Algorithm Design and Analysis of Problems in Manufacturing , Logistics , and Telecommunications : An Algorithmic Jam Session

The focus of this thesis is on algorithmic questions that are directly linked to practical problems from diverse applications like manufacturing, train scheduling or telecommunications. We present four problem settings together with combinatorial problems (or mathematical models) that are at the core of the practical applications. From this we derive both interesting theoretical and relevant practical results, which we back up by experiments. In detail, the topics of this thesis are as follows. Sequential Vector Packing We study a novel variant of the well known d-dimensional bin (or vector) packing problem that is motivated by an application from the manufacturing industry. Given a sequence of non-negative d-dimensional vectors, the goal is to pack these into as few bins as possible. In the classical problem the bin size vector is given and the sequence can be partitioned arbitrarily. We study a variation where the vectors have to be packed in the order in which they arrive. The bin size vector can be chosen once in the beginning, under the constraint that the coordinate-wise bounds sum up to at most a given total bin size. We give both theoretical results and practical algorithms that we test on the original data. Optimization of a Freight Train System We consider the optimization of a Swiss freight train service that is operated as a (multi-) hub spoke system. This can be seen as a more complicated version of classical vehicle routing problems. We derive several mathematical models, consider some theoretical questions linked to the operations at the hub, and test our models on the real-world instance. For the mathematical models we use linear programming based optimization techniques like branch and cut and column generation. OVSF Code Assignment Orthogonal Variable Spreading Factor (OVSF-) codes are used in UMTS to share the radio spectrum among several connections of possibly different bandwidth requirements. The combinatorial core of the OVSF code assignment problem is to assign some nodes of a complete binary tree of height h (the code tree) to n simultaneous connections, such that no two assigned nodes (codes) are on the same root-to-leaf path. A connection that uses a 2 fraction of the total bandwidth requires some code at depth d in the tree, but this code assignment is allowed to change over time. We consider the one-step code assignment problem: Given an assignment, move the minimum number of codes to serve a new request. Minn and Siu propose the so-called DCA-algorithm to solve the problem