We consider robust shortest path problems, where the aim is to find a path that optimizes the worst-case performance over an uncertainty set containing all relevant scenarios for arc costs. The usual approach for such problems is to assume this uncertainty set given by an expert who can advise on the shape and size of the set.Following the idea of data-driven robust optimization, we instead construct a range of uncertainty sets from the current literature based on real-world traffic measurements provided by the City of Chicago. We then compare the performance of the resulting robust paths within and outside the sample, which allows us to draw conclusions what the most suited uncertainty set is.Based on our experiments, we then focus on ellipsoidal uncertainty sets, and develop a new solution algorithm that significantly outperforms a stateof-the-art solver.robust shortest path problems, on the other hand, are NP-hard (see [20]), and real-time information has not been an option.To formulate a robust problem, it is necessary to have a description of all possible and relevant scenarios that the solution should prepare against, the so-called uncertainty set. We refer to the surveys [1,16,17] for a general overview on the topic. The current literature on robust shortest paths usually assumes this set to be given, by some mixture of data-preprocessing and expert knowledge that is not part of the study. This means that different types of sets have been studied (compare, e.g., [18,9]), but it has been impossible to address the question which would be the "right" choice.A recent paradigm shift is data-driven robust optimization (see [6]), where building the uncertainty set from raw observations is part of the robust optimization problem. This paper is the first to follow such a perspective for shortest path problems. Based on real-world observations from the City of Chicago, we build a range of uncertainty sets, calculate the corresponding robust solutions, and perform an in-depth analysis of their performance. This allows us to give an indication which set is actually suitable for our application, and which are not.In the second part of this paper, we then focus on the case of ellipsoidal uncertainty, and provide a branch-and-bound algorithm that is able to solve instances considerably faster than an off-the-shelf solver.Parts of this paper were previously published as a conference paper in [15]. In comparison, we provide a completely new set of experimental results based on an observation period of 46 days (instead of one single day), which leads to a more detailed insight into the performance of different uncertainty sets. Furthermore, we provide a new analysis for axis-parallel ellipsoidal uncertainty sets, including an efficient branch-and-bound algorithm that is able to outperform Cplex by several orders of magnitude, pushing robust shortest paths towards applicability in real-time navigation systems.The remainder of the paper is structured as follows. In Section 2 we briefly introduce the robust shortest path probl...

Motivated by the yield optimization problem in semiconductor manufacturing, we model the wafer to wafer integration problem as a special multi-dimensional assignment problem (called WWI-m), and study it from an approximation point of view. We give approximation algorithms achieving an approximation factor of 3 2 and 4 3 for WWI-3, and we show that extensions of these algorithms to the case of arbitrary m do not give constant factor approximations. We argue that a special case of the yield optimization problem can be solved in polynomial time.

We consider a special class of axial multi-dimensional assignment problems called multidimensional vector assignment (MVA) problems. An instance of the MVA problem is defined by m disjoint sets, each of which contains the same number n of p-dimensional vectors with nonnegative integral components, and a cost function defined on vectors. The cost of an m-tuple of vectors is defined as the cost of their component-wise maximum. The problem is now to partition the m sets of vectors into n m-tuples so that no two vectors from the same set are in the same m-tuple and so that the sum of the costs of the m-tuples is minimized. The main motivation comes from a yield optimization problem in semi-conductor manufacturing. We consider a particular class of polynomial-time heuristics for MVA, namely the sequential heuristics, and we study their approximation ratio. In particular, we show that when the cost function is monotone and subadditive, sequential heuristics have a finite approximation ratio for every fixed m. Moreover, we establish smaller approximation ratios when the cost function is submodular and, for a specific sequential heuristic, when the cost function is additive. We provide examples to illustrate the tightness of our analysis. Furthermore, we show that the MVA problem is APX-hard even for the case m = 3 and for binary input vectors. Finally, we show that the problem can be solved in polynomial time in the special case of binary vectors with fixed dimension p.

Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews. Area Editors: Approximation and heuristics Gerhard J. Woeginger The area covers all issues relevant to the development of efficient approximate solutions to computationally difficult problems. Examples are heuristic approaches like local search, worst case analysis or competitive analysis of approximation algorithms, complexity theoretic results, and computational investigations of heuristic approaches. Continuous optimization Hector Ramrez Cabrera Papers in all fields of continuous optimization that are relevant to operations research are welcome. These areas include, but are not restricted to, nonlinear programming (constrained or unconstrained, convexor nonconvex, smooth or nonsmooth, exact or heuristic, finite or infinite-dimensional), complementarity, variational inequalities, bilevel programming, and mathematical programs with equilibrium constraints. Financial engineering Kumar Muthuraman Financial engineering utilizes operations research methods (such as optimization, simulation, decision analysis and stochastic control) to analyze financial markets. This area is interested in papers that innovate in terms of methods or models that help financial applications. The studied problem examples include the pricing and hedging of financial instruments, credit and energy markets and portfolio selection AUTHOR INFORMATION PACK 29 Oct 2020 www.elsevier.com/locate/orl 2 Game theory Tristan Tomala The area published papers in game theory with relevance to the field of operations research. Graphs and networks Gianpaolo Oriolo The area seeks papers that apply, in original and insightful ways, discrete mathematics to advance the theory and practice of operations research, as well as those reporting theoretical or algorithmic advances for the area.Of particular, but not exclusive, interest are papers devoted to novel applications, telecommunications and transportation networks, graphs and web models and algorithms. Inventory control Sridhar Seshadri The area welcomes innovative papers focused on inventory management. Examples of topics include, but are not limited to supply chain management, pricing, capacity planning, multi-item/e...

We consider the multi-level bottleneck assignment problem (MBA). This problem is described in the recent book "Assignment Problems" by Burkard et al. (2009) on pages 188-189. One of the applications described there concerns bus driver scheduling. We view the problem as a special case of a bottleneck m-dimensional multi-index assignment problem. We give approximation algorithms and inapproximability results, depending upon the completeness of the underlying graph.