248 research outputs found
Volumetric center method for stochastic convex programs using sampling
We develop an algorithm for solving the stochastic convex program (SCP) by combining Vaidya's volumetric center interior point method (VCM) for solving non-smooth convex programming problems with the Monte-Carlo sampling technique to compute a subgradient. A near-central cut variant of VCM is developed, and for this method an approach to perform bulk cut translation, and adding multiple cuts is given. We show that by using near-central VCM the SCP can be solved to a desirable accuracy with any given probability. For the two-stage SCP the solution time is independent of the number of scenarios
Optimizing Equitable Resource Allocation in Parallel Any-Scale Queues with Service Abandonment and its Application to Liver Transplant
We study the problem of equitably and efficiently allocating an arriving
resource to multiple queues with customer abandonment. The problem is motivated
by the cadaveric liver allocation system of the United States, which includes a
large number of small-scale (in terms of yearly arrival intensities) patient
waitlists with the possibility of patients abandoning (due to death) until the
required service is completed (matched donor liver arrives). We model each
waitlist as a GI/MI/1+GI queue, in which a virtual server receives a donor
liver for the patient at the top of the waitlist, and patients may abandon
while waiting or during service. To evaluate the performance of each queue, we
develop a finite approximation technique as an alternative to fluid or
diffusion approximations, which are inaccurate unless the queue's arrival
intensity is large. This finite approximation for hundreds of queues is used
within an optimization model to optimally allocate donor livers to each
waitlist. A piecewise linear approximation of the optimization model is shown
to provide the desired accuracy. Computational results show that solutions
obtained in this way provide greater flexibility, and improve system
performance when compared to solutions from the fluid models. Importantly, we
find that appropriately increasing the proportion of livers allocated to
waitlists with small scales or high mortality risks improves the allocation
equity. This suggests a proportionately greater allocation of organs to smaller
transplant centers and/or those with more vulnerable populations in an
allocation policy. While our motivation is from liver allocation, the solution
approach developed in this paper is applicable in other operational contexts
with similar modeling frameworks.Comment: 48 Page
Distributionally Robust Optimization: A Review
The concepts of risk-aversion, chance-constrained optimization, and robust
optimization have developed significantly over the last decade. Statistical
learning community has also witnessed a rapid theoretical and applied growth by
relying on these concepts. A modeling framework, called distributionally robust
optimization (DRO), has recently received significant attention in both the
operations research and statistical learning communities. This paper surveys
main concepts and contributions to DRO, and its relationships with robust
optimization, risk-aversion, chance-constrained optimization, and function
regularization
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