130 research outputs found
A decomposition theory for vertex enumeration of convex polyhedra
In the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorit
Strain-aware assembly of genomes from mixed samples using flow variation graphs
The goal of strain-aware genome assembly is to reconstruct all individual haplotypes from a mixed sample at the strain level and to provide abundance estimates for the strains
Stochastic and Robust Scheduling in the Cloud
Users of cloud computing services are offered rapid access to computing resources via the Internet.
Cloud providers use different pricing options such as (i) time slot reservation in advance at a fixed
price and (ii) on-demand service at a (hourly) pay-as-used basis. Choosing the best combination
of pricing options is a challenging task for users, in particular, when the instantiation of computing
jobs underlies uncertainty.
We propose a natural model for two-stage scheduling under uncertainty that captures such
resource provisioning and scheduling problem in the cloud. Reserving a time unit for processing
jobs incurs some cost, which depends on when the reservation is made: a priori decisions, based
only on distributional information, are much cheaper than on-demand decisions when the actual
scenario is known. We consider both stochastic and robust versions of scheduling unrelated
machines with objectives of minimizing the sum of weighted completion times Pj wjCj and the makespan maxj Cj . Our main contribution is an (8+)-approximation algorithm for the min-sum
objective for the stochastic polynomial-scenario model. The same technique gives a (7.11 + )-
approximation for minimizing the makespan. The key ingredient is an LP-based separation
of jobs and time slots to be considered in either the first or the second stage only, and then
approximately solving the separated problems. At the expense of another our results hold for
any arbitrary scenario distribution given by means of a black-box. Our techniques also yield
approximation algorithms for robust two-stage scheduling
Minimizing bed occupancy variance by scheduling patients under uncertainty
International audienceIn this paper we consider the problem of scheduling patients in allocated surgery blocks in a Master Surgical Schedule. We pay attention to both the available surgery blocks and the bed occupancy in the hospital wards. More specifically, large probabilities of overtime in each surgery block are undesirable and costly, while large fluctuations in the number of used beds requires extra buffer capacity and makes the staff planning more challenging. The stochastic nature of surgery durations and length of stay on a ward hinders the use of classical techniques. Transforming the stochastic problem into a deterministic problem does not result into practically feasible solutions. In this paper we develop a technique to solve the stochastic scheduling problem, whose primary objective it to minimize variation in the necessary bed capacity, while maximizing the number of patients operated, and minimizing the maximum waiting time, and guaranteeing a small probability of overtime in surgery blocks. The method starts with solving an Integer Linear Programming (ILP) formulation of the problem, and then simulation and local search techniques are applied to guarantee small probabilities of overtime and to improve upon the ILP solution. Numerical experiments applied to a Dutch hospital show promising results
A probabilistic analysis of the multiknapsack value function
The optimal solution value of the multiknapsack problem as a function of the knapsack capacities is studied under the assumption that the profit and weight coefficients are generated by an appropriate random mechanism. A strong asymptotic characterization is obtained, that yiclds a closed form expression for certain special cases
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