An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks

We model evacuation in emergency situations by dynamic flow in a network. We want to minimize the aggregate evacuation time to an evacuation center (called a sink) on a path network with uniform edge capacities. The evacuees are initially located at the vertices, but their precise numbers are unknown, and are given by upper and lower bounds. Under this assumption, we compute a sink location that minimizes the maximum "regret." We present the first sub-cubic time algorithm in n to solve this problem, where n is the number of vertices. Although we cast our problem as evacuation, our result is accurate if the "evacuees" are fluid-like continuous material, but is a good approximation for discrete evacuees

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

E-commerce shipping through a third-party supply chain

We consider an e-commerce retailer who must ship orders from a warehouse to a set of customers with delivery deadlines. As is often the case, the retailer uses a third-party service provider to ensure its distribution. The retailer can enter the supply chain of the service provider at various levels. Entering it at a higher level entails lower sorting costs for the retailer, but higher delivery costs, and longer delivery times. The customer orders arrive at various moments over a rolling planning horizon. This means that the retailer must also make consolidation decisions. We model and solve the static and dynamic cases of this problem. The static case is modeled as an integer linear program and solved by CPLEX. We develop and compare four shipping policies for the dynamic case. Extensive computational results based on real location data from California and Texas are reported.</p