The document is the proceedings of the 16th International Conference on Project Management and Scheduling held in Rome, Italy from April 17-20, 2018. It contains 65 papers that were accepted for presentation at the conference on topics related to project management and scheduling. The conference was organized by the EURO Working Group on Project Management and Scheduling and had four plenary speakers discussing topics such as comparing event-node graphs with renewable resources and activity-node graphs with nonrenewable resources.
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This document provides an introduction to ordered binary decision diagrams (OBDDs), a data structure for representing and manipulating switching functions in computer-aided design of digital circuits. OBDDs were proposed as an improvement over binary decision diagrams by introducing an ordering of variables, which allows for a canonical and efficient representation. The document discusses the foundations and applications of OBDDs, including their use in formal verification of combinational and sequential circuits.
This document is the master's thesis of Miquel Perelló Nieto submitted to Aalto University. The thesis examines merging chrominance and luminance in early, medium, and late fusion using Convolutional Neural Networks (CNNs) for image classification. The thesis demonstrates that fusing luminance and chrominance channels can improve CNNs' ability to learn visual features and outperforms models that do not fuse the channels. The thesis contains background chapters on image classification, neuroscience, artificial neural networks, CNNs, and the history of connectionism. It then describes the author's experiments comparing CNN architectures that fuse luminance and chrominance channels at different stages to a basic CNN model.
NOVEL NUMERICAL PROCEDURES FOR LIMIT ANALYSIS OF STRUCTURES: MESH-FREE METHODSCanh Le
This thesis investigates novel numerical procedures for limit analysis of structures using meshfree methods and mathematical programming. A kinematic limit analysis formulation is developed using the Element-Free Galerkin (EFG) method and second-order cone programming (SOCP). An adaptive EFG scheme is also developed using error estimation. Additionally, an equilibrium formulation is presented using a meshfree moving least squares approximation of moment fields and SOCP. Numerical examples involving plates and slabs demonstrate the formulations. The research aims to develop efficient and robust computational tools for engineering limit analysis applications.
The document is Nathaniel Knapp's master's thesis titled "Parasite: Local Scalability Profiling for Parallelization" submitted to Technische Universität München. The thesis presents Parasite, a tool that measures the parallelism of function call sites in programs parallelized using Pthreads. Parasite calculates the parallelism ratio, which is an upper bound on potential speedup and useful for evaluating scalability. The thesis demonstrates Parasite on sorting algorithms, molecular dynamics simulations, and other programs to analyze parallelism and identify factors limiting scalability.
This document presents a master's thesis that designed coded excitation and filter techniques to improve 3D ultrasound computer tomography (USCT) imaging for early breast cancer detection. The thesis aimed to suppress side lobes and increase separability of reflections in USCT data by developing customized mismatch filters. Signal and image evaluations showed the best designed filter and coded excitation combination improved image contrast by 143% compared to the standard USCT approach, under the same system constraints.
Innovative Payloads for Small Unmanned Aerial System-Based PersonAustin Jensen
This document describes Austin Jensen's doctoral dissertation titled "Innovative Payloads for Small Unmanned Aerial System-Based Personal Remote Sensing and Applications". The dissertation focuses on using small unmanned aerial systems (UAS) as remote sensing platforms to collect aerial imagery and track radio-tagged fish. It presents novel methods for calibrating imagery from commercial cameras on UAS and estimating the location of radio-tagged fish using multiple UAS. The calibration methods allow imagery to be orthorectified and used to deliver actionable information to end users. Simulations evaluate the fish tracking methods and predict their real-world performance. The dissertation contributes to advancing UAS-based remote sensing for applications such as precision agriculture, vegetation mapping,
This thesis investigates heuristic and meta-heuristic algorithms for solving pickup and delivery problems. It focuses on representing solutions and neighborhood moves simply and effectively to handle difficult problem constraints. The thesis applies genetic algorithms, simulated annealing, hill climbing and variable neighborhood search to variants of the pickup and delivery problem with time windows. Experimental results indicate the success of the approach in handling constraints and devising robust solution mechanisms for real-world applications.
This thesis explores integrating hypermedia functionality into electronic patient journals (EPJs). The vision is that hypermedia links could allow healthcare workers to quickly share important patient information. Through open hypermedia technology and structural computing, a prototype framework is developed to provide generic hypermedia support. A pilot program demonstrates the framework's use within a simulated smaller-scale EPJ. Participatory design involves healthcare users and an EPJ developer to address integration challenges.
Algorithms And Data Structures In VLSI DesignLori Mitchell
This document provides an introduction to ordered binary decision diagrams (OBDDs), a data structure for representing and manipulating switching functions in computer-aided design of digital circuits. OBDDs were proposed as an improvement over binary decision diagrams by introducing an ordering of variables, which allows for a canonical and efficient representation. The document discusses the foundations and applications of OBDDs, including their use in formal verification of combinational and sequential circuits.
This document is the master's thesis of Miquel Perelló Nieto submitted to Aalto University. The thesis examines merging chrominance and luminance in early, medium, and late fusion using Convolutional Neural Networks (CNNs) for image classification. The thesis demonstrates that fusing luminance and chrominance channels can improve CNNs' ability to learn visual features and outperforms models that do not fuse the channels. The thesis contains background chapters on image classification, neuroscience, artificial neural networks, CNNs, and the history of connectionism. It then describes the author's experiments comparing CNN architectures that fuse luminance and chrominance channels at different stages to a basic CNN model.
NOVEL NUMERICAL PROCEDURES FOR LIMIT ANALYSIS OF STRUCTURES: MESH-FREE METHODSCanh Le
This thesis investigates novel numerical procedures for limit analysis of structures using meshfree methods and mathematical programming. A kinematic limit analysis formulation is developed using the Element-Free Galerkin (EFG) method and second-order cone programming (SOCP). An adaptive EFG scheme is also developed using error estimation. Additionally, an equilibrium formulation is presented using a meshfree moving least squares approximation of moment fields and SOCP. Numerical examples involving plates and slabs demonstrate the formulations. The research aims to develop efficient and robust computational tools for engineering limit analysis applications.
The document is Nathaniel Knapp's master's thesis titled "Parasite: Local Scalability Profiling for Parallelization" submitted to Technische Universität München. The thesis presents Parasite, a tool that measures the parallelism of function call sites in programs parallelized using Pthreads. Parasite calculates the parallelism ratio, which is an upper bound on potential speedup and useful for evaluating scalability. The thesis demonstrates Parasite on sorting algorithms, molecular dynamics simulations, and other programs to analyze parallelism and identify factors limiting scalability.
This document presents a master's thesis that designed coded excitation and filter techniques to improve 3D ultrasound computer tomography (USCT) imaging for early breast cancer detection. The thesis aimed to suppress side lobes and increase separability of reflections in USCT data by developing customized mismatch filters. Signal and image evaluations showed the best designed filter and coded excitation combination improved image contrast by 143% compared to the standard USCT approach, under the same system constraints.
Innovative Payloads for Small Unmanned Aerial System-Based PersonAustin Jensen
This document describes Austin Jensen's doctoral dissertation titled "Innovative Payloads for Small Unmanned Aerial System-Based Personal Remote Sensing and Applications". The dissertation focuses on using small unmanned aerial systems (UAS) as remote sensing platforms to collect aerial imagery and track radio-tagged fish. It presents novel methods for calibrating imagery from commercial cameras on UAS and estimating the location of radio-tagged fish using multiple UAS. The calibration methods allow imagery to be orthorectified and used to deliver actionable information to end users. Simulations evaluate the fish tracking methods and predict their real-world performance. The dissertation contributes to advancing UAS-based remote sensing for applications such as precision agriculture, vegetation mapping,
This thesis investigates heuristic and meta-heuristic algorithms for solving pickup and delivery problems. It focuses on representing solutions and neighborhood moves simply and effectively to handle difficult problem constraints. The thesis applies genetic algorithms, simulated annealing, hill climbing and variable neighborhood search to variants of the pickup and delivery problem with time windows. Experimental results indicate the success of the approach in handling constraints and devising robust solution mechanisms for real-world applications.
This thesis explores integrating hypermedia functionality into electronic patient journals (EPJs). The vision is that hypermedia links could allow healthcare workers to quickly share important patient information. Through open hypermedia technology and structural computing, a prototype framework is developed to provide generic hypermedia support. A pilot program demonstrates the framework's use within a simulated smaller-scale EPJ. Participatory design involves healthcare users and an EPJ developer to address integration challenges.
This thesis proposes a novel way to introduce self-configuration and self-optimization autonomic characteristics to algorithmic skeletons using event-driven programming techniques. By leveraging event-driven programming, the approach is not tied to a specific application architecture and allows for structural changes at runtime. It also enables estimates of future work to be calculated on-the-fly rather than relying on pre-calculated estimates. The thesis focuses on guaranteeing a given execution time for a skeleton by optimizing the number of threads. It contributes a novel event-based separation of concerns for skeletons and evaluates strategies for estimating execution times and parallelism levels.
This thesis proposes a novel way to introduce self-configuration and self-optimization autonomic characteristics to algorithmic skeletons using event-driven programming techniques. By leveraging events, the approach is not tied to a specific application architecture and allows for structural changes at runtime. It focuses on guaranteeing execution time for skeletons by optimizing thread allocation. Other contributions include a novel separation of concerns for skeletons using events, and evaluating estimation strategies for predicting future work.
This document is a thesis submitted by Livinus Obiora Nweke for the degree of Master of Science in Computer Science. The thesis proposes a framework for validating network artifacts in digital forensics investigations based on stochastic and probabilistic modeling of the internal consistency of artifacts. The framework consists of three phases - data collection, feature selection using Monte Carlo Feature Selection, and a validation process using logistic regression analysis. The framework is demonstrated on network artifacts from intrusion detection systems. The experiment results show the validity of the network artifacts and can support assertions from the artifacts in investigations.
This document discusses integrated multiscale modelling for predicting material failure and degradation over time. It makes three key points:
1. Integrated multiscale modelling combines high-fidelity physics models, empirical models based on historical data and testing, and semi-empirical models to predict how materials will perform under various conditions.
2. It allows creating "digital twins" of materials to simulate deformation and failure risk over time. Safety limits can be set and failure mitigation strategies optimized.
3. The document outlines the state of art in modelling approaches and how integrating models across scales and disciplines can improve predictions while quantifying uncertainty. Integrated modelling can enhance safety and sustainability in industry.
This document describes Walter Jesuslee Savio Rodrigues' PhD dissertation from the University of Rome Tor Vergata. The dissertation focuses on accelerating atomistic simulations of nanostructured devices using graphics processing units (GPUs). It presents GPU implementations of eigenvalue solvers like the Lanczos method and benchmarks their performance. Applications to realistic nanostructure simulations are also demonstrated. The goal of the work is to make large-scale atomistic simulations more accessible to researchers by taking advantage of modern GPU hardware.
This document presents a final report for a single machine scheduling problem with sequence dependent setup times at an aluminum powder coating plant. The report begins with background on the company, Wispeco Aluminum, which has been producing aluminum extrusion and powder coating since the 1920s. It then describes the project aim to develop an optimization model to improve scheduling at the plant. The report includes a literature review on single machine scheduling and heuristic techniques, an analysis of the current scheduling problem and plant data, the development of a conceptual model and genetic algorithm based solution model in MATLAB, testing and validation of the solution model, and proposed improvements and applications for the plant.
This document appears to be the thesis of Alexandros X. Kontarinis submitted to the National Technical University of Athens in 2015. The thesis examines mechanisms for elastic resource allocation in cloud computing environments using reinforcement learning techniques. Specifically, it studies algorithms where an intelligent agent decides on actions based on multiple criteria and learns to select actions that optimize its performance based on rewards received from the environment in response to its actions. The goal is to achieve efficient adaptive allocation of cloud computing resources.
This document provides an introduction to digital business ecosystems, including:
- It discusses the roots and development of digital business ecosystems as a concept originating from efforts to promote an information society and knowledge-based economy in Europe.
- It recognizes that businesses require new technologies, applications, and services to enable networked and collaborative operations in the knowledge-based economy.
- The document presents research on digital business ecosystems funded through European Commission projects, exploring technologies, economic and social aspects, case studies, and more.
This doctoral thesis by Juan Luis Jerez focuses on developing more efficient computational methods and custom hardware architectures for real-time optimal decision making and control applications. The thesis proposes techniques to exploit synergies between digital hardware, numerical algorithms, and algorithm design. These include custom storage schemes, parallel optimization approaches, tailored linear algebra methods for fixed-point arithmetic, and finite-precision analysis of first-order optimization methods. The techniques are demonstrated on examples such as a hardware-in-the-loop setup for model predictive control of a large airliner.
This document is a thesis submitted by Milan Bouda in partial fulfillment of the requirements for a Doctor of Philosophy degree. The thesis is dedicated to Bayesian estimation of DSGE models. It first outlines the history and development of DSGE modeling in the Czech Republic and worldwide. It then describes the comprehensive DSGE framework and provides details on specifying and estimating DSGE models within this framework. The thesis contains two empirical studies - the first estimates a New Keynesian DSGE model for the Czech Republic using Bayesian techniques, and the second develops a Small Open Economy DSGE model for the Czech Republic with a housing sector.
This document is a master's thesis submitted by R.Q. Vlasveld to Utrecht University in partial fulfillment of the requirements for a Master of Science degree. The thesis explores using one-class support vector machines (SVMs) for temporal segmentation of human activity time series data recorded by inertial sensors in smartphones. The author first reviews related work in temporal segmentation and change detection methods. An algorithm is then presented that uses an incremental SVDD model to detect changes between activities in a continuous data stream. The algorithm is tested on both artificial and real-world human activity data sets recorded by the author. Quantitative and qualitative results demonstrate the method can find changes between activities in an unknown environment.
This master's thesis explores designing, analyzing, and experimentally evaluating a distributed community detection algorithm. Specifically:
- A distributed version of the Louvain community detection method is developed using the Apache Spark framework. Its convergence and quality of detected communities are studied theoretically and experimentally.
- Experiments show the distributed algorithm can effectively parallelize community detection.
- Graph sampling techniques are explored for accelerating parameter selection in a resolution-limit-free community detection method. Random node selection and forest fire sampling are compared.
- Recommendations are made for choice of sampling algorithm and parameter values based on the comparison.
This document is the doctoral thesis of Juan A. Sillero Sepúlveda titled "High Reynolds Numbers Turbulent Boundary Layers". It contains acknowledgments, an index, and 6 chapters that study turbulent boundary layers at high Reynolds numbers through direct numerical simulation and analysis of one-point and two-point statistics, as well as velocity structures. The thesis was completed at the Polytechnic University of Madrid in June 2014 under the supervision of Dr. Javier Jiménez Sendín.
This document summarizes Guy Lebanon's PhD thesis on applying concepts from Riemannian geometry to statistical machine learning. It introduces statistical manifolds and examines the geometry of probability model spaces. It explores how this geometric perspective can provide theoretical insights into algorithms like AdaBoost and logistic regression. It also describes developing new algorithms by adapting existing methods like kernels and margin classifiers to non-Euclidean geometries appropriate for data like text documents. The goal is to enhance understanding of machine learning algorithms and develop new approaches by considering the intrinsic geometries of model and data spaces.
Integrating IoT Sensory Inputs For Cloud Manufacturing Based ParadigmKavita Pillai
The first step in thermoplastic recycling is identifying the plastic waste categorically. This manual task is often inefficiency and costly. This study therefore analyzes the problem and presents a automatic classifier based on a WSN infrastructure. The classifier fuses data from two different sources using Kalman filter and neural network. The algorithm is run on a matlab simulator to test the results
Clustering Financial Time Series and Evidences of Memory EGabriele Pompa, PhD
This document is a thesis that examines clustering and memory effects in financial time series. It begins with an introduction to relevant concepts in financial markets like the efficient market hypothesis and random walk models. It then discusses pattern recognition techniques like clustering and explores their application to time series data. The document outlines the Monte Carlo framework used in simulations. It analyzes memory effects through a "bounce" study of support and resistance levels. It presents an original Bayesian clustering algorithm applied to toy and real financial data. The results provide evidence of structural regularities among the time series analyzed.
This document provides an overview of the book "The Finite Volume Method in Computational Fluid Dynamics" by F. Moukalled, L. Mangani, and M. Darwish. The book covers the finite volume method (FVM) used in computational fluid dynamics (CFD) simulations. It discusses the numerical methods, algorithms, and applications of FVM in CFD. The book is intended for graduate students and provides the foundation needed to develop a robust CFD code using the unstructured finite volume method. It includes examples implemented in OpenFOAM and MATLAB.
This document is a thesis submitted by Tokelo Khalema to the University of the Free State in partial fulfillment of the requirements for a B.Sc. Honors degree in Mathematical Statistics. The thesis compares the Gaussian linear model, two Bayesian Student-t regression models, and the method of least absolute deviations through a Monte Carlo simulation study. The study aims to evaluate how soon and how severely the least squares regression model starts to lose optimality against these robust alternatives under violations of its assumptions. The document includes sections on robust statistical procedures, literature review of the models considered, research methodology, results and applications of the simulation study, and closing remarks.
This document describes Lars Sletbakk Brusletto's master's thesis on developing a computer vision-based obstacle avoidance system for remotely operated vehicles (ROVs). The thesis involved:
1) Creating obstacle avoidance algorithms using computer vision to detect obstacles in front of the ROV from a single camera image.
2) Testing the algorithms on an ROV in Trondheimsfjorden to avoid a transponder tower and communicate with the control program.
3) Simulating the Trondheimsfjorden mission and comparing different computer vision algorithms in the simulator.
Essay about Reading Free Essay Example. 006 Importance Of Reading Essay ~ Thatsnotus. Importance of reading books short essay in 2021 | Good transition words .... Essay On Books And Reading. 007 Books And Reading Essay Example ~ Thatsnotus. Issues Essay - Importance of Reading. How To Teach Reading Essay. Studies show reading this essay will make you smarter 76. Importance of Reading Essay. Write short essay on Books and reading | Essay Writing | English - YouTube. Reading to write essay | English (Advanced) - Year 11 HSC | Thinkswap. 20 Sample essay ideas | reading comprehension worksheets, english .... Essay how important is reading for our students.
Education in the Usa - 500 Words | Free Essay Example on GraduateWay. American Dream Essay Conclusion Best Of 54 Essays the American Dream .... AMERICA | Sample essay, Essay, Writing. Education In America Essay : Term paper download free. Essay on american education - Engelsk - Opgaver.com. What being an american means to me essays - eyeofthedaygdc.web.fc2.com. Proud to be an American. - GCSE Design & Technology - Marked by .... "Let America be America Again" - Free Essay Example | PapersOwl.com. What Is America Essay | What is america, Essay, Essay writing. Teach for america. Let America Be America Again Essay – Telegraph.
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This thesis proposes a novel way to introduce self-configuration and self-optimization autonomic characteristics to algorithmic skeletons using event-driven programming techniques. By leveraging event-driven programming, the approach is not tied to a specific application architecture and allows for structural changes at runtime. It also enables estimates of future work to be calculated on-the-fly rather than relying on pre-calculated estimates. The thesis focuses on guaranteeing a given execution time for a skeleton by optimizing the number of threads. It contributes a novel event-based separation of concerns for skeletons and evaluates strategies for estimating execution times and parallelism levels.
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This document discusses integrated multiscale modelling for predicting material failure and degradation over time. It makes three key points:
1. Integrated multiscale modelling combines high-fidelity physics models, empirical models based on historical data and testing, and semi-empirical models to predict how materials will perform under various conditions.
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3. The document outlines the state of art in modelling approaches and how integrating models across scales and disciplines can improve predictions while quantifying uncertainty. Integrated modelling can enhance safety and sustainability in industry.
This document describes Walter Jesuslee Savio Rodrigues' PhD dissertation from the University of Rome Tor Vergata. The dissertation focuses on accelerating atomistic simulations of nanostructured devices using graphics processing units (GPUs). It presents GPU implementations of eigenvalue solvers like the Lanczos method and benchmarks their performance. Applications to realistic nanostructure simulations are also demonstrated. The goal of the work is to make large-scale atomistic simulations more accessible to researchers by taking advantage of modern GPU hardware.
This document presents a final report for a single machine scheduling problem with sequence dependent setup times at an aluminum powder coating plant. The report begins with background on the company, Wispeco Aluminum, which has been producing aluminum extrusion and powder coating since the 1920s. It then describes the project aim to develop an optimization model to improve scheduling at the plant. The report includes a literature review on single machine scheduling and heuristic techniques, an analysis of the current scheduling problem and plant data, the development of a conceptual model and genetic algorithm based solution model in MATLAB, testing and validation of the solution model, and proposed improvements and applications for the plant.
This document appears to be the thesis of Alexandros X. Kontarinis submitted to the National Technical University of Athens in 2015. The thesis examines mechanisms for elastic resource allocation in cloud computing environments using reinforcement learning techniques. Specifically, it studies algorithms where an intelligent agent decides on actions based on multiple criteria and learns to select actions that optimize its performance based on rewards received from the environment in response to its actions. The goal is to achieve efficient adaptive allocation of cloud computing resources.
This document provides an introduction to digital business ecosystems, including:
- It discusses the roots and development of digital business ecosystems as a concept originating from efforts to promote an information society and knowledge-based economy in Europe.
- It recognizes that businesses require new technologies, applications, and services to enable networked and collaborative operations in the knowledge-based economy.
- The document presents research on digital business ecosystems funded through European Commission projects, exploring technologies, economic and social aspects, case studies, and more.
This doctoral thesis by Juan Luis Jerez focuses on developing more efficient computational methods and custom hardware architectures for real-time optimal decision making and control applications. The thesis proposes techniques to exploit synergies between digital hardware, numerical algorithms, and algorithm design. These include custom storage schemes, parallel optimization approaches, tailored linear algebra methods for fixed-point arithmetic, and finite-precision analysis of first-order optimization methods. The techniques are demonstrated on examples such as a hardware-in-the-loop setup for model predictive control of a large airliner.
This document is a thesis submitted by Milan Bouda in partial fulfillment of the requirements for a Doctor of Philosophy degree. The thesis is dedicated to Bayesian estimation of DSGE models. It first outlines the history and development of DSGE modeling in the Czech Republic and worldwide. It then describes the comprehensive DSGE framework and provides details on specifying and estimating DSGE models within this framework. The thesis contains two empirical studies - the first estimates a New Keynesian DSGE model for the Czech Republic using Bayesian techniques, and the second develops a Small Open Economy DSGE model for the Czech Republic with a housing sector.
This document is a master's thesis submitted by R.Q. Vlasveld to Utrecht University in partial fulfillment of the requirements for a Master of Science degree. The thesis explores using one-class support vector machines (SVMs) for temporal segmentation of human activity time series data recorded by inertial sensors in smartphones. The author first reviews related work in temporal segmentation and change detection methods. An algorithm is then presented that uses an incremental SVDD model to detect changes between activities in a continuous data stream. The algorithm is tested on both artificial and real-world human activity data sets recorded by the author. Quantitative and qualitative results demonstrate the method can find changes between activities in an unknown environment.
This master's thesis explores designing, analyzing, and experimentally evaluating a distributed community detection algorithm. Specifically:
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- Graph sampling techniques are explored for accelerating parameter selection in a resolution-limit-free community detection method. Random node selection and forest fire sampling are compared.
- Recommendations are made for choice of sampling algorithm and parameter values based on the comparison.
This document is the doctoral thesis of Juan A. Sillero Sepúlveda titled "High Reynolds Numbers Turbulent Boundary Layers". It contains acknowledgments, an index, and 6 chapters that study turbulent boundary layers at high Reynolds numbers through direct numerical simulation and analysis of one-point and two-point statistics, as well as velocity structures. The thesis was completed at the Polytechnic University of Madrid in June 2014 under the supervision of Dr. Javier Jiménez Sendín.
This document summarizes Guy Lebanon's PhD thesis on applying concepts from Riemannian geometry to statistical machine learning. It introduces statistical manifolds and examines the geometry of probability model spaces. It explores how this geometric perspective can provide theoretical insights into algorithms like AdaBoost and logistic regression. It also describes developing new algorithms by adapting existing methods like kernels and margin classifiers to non-Euclidean geometries appropriate for data like text documents. The goal is to enhance understanding of machine learning algorithms and develop new approaches by considering the intrinsic geometries of model and data spaces.
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This document describes Lars Sletbakk Brusletto's master's thesis on developing a computer vision-based obstacle avoidance system for remotely operated vehicles (ROVs). The thesis involved:
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2) Testing the algorithms on an ROV in Trondheimsfjorden to avoid a transponder tower and communicate with the control program.
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9
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Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
3. Proceedings of the 16th International Conference on Project Management and
Scheduling
PMS 2018 - April 17-20, 2018 - Rome, Italy
ISBN: 9788894982022
Editors:
Massimiliano Caramia
Lucio Bianco
Stefano Giordani
Address of the Editors:
University of Rome “Tor Vergata”
Dipartimento di Ingegneria dell’Impresa
Via del Politecnico, 1
00133 Roma - Italy
Tel. +39 06 72597360
Fax. +39 06 72597305
email: caramia@dii.uniroma2.it
Published by:
TexMat
Via di Tor Vergata, 93-95
00133 Roma
Tel. +39 06 2023572
www.texmat.it
e-mail: info@texmat.it
Place and Date of Publication:
Rome (Italy), March 31, 2018
i
5. PMS 2018 Preface
Preface
This volume contains the papers that will be presented at PMS 2018, the 16th
International
Conference on Project Management and Scheduling to be held on April, 17-20 2018 in Rome
- Italy.
The EURO Working Group on Project Management and Scheduling was established by Pro-
fessors Luı́s Valadares Tavares and Jan Weglarz during the EURO VIII Conference, Lisbon, in
September 1986. It was decided to organize a workshop every two years. Gathering the most
promising theoretical and applied advances in Project Management and Scheduling, and assess-
ing both the state-of-the-art of this field and its potential to support management systems are
the main objectives of these workshops.
76 extended abstracts have been submitted to the PMS 2018 Confenrece. These valuable con-
tributions were reviewed by 2 referees who are members of the International Program Committee
and distinguished researchers of the associated fields. The proceedings at hand contain the 65
papers that were finally accepted for presentation at the conference. There papers involves 165
authors from 23 different countries.
The 16th
edition of PMS has four plenary speakers: Professor Jacques Carlier (Univer-
sité de Technologie de Compiègne) will present the talk “Comparing event-node graphs with
nonrenewable resources and activity-node graphs with renewable resources”, Professor Erwin
Pesch (University of Siegen) will discuss on “Optimization problems in intermodal transport”,
Professor Ruben Ruiz (University of Valencia) and Professor Erik Demeulemeester (Katholic
University of Leuven) will delight us talking on “Simple metaheuristics for flowshop scheduling:
all you need is local search” and “On the construction of optimal policies for the RCPSP with
stochastic activity durations”, respectively.
The scientific program and the social events will give to all the participants an opportunity
to share research ideas and debate on recent advances on project managment and scheduling. I
am sure that together we will contribute to make PMS 2018 a great success.
Welcome in Rome and have an enjoyable stay!
Rome, 17th April 2018 Massimiliano Caramia (Conference Chair)
iii
7. PMS 2018 Committees
Organizing Committee
Massimiliano Caramia (Chairman) Università di Roma “Tor Vergata” (Italy)
Lucio Bianco Università di Roma “Tor Vergata” (Italy)
Stefano Giordani Università di Roma “Tor Vergata” (Italy)
Program Committee
Alessandro Agnetis Università di Siena (Italy)
Ali Allahverdi Kuwait University (Kuwait)
Christian Artigues LAAS-CNRS (France)
Francisco Ballestrin Universitat de València (Spain)
Fayez Boctor Université Laval (Canada)
Jazek Blażewicz Poznań University of Technology (Poland)
Massimiliano Caramia Università di Roma “Tor Vergata” (Italy)
Jacques Carlier Université de Technologie de Compiègne (France)
Erik Demeulemeester Katholieke Universiteit Leuven (Belgium)
Joanna Józefowska Poznań University of Technology (Poland)
Sigrid Knust Universität Osnabrück (Germany)
Rainer Kolisch Technische Universität München (Germany)
Mikhail Kovalyov National Academy of Sciences of Belarus (Belarus)
Wieslaw Kubiak Memorial University (Canada)
Erwin Pesch Universität Siegen (Germany)
Chris Potts University of Southampton (United Kingdom)
Rubén Ruiz Universitat Politècnica de València (Spain)
Avraham Shtub Technion - Israel Institute of Technology (Israel)
Funda Sivrikaya Şerifoğlu Istanbul Bilgi Üniversitesi (Turkey)
Vincent T’Kindt Université François Rabelais Tours (France)
Norbert Trautmann Universität Bern (Switzerland)
Mario Vanhoucke Ghent University (Belgium)
Jan Weglarz Poznań University of Technology (Poland)
Jürgen Zimmermann Technische Universität Clausthal (Germany)
Linet Özdamar Yeditepe Üniversitesi (Turkey)
v
15. PMS 2018 Author Index
Author Index
Absi, Nabil 1
Agnetis, Alessandro 5, 9
Al Hasan, Hasan 13
Allahverdi, Ali 26, 32
Andrés, Carlos 17
Anselmet, Marie-Christine 181
Arkhipov, Dmitry 22
Artigues, Christian 1, 165, 181
Aydilek, Asiye 26, 32
Aydilek, Harun 26, 32
Balouka, Noemie 37
Battaı̈a, Olga 22
Bellenguez-Morineau, Odile 255
Berghman, Lotte 5
Berlinska, Joanna 42
Bianco, Lucio 46
Billaut, Jean-Charles 225
Boctor, Fayez 50
Boysen, Nils 55
Briand, Cyril 5, 58
Bridelance, Jerome 62
Briskorn, Dirk 66
Bultmann, Matthias 70
Burgelman, Jeroen 74
Cafieri, Sonia 119
Caramia, Massimiliano 46
Carlier, Jacques 78
Chen, Bo 9
Codou Ndiaye, Jeanine 58
Coelho, Leandro 250
Cohen, Izack 37
Coindreau, Marc-Antoine 79
Dauzère-Pérès, Stéphane 229
Della Croce, Federico 221
Demeulemeester, Erik 83, 152
Di Gioacchino, Roberto 160
Dolceamore, Simone 88
Eberle, Franziska 92
Ekici, Ali 96
xiii
16. PMS 2018 Author Index
Fanjul-Peyró, Luis 195
Ferenczi, Balázs 276
Fischer, Felix 92
Fliedner, Malte 66
Gallay, Olivier 79
Gerhards, Patrick 100
Giordani, Stefano 46
Gonzalez-Neira, Eliana Marı́a 104
Guan, Xin 267
Guida, Pier Luigi 110
Guéret, Christelle 13
Gyorgyi, Peter 115
Gültekin, Hakan 237
Gürel, Sinan 237
Hamaz, Idir 119
Haı̈t, Alain 165
Hegyháti, Máté 123, 276
Hoffmann, Luise-Sophie 128
Hong, Juntaek 136
Houssin, Laurent 119
Kedad-Sidhoum, Safia 1
Kellenbrink, Carolin 128, 205
Kis, Tamas 115
Kloster, Oddvar 185
Knust, Sigrid 70
Lange, Julia 132
Lazarev, Alexander 22
Lee, Kangbok 136
Lemoine, David 13
Lopez, Pierre 181
Lucidi, Stefano 141
Maccarrone, Ludovica 141
Maecker, Söhnke 145
Maenhout, Broos 246
Maheut, Julien 17
Mannino, Carlo 149, 185
Manzini, Massimo 152
Martens, Annelies 156
Martineau, Patrick 263
Matuschke, Jannik 92
Megow, Nicole 92
Minelle, Federico 160
Montoya-Torres, Jairo R. 104
xiv
17. PMS 2018 Author Index
Morin, Pierre-Antoine 165
Ngueveu, Sandra Ulrich 1
Nicosia, Gaia 9
Odedairo, Babatunde Omoniyi 169
Oladokun, Victor Oluwasina 169
Ozener, Okan 96
Oğuz, Ceyda 233
Pacifici, Andrea 9
Parlouar, Rémi 58
Perea, Federico 195
Pesch, Erwin 175
Pirozzi, Massimo 176
Polo Mejia, Oliver 181
Rannou, Janik 1
Rihm, Tom 242
Riise, Atle 185
Rivreau, David 13
Rozycki, Rafal 189
Ruiz, Rubén 194, 195
Różycki, Rafal 199
Saadi, Omar 1
Sacco, Giovanni 110
Saner, Nadine 242
Santini, Stefano 160
Sarikaya, Merve Burcu 96
Sartor, Giorgio 149
Schittekat, Patrick 149, 185
Schnabel, Andre 205
Sedding, Helmut A. 209
Servranckx, Tom 213
Shang, Lei 221
Shen, Liji 145
Soukhal, Ameur 263
Stephan, Konrad 55
Stolfi, Franco 160
Stürck, Christian 217
T’Kindt, Vincent 221
Ta, Thanh Thuy Tien 225
Tamssaouet, Karim 229
Tarhan, İstenç 233
Tatar, Nurdan 237
Trautmann, Norbert 242
xv
18. PMS 2018 Author Index
Tschöke, Martin 66
Urgo, Marcello 88, 152
Van Den Eeckhout, Mick 246
Vanhoucke, Mario 62, 74, 156, 213, 246
Vié, Marie-Sklaerder 250
Waldherr, Stefan 70
Waligóra, Grzegorz 189, 199
Wang, Tianyu 255
Watermeyer, Kai 259
Weidinger, Felix 55
Weglarz, Jan 199
Yugma, Claude 229
Zahout, Boukhalfa 263
Zhang, Yao 267
Zimmermann, Adrian 242
Zimmermann, Jürgen 259
Zufferey, Nicolas 79, 250, 272
Zuo, Fei 267
Ősz, Olivér 276
xvi
19. PMS 2018 Keyword Index
Keyword Index
Activities scheduling 169
Air traffic control 149
Aircraft assembly 88
Alternative project structure 213
Analytical tolerance limits 156
Approximation algorithm 92
Assembly flowshop 17, 26
Assembly line 152
Assignment and scheduling 58
Bargaining problems 9
Batch delivery 233
Batching 229
Benchmark instances 100
Benders’ reformulation 149
Bicriteria optimization 237
Blocking 17, 132
Branch and bound 259
Budgeted uncertainty set 119
Buffer monitoring 156
Buffer size 17
Carpooling 79
Chance constrained optimization 46
Characterization 225
Claim management 110
Column generation 165, 233
Computational complexity 66, 209
Conditional Value at Risk 88
Conflict resolution 185
Constraint programming 22
Context based risk analysis 160
Continuous resource 189
Continuous time mixed integer linear
programming 242
Crossdocking 5
Cyclic scheduling 119
Data gathering network 42
Deadline 225
Decision support system 267
Decomposition 246
Delivery times 145
Deterioration 276
xvii
20. PMS 2018 Keyword Index
Discrete continuous scheduling 189
Discrete time/resource trade-off 246
Distribution planning 250
Doubly constrained resource 189
Dual gripper 237
Due dates 276
Dynamic programming 1, 136, 233
E-government 160
Earliness 104
Eligibility constraints 136
Energy 199
Energy optimization 237
Equal processing time jobs 136
eS-graph 123
Exact methods 195
Exponential time algorithm 221
Fairness 9
Flexible project 128
Flow shop 42, 70, 152
Forge 276
Fuzzy mathematical programming 267
Genetic algorithm 128, 205
Grey box optimization 141
Handover relation 66
Heuristics 50, 145, 205, 263
Hotspot problem 149
Idleness cost 169
Integer programming 5, 50, 149, 255
Iterated local search 246
Job shop scheduling 132, 185, 272
Just in time 221
KPI 176
Limited memory 42
Linear algebra 74
Linear programming 185
Local search 205, 229
Lot sizing 1
Lot sizing and scheduling 50
Makespan 32
xviii
21. PMS 2018 Keyword Index
Maximum tardiness 26
Memetic algorithm 145
Metaheuristics 145, 233
Mixed integer linear programming 1, 13, 58, 141, 145, 165, 242, 263, 276
MMLIB 217
Mode reduction 217
Modeling technique 123
Multi skill 181
Multi-mode resource availability cost
problem 100
Multi-mode resource constrained project
scheduling problem 217
Multi-mode resource investment problem 100
Multi-project experimental outcome 160
Multi-project scheduling 128
Multi-robot pick-and-place 58
Multiagent scheduling 9, 263
New objective function 225
No wait 32
Non-renewable resources 115
Nuclear laboratory 181
Operating rooms in health services 13
Optimal policies 83
Optimization 181
Order acceptance 233
Order consolidation 55
Overcapacity 205
Parallel machine scheduling 5, 96, 145, 189, 195, 229, 255
Pareto optimization 263
Partially renewable resources 259
Periodical aggregation 165
PERT 46, 74
Piecewise linear convex processing time 209
Planning 165
Pliability 70
Polynomial algorithms 22
Portfolio management 62
Power 199
Precedence constraints 255
Preemptive scheduling 181
Preprocessing 217
Proactive reactive scheduling 152
Production planning 250
Project 165
Project control 156
xix
22. PMS 2018 Keyword Index
Project management 110, 169
Project network 123
Project planning 22
Project risk management 160, 267
Project scheduling 37, 46, 74, 100, 141, 213, 259
Project staffing 246
Propagator 22
Qualitative criteria 104
RCMPSP-PS 128
Release dates 136
Resource availability 62
Resource constrained project scheduling
problem 83, 169, 181, 205, 242
Resource transfers 62
Risk response action 267
Robotic cell scheduling 237
Robust optimization 37, 119
Robustness 104
Schedule delay analysis 110
Scheduling under energy constraints
and costs 1
Semiconductor manufacturing 229
Sequence dependent setup times 96, 233
Server problem 199
Setup times 26, 195
Simulated annealing 26, 132
Single machine scheduling 55, 115, 221, 225, 263
Single processor 199
Stakeholder 176
Sterilization unit 13
Stochastic activity durations 83
Stochastic permutation flow shop 104
Stochastic scheduling 88, 92
Success 176
Supply chain management 250
Synchronization 79
Synchronous movement 70
Tabu search 213, 272
Tardiness 104
Time dependent scheduling 209
Total completion time 92, 136
Total tardiness 32, 132
Total weighted completion time 115
Transshipment terminals 66
xx
25. Scheduling energy-consuming jobs on parallel machines
with piecewise-linear costs and storage resources
A lot-sizing and scheduling perspective
Nabil Absi1
, Christian Artigues2
, Safia Kedad-Sidhoum3
, Sandra U. Ngueveu2
, Janik
Rannou2
, et Omar Saadi3
1
Mines Saint-Etienne and UMR CNRS 6158 LIMOS, Gardanne, France
absi@emse.fr
2
LAAS-CNRS, Université de Toulouse, CNRS, INP, Toulouse, France
sungueve,artigues@laas.fr
3
Sorbonne Université, UPMC, UMR 7606, LIP6, Paris, F-75005, France
safia.kedad-sidhoum@lip6.fr
Keywords: Scheduling under energy constraints and costs, Mixed-integer programming,
Lot-sizing, Dynamic programming
1 Problem formulation and complexity
In this paper, a scheduling and energy source assignment problem is studied. The
problem is abstracted from several applications including data centers (Guérout et al. 2017),
smart buildings (Desdouits et al. 2016), hybrid vehicles (Caux et al. 2017, Ngueveu et
al. 2017) and manufacturing (Haouassi et al. 2016). A set of jobs J has to be scheduled
on a set of energy consuming machines M. The energy consumed by a machine k has a
fixed part Dk depending on whether the machine is switched on or off and a variable part
depending on the tasks that are currently in process. Each task j requires an amount Djk
of energy at each time period it is processed on machine k. We are interested in optimizing
the total energy cost induced by energy production required to satisfy the total energy
demand of a given schedule over a fixed discrete horizon T = {1, . . . , |T|}. At each time
period, the energy required by the schedule can be supplied by two energy sources. One
source is reversible, such as batteries and super-capacitors. Such a source is able not only
to produce energy but also to retrieve it assuming a limited capacity Q. Such a resource is
equivalent to a continuously-divisible storage resource in the scheduling terminology. The
second source is a non-reversible source, only able to produce energy, such as the external
power grid (assuming here that energy cannot be sold to the network). This source is
assumed of infinite capacity, but its usage comes with a cost (see below). In this paper, we
consider a parallel machine environment, such that pj units of each task j must be scheduled
preemptively inside a time window [rj, dj] and have to be assigned at each time period to
one and only one machine. Job units also require resources from a set R (e.g. CPU, RAM)
on their assigned machines. A job requires a non-negative amount cjr on each resource
r ∈ R. On each machine k, resource r is available in a limited amount Ckr. The energy
cost for a period of the scheduling horizon is a piecewise linear (PWL) function ft, t ∈ T, of
the required amount of energy on the non-reversible source. The PWL function is assumed
to be time dependent. This allows to model time dependent electricity prices as well as
previsions of photovoltaic production since the cost can be zero up to a required amount
of energy corresponding to the expected photovoltaic production on the considered time
period. We introduce variables yjkt ∈ {0, 1} indicating whether one unit of job j is assigned
to machine k at time t and zkt ∈ {0, 1} indicating whether machine k is switched on at time
t. Continuous variables are used for energy amounts: xt ≥ 0 gives the amount of energy
used on the non-reversible source at time t, st ≥ 0 is the level of energy remaining in the
1
26. non-reversible source at time t (s0 is a constant indicating the initial energy level). Based
on these variables, we define a MILP formulation of the problem aiming at minimizing the
total energy cost.
minimize
P
t∈T ft(xt) (1)
subject to P
k∈M yjkt ≤ 1, j ∈ J , t ∈ T (2)
P
k∈M
P
t∈T yjkt = pj, j ∈ J (3)
P
j∈J cjryjkt ≤ Ckr, k ∈ M, r ∈ R, t ∈ T (4)
zkt − yjkt ≥ 0, k ∈ M, j ∈ J , t ∈ T (5)
xt + st − st−1 −
P
j∈J
P
k∈M Djkyjkt −
P
k∈M Dkzkt = 0, t ∈ T (6)
s|T | − s0 ≥ 0, (7)
st − Q ≤ 0, t ∈ T (8)
st ≥ 0 t ∈ T (9)
xt ≥ 0 t ∈ T (10)
yjkt ∈ {0, 1} j ∈ J , k ∈ M, t ∈ T (11)
zkt ≥ 0 k ∈ M, t ∈ T (12)
The total energy cost minimization objective (1) is considered. Constraints (2) state that
a job may be in process on only one machine at a given time. Constraints (3) enforce each
unit of a job to be scheduled on one machine. Constraints (4) are the resource constraints.
Constraints (5) enforce a machine to be switched on at each time it processes at least one
job. Constraints (6) are the energy balance constraints between the schedule demand, the
energy provided by the non-reversible source (xt) and the energy taken from or provided to
the reversible source (st − st−1, that can be positive or negative). Constraint (7) enforces
the final energy level in the reversible source to be at least the initial one. Constraints
(8) are the reversible source capacity constraints (storage limit). Scheduling preemptive
jobs with PWL energy costs is NP-hard, even with an unlimited number of machines and
single non-reversible source (Ngueveu et al. 2016). Therefore the proposed MILP becomes
intractable as the problem size increases.
2 A lot-sizing and scheduling matheuristic
We propose a natural decomposition of the problem. Let dt =
P
j∈J
P
k∈M Djkyjkt
+
P
k∈M Dkzkt denote the total energy demand of a fixed schedule at time t. Then con-
straints (6) can be rewritten
xt + st − st−1 − dt = 0, t ∈ T (13)
Now observe that for fixed dt, problem LSP: min
P
t∈T ft(xt) s.t. (7–10), (13) is a single-
item (continuous) lot sizing problem with PWL production costs where dt is the demand
for period t, xt is the production variable for period t, and st is the variable giving the
amount of inventory at the end of period t. In Absi et al. (2017), the problem is shown to
be NP-hard but for integer inventory levels, a pseudo-polynomial dynamic programming
(DP) algorithm of complexity O(T2
qd) where d is the average demand and q is the average
number of breakpoints of the PWL functions ft is given, generalizing the results of Shaw
and Wagelmans (1998). On the other hand, if the variables st are fixed, by performing
change of variables xt ← xt − st + st−1 for all t, we obtain
xt =
X
j∈J
X
k∈M
Djkyjkt +
X
k∈M
Dkzkt, t ∈ T (14)
2
27. and problem MSP: min
P
t∈T f′
t(xt) =
P
t∈T ft(xt − st + st−1) s.t. (2–5), (10–12), (14),
which is a parallel machine scheduling problem with PWL costs and a single non-reversible
source, NP-hard in the strong sense as shown in Ngueveu et al. (2016).
A matheuristic is obtained by solving alternatively MSP and LSP. Starting with initial
reversible source transferred amounts st − st−1 = 0 for all t, MSP is solved and the output
energy demand (dt)t∈T is used as input of LSP. The output inventory levels are used to
update the PWL functions f′
t. Then, MSP is solved again, and so on until no improvement
is observed in the objective function.
We first compare the MILP (solved with Cplex) and the pseudo polynomial DP algo-
rithm with fixed demands (only LSP), see table 1. The merits and the drawback of the
two approaches are illustrated on 4 instances with T = 1000, q = 10 breakpoints, and
varying average maximal capacities Q and demands d. Under a 300s time limit for the
MILP, the CPU times (in seconds) and obtained costs are compared. It appears that no
algorithm dominates the other one in terms of CPU time, while the DP is more impacted
by the maximal available capacity for the reversible source. However the MILP shows a
more erratic and unpredictable behavior. Note that due to the integrity requirement of the
inventory levels, the DP costs are higher than the MILP costs.
Table 1. Comparison of MILP and DP on the lot sizing problem (LSP)
T q Q d MILP cost MILP CPU DP cost DP CPU
1000 10 1000 100 6661 300 6916 14.16
1000 10 10000 100 4396 2.90 4508 279
1000 10 100 2000 975523 0.57 975617 1.31
1000 10 1000 2000 940165 300 937886 15
Finally we compare the MSP/LSP decomposition matheuristic (MH) with the full MILP
to solve the global problem. We also illustrate the cost and CPU time differences on 4
instances with varying horizon, number of machines, number of jobs (see table 2). On 3
instances (marked with a ∗) the full MILP reached the time limit. The matheuristic is
only slightly faster than the MILP except on the last instance, where it is much faster.
The costs can be close to the MILP ones although important gaps can also be observed.
In parenthesis, the maximal CPU time per iteration and the iteration number assigned to
MH is indicated. A closer analysis of the CPU times between MSP and LSP reveals that
90% of the CPU time is spent on solving the scheduling problem MSP.
Table 2. Comparison of full MILP and matheuristic on the global problem
T |M| |J | MILP cost MILP CPU MH cost MH CPU
30 2 50 11280 450∗
11280 154 (150× 3)
60 4 150 25966 2000∗
26183 1893 (1000× 2)
120 2 150 5944 2000∗
6972 1855 (1000× 2)
120 1 150 11255 1353 11265 228 (200× 10)
3
28. 3 Conclusion
We have proposed an original lot sizing and scheduling decomposition approach to
solve an energy management and scheduling problem on parallel machines. The lot sizing
subproblem can be solved considerably faster than the scheduling subproblem and conse-
quently, further research on the problem should focus on improvement of the scheduling
solution procedure. To improve the decomposition heuristic, optimality cuts issued from
lot sizing could be designed for the scheduling problem. Another interesting issue is to
consider a non ideal yield of the reversible source. In practice, due to energy conversion
and losses only a fraction of st − st−1 is available to fulfill the demand and a possibly non
linear efficiency function g(st − st − 1) has to be used to compute the obtained energy. It
remains to know whether efficient lot sizing procedure can be devised with such efficiency
functions.
Acknowledgements
This research benefited from the support of the FMJH Program PGMO and from the
support of EDF, Thales, Orange. It also benefited from funding from the Cellule Energie
of the CNRS.
References
Absi N., C. Artigues, S. Kedad-Sidhoum, S.U. Ngueveu and O. Saadi, 2017, “Lot-sizing models
for energy management”. LAAS report.
Caux S., Y. Gaoua, and P. Lopez, 2017, “A combinatorial optimisation approach to energy man-
agement strategy for a hybrid fuel cell vehicle”. Energy, Vol. 133, pp.219-230.
Desdouits C., M. Alamir, R. Giroudeau and C. Le Pape, 2016, “The Sourcing Problem - Energy
Optimization of a Multisource Elevator”, ICINCO, Vol. 1, pp. 19-30.
Guérout T., Y. Gaoua, C. Artigues, G. Da Costa, P. Lopez and T. Monteil, 2017, “Mixed in-
teger linear programming for quality of service optimization in Clouds” Future Generation
Computer Systems 71: 1–17.
Haouassi M., C. Desdouits, R. Giroudeau and C. Le Pape, 2016, “Production scheduling with a
piecewise-linear energy cost function” IEEE Symposium Series on Computational Intelligence
(SSCI), pp. 1-8.
Ngueveu S. U., C. Artigues and P. Lopez, 2016, “Scheduling under a non-reversible energy source:
An application of piecewise linear bounding of non-linear demand/cost functions”, Discrete
Applied Mathematics, Vol. 208, pp. 98-113.
Ngueveu S.U., S. Caux, F. Messine and M. Guemri, 2017, “Heuristics and lower bound for energy
management in hybrid-electric vehicles”, 4OR, to appear.
Shaw D. X., A. P. Wagelmans, 1998, “An algorithm for single-item capacitated economic lot sizing
with piecewise linear production costs and general holding costs”, Management Science, Vol.
44, pp. 831-838.
4
29. The truck scheduling problem at cross docking
terminals: Formulations and valid inequalities
A. Agnetis1
, L. Berghman2
and C. Briand3
1
A. Agnetis, Università degli Studi di Siena, DIISM, Siena, Italy
agnetis@diism.unisi.it
2
L. Berghman, Université de Toulouse - Toulouse Business School,
20 BD Lascrosses – BP 7010, 31068 Toulouse Cedex 7, France
l.berghman@tbs-education.fr
3
C. Briand, LAAS-CNRS, Université de Toulouse, UPS, Toulouse, France
briand@laas.fr
Keywords: crossdocking, truck scheduling, parallel machine scheduling, integer linear pro-
gramming.
1 Introduction
Crossdocking is a warehouse management concept in which items delivered to a ware-
house by inbound trucks are immediately sorted out, reorganized based on customer de-
mands and loaded into outbound trucks for delivery to customers, without requiring ex-
cessive inventory at the warehouse (J. van Belle et al. 2012). If any item is held in storage,
it is usually for a brief period of time that is generally less than 24 hours. Advantages
of crossdocking can accrue from faster deliveries, lower inventory costs, and a reduction
of the warehouse space requirement (U.M. Apte and S. Viswanathan 2000, N. Boysen et
al. 2010). Compared to traditional warehousing, the storage as well as the length of the
stay of a product in the warehouse is limited, which requires an appropriate coordination
of inbound and outbound trucks (N. Boysen 2010, W. Yu and P.J. Egbelu 2008).
The truck scheduling problem, which decides on the succession of truck processing at the
dock doors, is especially important to ensure a rapid turnover and on-time deliveries. The
problem studied concerns the operational level: trucks are allocated to the different docks
so as to minimize the storage usage during the product transfer. The internal organization
of the warehouse (scanning, sorting, transporting) is not explicitly taken into consideration.
We also do not model the resources that may be needed to load or unload the trucks, which
implies the assumption that these resources are available in sufficient quantities to ensure
the correct execution of an arbitrary docking schedule.
In this abstract, we present a time-indexed formulation, a network formulation and some
valid inequalities. Experimental results will be presented during the talk at the conference.
2 Detailed problem statement
We examine a crossdocking warehouse where incoming trucks i ∈ I need to be unloaded
and outgoing trucks o ∈ O need to be loaded (where I is the set containing all inbound
trucks while O is the set containing all outbound trucks). The warehouse features n docks
that can be used both for loading and unloading. The processing time of truck j ∈ I ∪ O
equals pj. This processing time includes the loading or unloading but also the transporta-
tion of goods inside the crossdock and other handling operations between dock doors. It
is assumed that there is sufficient workforce to load/unload all docked trucks at the same
time. Hence, a truck assigned to a dock does not wait for the availability of a material
handler.
5
30. The products on the trucks are packed on unit-size pallets, which move collectively as
a unit: re-packing inside the terminal is to be avoided. Each pallet on an inbound truck
i needs to be loaded on an outbound truck o, which gives rise to a start-start precedence
constraint (i, o) ∈ P ⊂ I × O, with P the set containing all couples of inbound trucks i
and outbound trucks o that share a precedence constraint. Each truck j has a release time
rj (planned arrival time) and a deadline ˜
dj (its latest departure time).
Products can be transshipped directly from an inbound to an outbound truck if the
outbound truck is placed at a dock. Otherwise, the products are temporarily stored and
will be loaded later on. Each couple (i, o) ∈ P has a weight wio, representing the number of
pallets that go from inbound truck i to outbound truck o. The problem aims at determining
time-consistent start times si and so of unload and load tasks i and o so as to minimize
the weighted sum of sojourn times of the pallets stocked in the warehouse. Remark that
the time spent by a pallet in the storage area is equal to the flow time of the pallet: the
difference between the start of loading the outbound trailer and the start of unloading the
inbound trailer (i.e., so − si).
Our problem can be modeled as a parallel machine scheduling problem with release
dates, deadlines, and precedence constraints, denoted by Pm|ri, ˜
di, prec|−. As this problem
is a generalization of the 1|rj, ˜
dj|− problem which is NP-complete (J.K. Lenstra et al. 1977),
even finding a feasible solution for the problem is NP-complete.
3 Time-indexed formulation
A time-indexed formulation discretizes the continuous time space into periods τ ∈
T of a fixed length. Let period τ be the interval [t − 1, t[. It is well known that time-
indexed formulations perform well for scheduling problems because the linear programming
relaxations provide strong lower bounds (M. E. Dyer and L. A. Wolsey 1990).
For all inbound trucks i ∈ I and for all time periods τ ∈ Ti, we have
xiτ =
1 if the unloading of inbound truck i is
started during time period τ,
0 otherwise,
(1)
with Ti = {ri + 1, ri + 2, . . . , ˜
di − pi + 1}, the relevant time window for inbound truck i.
Additionally, for all outbound trucks o ∈ O and for all time periods τ ∈ To, we have
yoτ =
1 if the loading of outbound truck o is
started during time period τ,
0 otherwise,
(2)
with To = {ro + 1, ro + 2, . . . , ˜
do − po + 1}, the relevant time window for outbound truck o.
A time-indexed formulation for the considered truck scheduling problem is the following:
min z =
X
(i,o)∈P
X
τ∈T
wioτ (yoτ − xiτ ) (3)
6
31. subject to
X
τ∈Ti
xiτ = 1 ∀i ∈ I (4)
X
τ∈To
yoτ = 1 ∀o ∈ O (5)
X
τ∈T
τ (xiτ − yoτ ) ≤ 0 ∀(i, o) ∈ P (6)
X
i∈I
τ
X
u=τ−pi+1
xiu +
X
o∈O
τ
X
u=τ−po+1
you ≤ n ∀τ ∈ T (7)
xiτ ∈ {0, 1} ∀i ∈ I; ∀τ ∈ Ti (8)
yoτ ∈ {0, 1} ∀o ∈ O; ∀τ ∈ To (9)
The objective function (3) minimizes the total weighted usage of the storage area. Con-
straints (4) and (5) demand each truck to be assigned to exactly one gate. Constraints (6)
ensure that if there exists a precedence constraint between inbound truck i and outbound
truck o, then o cannot be processed before i. Constraints (7) enforce the capacity of the
docks for any period τ ∈ T .
4 Network formulation
The formulation below makes use of the well-known concept of a critical set (see e.g. (M.
Lombardi and M. Milano 2012)), i.e., a set of tasks which cannot all be performed in
parallel. We introduce a pair of disjunctive precedence constraints for each task pair (u, v) ∈
(I ∪ O)2
with [ru, du] ∩ [rv, dv] 6= ∅, belonging to a critical set (the set of these task pairs is
further referred as C). We let E be the set of all critical sets. Additionally, we also refer to ek
as a specific critical set of k elements and to Em
⊂ E as the set of all minimal critical sets.
To model the disjunction, binary variables αuv are introduced such that αuv = 1 ≡ u ≺ v.
Our problem can be modelled as follows:
min
X
o∈O
sopo −
X
i∈I
sipi (10)
subject to
so − si ≥ 0 ∀(i, o) ∈ P (11)
sv − su + αuv(Muv − pu) ≥ Muv ∀(u, v) ∈ C (12)
sv − s0 ≥ rv ∀v ∈ I ∪ O (13)
s0 − su ≥ pu − du ∀u ∈ I ∪ O (14)
X
(u,v)∈en+1
αuv ≥ 1 ∀en+1 ∈ Em
(15)
αuv ∈ {0, 1} ∀(u, v) ∈ C (16)
su ∈ R ∀u ∈ I ∪ O (17)
with Muv = pu − du + rv and 0 a dummy vertex, which is introduced to represent the
time origin s0 = 0. Note that obviously αuv + αvu ≤ 1, even though this constraint is not
mandatory for the formulation accuracy.
Remark that constraints (15) express the limited capacity of the crossdocking terminal.
Their number is exponential, as the number of minimal critical sets is exponential. Even
7
32. though including only minimal critical sets is sufficient, we can also consider the non-
minimal critical sets, generalizing (15) as:
X
(u,v)∈ek
αuv ≥ k − n ∀ek ∈ E (18)
with n + 1 ≤ k ≤ I ∪ O .
We will show that this family of constraints can be strengthened by augmenting the
right-and-side, so that it can be replaced by:
X
(u,v)∈ek
αuv ≥
(k − n)(k − n + 1)
2
∀ek ∈ E (19)
5 Solving methodology framework
Intuitively, only a small number of constraints (19) may be required into the formulation
to obtain a feasible (optimal) solution. Consequently, we consider the following cutting-
plane method which consists in introducing progressively constraints of type (19). First, the
problem is solved without any constraint of type (19) using a MILP solver. Then, violated
constraints of type (19) are added for some k > n involving a critical set ek and the solver
is launched again. Now, each time a feasible solution is found by the solver in course of
the branch-and-cut process, violated constraints of type (19) are added on-the-fly. Note
that if such a solution is feasible with respect to the resource capacity, then it is an upper
bound of the initial problem. When the MILP solver ends up with an optimal solution
also capacity-feasible, it is also optimal. Otherwise, violated constraints of type (19) can
be added again and another MILP is ran. Within various computational time limitation
assumptions, the above methodology will be compared in terms of performance (quality of
the upper and lower bounds) with the time-indexed linear programming approach on a set
of artificial problem instances.
References
U.M. Apte and S. Viswanathan, Effective cross docking for improving distribution efficiencies,
International Journal of Logistics: Research and Applications, 3 (3), 291–302.
N. Boysen, Truck scheduling at zero-inventory cross docking terminals, Computers & Operations
Research, 37, 32–41.
N. Boysen and M. Fliedner and A. Scholl, Scheduling inbound and outbound trucks at cross
docking terminals, OR Spectrum, 32, 135–161.
M. E. Dyer and L. A. Wolsey, Formulating the single machine sequencing problem with release
dates as a mixed integer problem, Discrete Applied Mathematics, 26, 255–270.
J.K. Lenstra and A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling prob-
lems, Annals of Discrete Mathematics, 1, 343–362.
M. Lombardi and M. Milano, A min-flow algorithm for Minimal Critical Set detection in Resource
Constrained Project Scheduling, Artificial Intelligence, 182-183, 58–67.
J. van Belle and P. Valckenaers and D. Cattrysse, Cross docking: State of the art, Omega,40 (6),
827–846.
W. Yu and P.J. Egbelu, Scheduling of inbound and outbound trucks in cross docking systems with
temporary storage, International Journal of Production Economics„ 184, 377–396.
8