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Models and Algorithms for Solving Packing Problems in Logistics

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Models and algorithms for solving packing problems in logistics DISSERTATION FOR THE DEGREE OF DOCTOR OF COMPUTER SCIENCE TO BE PRESENTED WITH DUE PERMISSION OF THE DEPARTMENT OF COMPUTER SCIENCE, FOR PUBLIC EXAMINATION AND DEBATE Author: Mar´ıa Teresa Alonso Mart´ınez Supervisors: Dr. Ramon´ Alvarez-Vald´ es´ Olagu´ıbel Dr. Francisco Parreno˜ Torres “We ourselves feel that what we are doing is just a drop in the ocean. But the ocean would be less because of that missing drop.” Mother Teresa. Acknowledgements This is the last page of my dissertation that I write. I could not imagine myself in this situation, but finally it has arrived. I have written my Thesis. Now it is time to think about the process that has brought me here and express my gratitude to that people that have helped me to do it. As everybody can imagine, it is rather difficult to thank all the people that have contributed to this Thesis, along my career and also in my per- sonal life. Therefore, I would like to thank all these people since they have marked my life and there are no words to express my gratitude, especially my heroines, those women who have marked my life in any sense. They remain with me forever, wherever they may be. Firstly, I would like to highlight the work of my supervisors, Ramon´ Alvarez-Vald´ es´ and Francisco Parreno.˜ Without their help and guidance it would have been impossible to reach this step. From the beginning, they had surprising confidence in my skills and work, and they were right. Fi- nally, here I am, completing my Thesis. Many thanks for believing in me and for giving me the chance. Secondly, I would like to mention the work of my collaborators, Manuel Iori and Joaquim Gromicho, who accepted me and gave me the opportu- nity to work with them. Special thanks to Jose Tamarit, I miss those pieces of knowledge that only you have about the tools. Thirdly, I would like to thank all my teachers and lectures. I am here in great part because of your dedication to the world of teaching. I love learning. Thank you for your education you impart and your lessons in life. Fourthly, I want to express my gratitude to my family, especially my parents, Carmen and Jorge, for giving me the opportunities, that have enabled me to be here. There are no words to express my gratitude and love for them. Special thanks to Jose, my boyfriend, you always encouraged me to continue, supporting me during these years and sweetening my life every- day. Together we will be great. All of them are in this Thesis, not in the content, but they are present in the spirit that has led me here. Life continues and I hope all of them continue with me.THANK YOU. Abstract Nowadays, Logistics is an important sector in the process of making goods. The global world means that products are made in one part of the word but are purchased by customers located in another part of the word. Here is where Logistics, the process of warehousing and transportation, plays an important role in the sales process. Many optimization problems arise in this context and the companies have to take decisions that affect their economy, e.g., when the products are finished, it is necessary for them to be packed into an appropriate box, deciding which size of boxes is the correct one to meet all the demand for the different products. If the demand is big enough and the location of the customers is far away, it is usual for the products to be sent in containers. How to load the containers while trying to occupy the space as much as possible, is another decision that has to be taken. In contrast, if the cus- tomer is not far away, the products can be delivered by truck. How to place the load onto the truck in order to maximize the load while respecting the law of each country is other decision that has to be taken. All these decisions have a great impact on the cost of the products, so taking the correct decisions is important for the companies. In this Thesis we address these problems that arise in the logistic area. All the problems are real problems that companies face on a daily basis. Each chapter presents a problem with an introduction explaining the con- text, an analysis of the data provided by the companies, and our solution. We have tried to solve them by applying different methods and techniques that provide good solutions for each one. We have used mathematical models and metaheuristics to obtain solutions. All the approaches are in- troduced in each chapter, with the corresponding results and conclusions. v What we want is to solve these problems efficiently, thus providing good solutions for the companies, adding a drop, our drop, to the ocean of re- search. Contents Abstract v 1 Introduction 1 1.1 Logistics . .2 1.2 Distribution process . .5 1.3 Cutting and packing problems . 10 1.4 Motivation . 16 1.5 Thesis structure . 17 2 The problem of packing products into shippers 19 2.1 Introduction . 19 2.2 Literature review . 22 2.3 Problem formulation . 24 2.4 Lower bounds . 29 2.4.1 Bound based on a multi-knapsack problem . 30 2.4.2 Imposing the maximum number of shipper sizes . 31 2.4.3 A model based on the p-median and the facility lo- cation models . 31 2.5 Obtaining feasible solutions . 33 2.5.1 Generating packing patterns . 34 2.5.2 Reducing the set of possible shipper types . 35 2.6 Improving the feasible solution . 36 2.6.1 Reducing the size of the shipper types chosen . 36 2.6.2 Using an algorithm for the Multiple Bin-Size Bin Pack- ing Problem . 37 2.6.3 Partial substitution of the shipper types selected . 37 vii 2.7 Experimental results . 38 2.7.1 Instances . 39 2.7.2 Solving the problem defined by the sample of orders 40 2.7.3 Applying the procedures to large samples of future orders . 45 2.8 Summary . 48 3 The problem of packing shippers into containers 49 3.1 Introduction . 49 3.2 Literature review . 50 3.2.1 Container constraints . 51 3.2.2 Item constraints . 52 3.2.3 Cargo constraints . 53 3.2.4 Load constraints . 54 3.2.5 Solution approach . 54 3.2.6 Load-bearing strength . 55 3.3 Problem formulation . 57 3.4 Data structure . 58 3.5 Constructive algorithm . 60 3.6 Criteria for selecting the block to pack . 63 3.7 GRASP algorithm . 65 3.7.1 Constructive phase . 67 3.7.2 Improvement phase . 68 3.8 Computational results . 71 3.8.1 Comparing the performance of the objective functions 73 3.8.2 Choosing the best strategies . 75 3.8.3 Results of the improvement phase . 76 3.8.4 Comparison with other heuristic algorithms . 78 3.8.5 Comparison with the exact approach of Junqueira et al. [54] . 80 3.8.6 Extending the study to a new set of test instances . 82 3.9 Summary . 83 4 A case study of delivering products by trucks 85 4.1 Introduction . 85 4.1.1 Pallet building . 86 4.1.2 Truck loading . 88 4.1.3 Objective . 90 4.2 Literature review . 91 4.3 Problem Approach . 94 4.4 Approximate approach . 94 4.4.1 Problem formulation . 95 4.4.2 Data analysis . 96 4.4.3 The problem approach . 103 4.4.4 Constructive phase . 104 4.4.5 Deterministic constructive results . 107 4.4.6 Randomized constructive algorithm . 110 4.5 Solving the problem by using mathematical models . 112 4.5.1 Problem formulation . 112 4.5.2 Data analysis . 116 4.5.3 Basic models . 119 4.5.4 Introducing pallets into the model . 127 4.5.5 Additional constraints . 133 4.6 Summary . 141 5 Conclusions, Contributions and Future Work 143 5.1 Conclusions . 143 5.2 Contributions . 145 5.3 Future Work . 146 5.4 Publications and Collaborations . 147 5.4.1 Papers published in JCR journals . 148 5.4.2 International Conference Papers . 148 5.4.3 International Collaborations . 150 5.4.4 Projects . 150 5.4.5 Research activities . 151 Bibliography 153 List of Figures 1.1 Annual growth rate in EU 1995-2012 . .3 1.2 Material and information flow in logistics processes . .4 1.3 Types of containers . .9 1.4 Packing problem structure . 11 1.5 Basic C&P problems . 15 1.6 Overview of the Thesis structure . 18 2.1 Different types of shippers . 21 2.2 Two types of standard shippers sizes . 25 2.3 Percentage deviation. Shippers vs. orders . 44 2.4 Distribution of waste percentages . 46 3.1 Arrangement of three boxes . 59 3.2 Types of blocks for 12 identical boxes . 62 3.3 Improving solutions eliminating stacks . 70 3.4 An example of exchanging blocks . 71 3.5 An example of filling a partial solution . 72 3.6 Percentage occupation of each heuristic . 75 4.1 Dimensions and axles positions of the truck . 89 4.2 Cereal box . 95 4.3 Layer of cereal boxes . 96 4.4 Pallet with 4 layers of cereal boxes . 96 4.5 Truck overview, divided into two parts . 105 4.6 First floor arrangement . 106 4.7 Pallets arranged at the second level . 106 4.8 Solution for instance 1 with two trucks . 108 xi 4.9 Pallet positions on the truck floor .
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