate the different important elements in the definition of the Makespan reduction objectives and their applicability in the industry. Two hundred papers were identified on the subject of this study. After applying a group of eligibility criteria, 63 articles were analyzed, concluding that Lot Streaming can be applied in different types of industrial processes, always keeping the main objective of reducing Makespan, becoming an excellent improvement tool, thanks to the use of different optimization algorithms, attached to the reality of each industry.This work was supported by the Universidad Tecnica de Ambato (UTA) and their Research and Development Department (DIDE) under project CONIN-P-256-2019, and SENESCYT by grants “Convocatoria Abierta 2011” and “Convocatoria Abierta 2013”

No-wait scheduling of a two-machine flow-shop to minimize the makespan under non-availability constraints and different release dates

International audienceIn this paper, we consider the two-machine no-wait flow-shop scheduling problem, when every machine is subject to one non-availability constraint and jobs have different release dates. The non-availability intervals of the machines overlap and they are known in advance. We aim to find a non-resumable schedule that minimises the makespan. We propose several lower bounds and upper bounds. These bounding procedures are used in a branch-and-bound algorithm. Computational experiments are carried out on a large set of instances and the obtained results show the effectiveness of our method

Estado del arte de las aplicaciónes del concepto de Lot Streaming a la secuenciación en talleres de flujo

[ES] El presente estudio, versa en una revisión de los articulaos publicados sobre la aplicación del concepto de Lot Streaming y su aplicación en la secuenciación de talleres de flujo. Los documentos se clasificaron de acuerdo a los dimensionamientos que se asocian a evidenciar las combinaciones y comparaciones de diversos algoritmos utilizados para mejorar los talleres de flujo a través de la división de Sub-lotes. Lo cual representa un particular enfoque para la revisión de artículos e investigadores que han abordado esta temática, aplicando una metodología con un enfoque cualitativo, por cuanto la información se sistematizó a través del software Atlas_ti en correspondencia a las variables exploradas en cada estudio que identifican la eficacia de la división de lotes en la solución de problemas de talleres de flujo. La mayoría de los estudios identificaron algoritmos genéticos y genéticos híbridos, mostrando algunas desventajas frente a los tradicionales y en pocos estudios evidenciando la eficacia en su aplicación.[EN] The present study is based on a review of the articles published on the application of the Lot Streaming concept and its application in the sequencing of flow workshops. The documents were classified according to the sizing that is associated to evidence the combinations and comparisons of different algorithms used to improve the workshops of flow through the division of sublots. This represents a particular approach to the review of articles and researchers that have addressed this issue, applying a methodology with a qualitative approach, as the information is systematized through the Atlas_ti software in correspondence to the variables explored in each study that identify the efficiency of the division of batches in the solution of problems of flow workshops. The majority of the studies identified hybrid genetic and genetic algorithms, showing some disadvantages compared to the traditional ones and in few studies showing the efficacy in their application.Velecela Rojas, SJ. (2018). Estado del arte de las aplicaciónes del concepto de Lot Streaming a la secuenciación en talleres de flujo. http://hdl.handle.net/10251/110033TFG

Scheduling of biological samples for DNA sequencing

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 95-97).In a DNA sequencing workflow, a biological sample has to pass through multiple process steps. Two consecutive steps are hydroshearing and library construction. Samples arrive randomly into the inventory and are to complete both processes before their due dates. The research project is to decide the optimal sequence of samples to go through these two processes subject to operational constraints. Two approaches, namely, heuristic and integer programming have been pursued in this thesis. A heuristic algorithm is proposed to solve the scheduling problem. A variant of the problem involving deterministic arrivals of samples is also considered for comparison purposes. Comparison tests between the two approaches are carried out to investigate the performance of the proposed heuristic for the original problem and its variant. Sensitivity analysis of the schedule to parameters of the problem is also conducted when using both approaches.by Yuwei Hu and Chin Soon Lim.S.M

Ordonnancement des systèmes de production flexibles soumis à différents types de contraintes de blocage

This thesis deals mainly with makespan minimization in Flow-Shop and hybrid Flow-Shop scheduling problems where mixed blocking constraints are considered. In Flow-Shop scheduling problem, a set of N jobs must be executed on a set of M machines. All jobs require the same operation order that must be executed according to the same manufacturing process. Each machine can only execute one job at any time. Pre-emptive operation is not authorized in presented work. In case of hybrid Flow-Shop, at any processing stage k, there exist one or more identical machines Mk. Objective function consists in determining best schedule in order to reduce makespan, i.e. time where all operations are completed.The most common scheduling problem is classical flowshop where buffer space capacity between machines is considered as unlimited. Other problems are characterized by the fact that the storage capacity is limited or null and which generates one blocking constraint. This constraint can be a classical blocking (RSb) or particular blocking (RCb or RCb*). In our works, we present a general case which can be derived from industry and modeled as Flow-Shop and hybrid Flow-Shop systems subject simultaneously to different blocking.To solve these problems, we studied in this thesis complexity of these systems and we proposed exact methods, approached methods and lower bounds.Ce sujet de thèse concerne de manière générale l'évaluation des performances et l'ordonnancement dans des systèmes de production flexibles et principalement les problèmes d'ordonnancement d'atelier de type Flow-Shop et Flow-Shop hybride. Le problème d'ordonnancement d'un Flow-Shop peut être défini ainsi : un ensemble de N jobs composés chacun de M opérations, doivent passer sur M machines dans le même ordre. Une machine peut exécuter une seule opération à la fois, chaque job ne peut avoir qu'une seule opération en cours de réalisation simultanément et la préemption n'est pas autorisée. Dans le cas des Flow-Shops hybrides, Mk machines identiques sont disponibles à chaque étage k en un ou plusieurs exemplaires. Pour cette étude, notre objectif est toujours de minimiser le temps total d'exécution aussi appelé makespan.Les problèmes d'ordonnancement les plus répandus sont de type Flow-Shop classique où les espaces de stockage entre les machines sont considérées comme infinies. D’autres problèmes sont caractérisés par des capacités de stockage limitées ou nulles qui engendre une seule contrainte de blocage. Cette contrainte peut être un blocage classique (de type RSb) ou particulier (de type RCb ou RCb*). Dans nos travaux de recherche, nous présentons un cas général qui peut être tiré de l'industrie et modélisé sous forme de systèmes de type Flow-Shop et Flow-Shop hybride soumis simultanément à plusieurs types de blocage. Pour résoudre ce genre de problèmes, nous avons étudié dans cette thèse la complexité de ces systèmes et nous avons proposé des méthodes exactes, des méthodes approchées ainsi que des bornes inférieures

The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances

The Slim Branch and Price Method with an Application to the Hamiltonian p-median Problem

The main objective of this dissertation is to present a new exact optimization method, the Slim Branch and Price (SBP) method, which is an improvement over the traditional Branch and Price (B&P) framework. SBP can be used to solve a large class of combinatorial optimization problems that can be solved by B&P type algorithms and that have binary master problems with fixed support (i.e., the sum of the variables in any feasible solution is fixed). This is an important class of problems as it includes several classical and fundamental problems. Towards this objective, this dissertation develops three algorithms to solve an interesting optimization problem, the Hamiltonian p-median problem (HpMP), which is a generalization of the wellknown traveling salesman problem. In HpMP, the target is to find p cycles that partition a given undirected graph with the objective of minimizing the total sum of the costs of these p cycles. This dissertation is divided into three main parts with the objective of showing the superiority of SBP over B&P while using HpMP as a running example. Towards this objective, the first part presents a B&P algorithm for HpMP, the second part presents SBP and how it can be tailored to solve HpMP, and finally, the third part explains how the preprocessing techniques developed for integer programs can dramatically enhance the performance of SBP. In the first part, we devise a Branch and Price algorithm that is able to solve instances with up to 318 nodes (within acceptable optimality gaps). To achieve this, we modified the set partitioning formulation of HpMP|a minor modification yet with significant algorithmic and computational advantages. Furthermore our computational results demonstrate that the practical complexity of HpMP and the performance of the algorithms to solve it strongly depend on the value of p. In addition, in order to solve the pricing problem we make contributions on a couple of problems that are important on their own right: 1) we develop a new efficient algorithm to find the least cost cycle in undirected graphs with arbitrary edge costs and no negative cycles; and 2) we develop an algorithm to find the most negative cycle in undirected graphs with arbitrary edge costs. Finally, we prove that for every value of p, HpMP is NP-hard even when restricted to Euclidean graphs. In the second part, we present SBP method which is an improvement over traditional B&P in the case of binary master problems with fixed support. The main advantage in SBP is that the branching tree has only one main branch with several leaves. In addition, we show that all the problems defined on the leaves can be merged to form a larger problem that can be solved very fast without further branching. We illustrate the computational advantage of SBP over B&P on HpMP. In particular, within one hour time limit, SBP can solve to optimality instances with up to 200 nodes; whereas B&P can solve to optimality instances with up to 127 nodes. In the third part, we exploit the reduced cost fixing preprocessing technique to enhance the performance of B&P. To this end, we develop a heuristic based on k-opt moves to find good feasible solutions for HpMP. We also introduce two separation algorithms to improve the linear programming relaxation of the natural variable space model of HpMP. Using these upper and lower bounds, reduced cost fixing was then implemented to reduce the graph size by deleting the edges that cannot be in any optimal solution. We compared the computational times reported by SBP with preprocessing versus those reported by SBP without preprocessing. The former algorithm performed better than the latter algorithm in 88.3% of the test instances