Algorithms for the Bin Packing Problem with Scenarios

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For this problem, we propose an absolute approximation algorithm whose ratio is bounded by the square root of the number of scenarios times the approximation ratio for an algorithm for the vector bin packing problem. We also show how an asymptotic polynomial-time approximation scheme is derived when the number of scenarios is constant. As a practical study of the problem, we present a branch-and-price algorithm to solve an exponential model and a variable neighborhood search heuristic. To speed up the convergence of the exact algorithm, we also consider lower bounds based on dual feasible functions. Results of these algorithms show the competence of the branch-and-price in obtaining optimal solutions for about 59% of the instances considered, while the combined heuristic and branch-and-price optimally solved 62% of the instances considered

Online Bin Covering with Limited Migration

Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective. In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small epsilon). We therefore resolve the competitiveness of the bin covering problem with migration

Bin Packing through Machine Learning

In this thesis project we propose a wide range of Machine Learning techniques for dealing with the Bin Packing problem. The business domain is transportation optimization, a popular application field of Operational Research methods. The work is inspired by a real project by the consulting firm Horsa Group. The aim is to inspect the business problem from a mathematical point of view and to focus on different state-of-the-art techniques involving Machine Learning. The objective is to give an overview of the different possible approaches for further developments and compare the pros and cons of possible solutions. We will also compare the performances of those techniques on generated example data and real-world data. The final goal is to reduce the costs of the shipping process by increasing efficiency. The focus will be on how the shipping pallets are composed, packing the items with an efficient and scalable framework. The road map consists in defining in a formal way the Operational Research problem and the business problem, to compare classical approaches with some of the methods that nowadays are more and more popular and involve Machine Learning techniques. Some of those approaches involve Deep Reinforcement Learning and Graph Neural Networks. Finally, we will inspect a wide range of possibilities for making the bin packing process more efficient, simulating different real case scenarios. The aim is to give a clear overview of future developments in Bin Packing Optimization algorithms. Those developments can make the company’s shipping software scalable and well-performing, with more efficient use of resources.In this thesis project we propose a wide range of Machine Learning techniques for dealing with the Bin Packing problem. The business domain is transportation optimization, a popular application field of Operational Research methods. The work is inspired by a real project by the consulting firm Horsa Group. The aim is to inspect the business problem from a mathematical point of view and to focus on different state-of-the-art techniques involving Machine Learning. The objective is to give an overview of the different possible approaches for further developments and compare the pros and cons of possible solutions. We will also compare the performances of those techniques on generated example data and real-world data. The final goal is to reduce the costs of the shipping process by increasing efficiency. The focus will be on how the shipping pallets are composed, packing the items with an efficient and scalable framework. The road map consists in defining in a formal way the Operational Research problem and the business problem, to compare classical approaches with some of the methods that nowadays are more and more popular and involve Machine Learning techniques. Some of those approaches involve Deep Reinforcement Learning and Graph Neural Networks. Finally, we will inspect a wide range of possibilities for making the bin packing process more efficient, simulating different real case scenarios. The aim is to give a clear overview of future developments in Bin Packing Optimization algorithms. Those developments can make the company’s shipping software scalable and well-performing, with more efficient use of resources

Generalized Assignment of Time-Sensitive Item Groups

We study the generalized assignment problem with time-sensitive item groups (chi-AGAP). It has central applications in advertisement placement on the Internet, and in virtual network embedding in Cloud data centers. We are given a set of items, partitioned into n groups, and a set of T identical bins (or, time-slots). Each group 1 0 and a non-negative utility u_{it} when packed into bin t in chi_j. A bin can accommodate at most one item from each group and the total size of the items in a bin cannot exceed its capacity. The goal is to find a feasible packing of a subset of the items in the bins such that the total utility from groups that are completely packed is maximized. Our main result is an Omega(1)-approximation algorithm for chi-AGAP. Our approximation technique relies on a non-trivial rounding of a configuration LP, which can be adapted to other common scenarios of resource allocation in Cloud data centers