A deep cut ellipsoid algorithm for convex programming

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported

On the Introduction of an Agile, Temporary Workforce into a Tandem Queueing System

We consider a two-station tandem queueing system where customers arrive according to a Poisson process and must receive service at both stations before leaving the system. Neither queue is equipped with dedicated servers. Instead, we consider three scenarios for the fluctuations of workforce level. In the first, a decision-maker can increase and decrease the capacity as is deemed appropriate; the unrestricted case. In the other two cases, workers arrive randomly and can be rejected or allocated to either station. In one case the number of workers can then be reduced (the controlled capacity reduction case). In the other they leave randomly (the uncontrolled capacity reduction case). All servers are capable of working collaboratively on a single job and can work at either station as long as they remain in the system. We show in each scenario that all workers should be allocated to one queue or the other (never split between queues) and that they should serve exhaustively at one of the queues depending on the direction of an inequality. This extends previous studies on flexible systems to the case where the capacity varies over time. We then show in the unrestricted case that the optimal number of workers to have in the system is non-decreasing in the number of customers in either queue.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47647/1/11134_2005_Article_2441.pd