Packing a Knapsack of Unknown Capacity

We study the problem of packing a knapsack without knowing its capacity. Whenever we attempt to pack an item that does not fit, the item is discarded; if the item fits, we have to include it in the packing. We show that there is always a policy that packs a value within factor 2 of the optimum packing, irrespective of the actual capacity. If all items have unit density, we achieve a factor equal to the golden ratio. Both factors are shown to be best possible. In fact, we obtain the above factors using packing policies that are universal in the sense that they fix a particular order of the items and try to pack the items in this order, independent of the observations made while packing. We give efficient algorithms computing these policies. On the other hand, we show that, for any alpha>1, the problem of deciding whether a given universal policy achieves a factor of alpha is coNP-complete. If alpha is part of the input, the same problem is shown to be coNP-complete for items with unit densities. Finally, we show that it is coNP-hard to decide, for given alpha, whether a set of items admits a universal policy with factor alpha, even if all items have unit densities

Feasibility Tests for Recurrent Real-Time Tasks in the Sporadic DAG Model

A model has been proposed in [Baruah et al., in Proceedings of the IEEE Real-Time Systems Symposium 2012] for representing recurrent precedence-constrained tasks to be executed on multiprocessor platforms, where each recurrent task is modeled by a directed acyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and have to be completed within some specified relative deadline. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The feasibility problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines on a specified number of dedicated processors. The case of a single task has been considered in [Baruah et al., 2012]. The main contribution of this paper is to consider the case of multiple tasks. We show that EDF has a speedup bound of 2-1/m, where m is the number of processors. Moreover, we present polynomial and pseudopolynomial schedulability tests, of differing effectiveness, for determining whether a set of sporadic DAG tasks can be scheduled by EDF to meet all deadlines on a specified number of processors

Fast Robust Shortest Path Computations

We develop a fast method to compute an optimal robust shortest path in large networks like road networks, a fundamental problem in traffic and logistics under uncertainty. In the robust shortest path problem we are given an s-t-graph D(V,A) and for each arc a nominal length c(a) and a maximal increase d(a) of its length. We consider all scenarios in which for the increased lengths c(a) + bar{d}(a) we have bar{d}(a) <= d(a) and sum_{a in A} (bar{d}(a)/d(a)) <= Gamma. Each path is measured by the length in its worst-case scenario. A classic result [Bertsimas and Sim, 2003] minimizes this path length by solving (|A| + 1)-many shortest path problems. Easily, (|A| + 1) can be replaced by |Theta|, where Theta is the set of all different values d(a) and 0. Still, the approach remains impractical for large graphs. Using the monotonicity of a part of the objective we devise a Divide and Conquer method to evaluate significantly fewer values of Theta. This methods generalizes to binary linear robust problems. Specifically for shortest paths we derive a lower bound to speed-up the Divide and Conquer of Theta. The bound is based on carefully using previous shortest path computations. We combine the approach with non-preprocessing based acceleration techniques for Dijkstra adapted to the robust case. In a computational study we document the value of different accelerations tried in the algorithm engineering process. We also give an approximation scheme for the robust shortest path problem which computes a (1 + epsilon)-approximate solution requiring O(log(d^ / (1 + epsilon))) computations of the nominal problem where d^ := max d(A) / min (d(A){0})

Robust Appointment Scheduling

Health care providers are under tremendous pressure to reduce costs and increase quality of their services. It has long been recognized that well-designed appointment systems have the potential to improve utilization of expensive personnel and medical equipment and to reduce waiting times for patients. In a widely influential survey on outpatient scheduling, Cayirli and Veral (2003) concluded that the "biggest challenge for future research will be to develop easy-to-use heuristics." We analyze the appointment scheduling problem from a robust-optimization perspective, and we establish the existence of a closed-form optimal solution--arguably the simplest and best `heuristic\u27 possible. In case the order of patients is changeable, the robust optimization approach yields a novel formulation of the appointment scheduling problem as that of minimizing a concave function over a supermodular polyhedron. We devise the first constant-factor approximation algorithm for this case

Online railway delay management: Hardness, simulation and computation

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Delays in a railway network are a common problem that railway companies face in their daily operations. When a train is delayed, it may either be beneficial to let a connecting train wait so that passengers in the delayed train do not miss their connection, or it may be beneficial to let the connecting train depart on time to avoid further delays. These decisions naturally depend on the global structure of the network, on the schedule, on the passenger routes and on the imposed delays. The railway delay management (RDM) problem (in a broad sense) is to decide which trains have to wait for connecting trains and which trains have to depart on time. The offline version (i.e. when all delays are known in advance) is already NP-hard for very special networks. In this paper we show that the online railway delay management (ORDM) problem is PSPACE-hard. This result justifies the need for a simulation approach to evaluate wait policies for ORDM. For this purpose we present TOPSU—RDM, a simulation platform for evaluating and comparing different heuristics for the ORDM problem with stochastic delays. Our novel approach is to separate the actual simulation and the program that implements the decision-making policy, thus enabling implementations of different heuristics to ‘‘compete’’ on the same instances and delay distributions. We also report on computational results indicating the worthiness of developing intelligent wait policies. For RDM and other logistic planning processes, it is our goal to bridge the gap between theoretical models, which are accessible to theoretical analysis, but are often too far away from practice, and the methods which are used in practice today, whose performance is almost impossible to measure.EU/FP6/021235-2/EU/Algorithms for Robust and on-line Railway optimisation: Improving the validity and reliability of large-scale systems/ARRIVA

Integration of SAP Campus Management into a University SOA

This case study depicts the integration of a legacy university resource planning system (URP) into a Service-oriented Architecture (SOA). The idea is to add the functionality of generating so-called Bologna-conforming Transcript of Records to SAP Campus Management (SAP CM). This is done by adding Web service interfaces to SAP CM that are orchestrated in the SOA using the Business Process Execution Language (BPEL). User Interaction is handled via a central University Portal

Strong formulations for the Multi-module PESP and a quadratic algorithm for Graphical Diophantine Equation Systems

The Periodic Event Scheduling Problem (PESP) is the method of choice for real-world periodic timetabling in public transport. Its MIP formulation has been studied intensely for the case of uniform modules, i.e., when all events have the same period. In practice, multiple modules are equally important. The strength of current methods for uniform modules rests on three ingredients: Every feasible instance allows for an optimal solution with a certain structure. Therefore, it can be reformulated with the use of an integral cycle basis. Finally, a certain type of rounding cuts arising from cycles has proven very powerful. All of this fails in the multi-module case. Therefore, applications with multiple periods were hardly solvable so far. We analyze a certain type of Diophantine equation systems closely related to the multi-module PESP. Thereby, we identify a structure, so-called sharp trees, that allows to solve the system in O (n^2) time. We show, a sharp tree is guaranteed to exist and found by a similar algorithm, if the modules form a linear lattice. Based on this we develop the machinery to solve multi-module PESPs on real-world scale. In particular, we recover all three ingredients for the multi-module case. In our computational results the new MIP-formulations drastically improve the solvability of multi-module PESPs. We also demonstrate that without sharp trees no similar approach can be hoped for

Increasing speed scheduling and Flow scheduling

Network flows and scheduling have been studied intensely, but separately. In many applications a joint optimization model for routing and scheduling is desireable. Therefore, we study flows over time with a demand split into jobs. The objective is to minimize the weighted sum of completion times of these jobs. This is closely related to preemptive scheduling on a single machine with a processing speed increasing over time. For both, flow scheduling and increasing speed scheduling, we provide an EPTAS. Without release dates we can proof a tight approximation factor of (sqrt{3}+1)/2 for Smith's rule, by fully characterizing the worst case instances. We give exact algorithms for some special cases and a dynamic program for speed functions with a constant number of speeds. We can proof a competitive ratio of 2 for the online version. We also study the class of blind algorithms, i.e., those which schedule without knowledge of the speed function. For both online, and blind algorithm we provide a lower bound