Vivek F. Farias

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In this paper we study resource allocation problems that involve multiple self-interested parties or players, and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a “fair” allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus(More)
We present a novel linear program for the approximation of the dynamic programming costto-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural ‘projection’ of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are(More)
T paper deals with a basic issue: How does one approach the problem of designing the “right” objective for a given resource allocation problem? The notion of what is right can be fairly nebulous; we consider two issues that we see as key: efficiency and fairness. We approach the problem of designing objectives that account for the natural tension between(More)
We introduce the pathwise optimization (PO) method, a new convex optimization procedure to produce upper and lower bounds on the optimal value (the ‘price’) of a high-dimensional optimal stopping problem. The PO method builds on a dual characterization of optimal stopping problems as optimization problems over the space of martingales, which we dub the(More)
A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the ‘right’ model of choice to use. Thus motivated, we visit the following problem: For a ‘generic’ model of consumer choice (namely,(More)
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP naturally restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program – the ‘smoothed approximate linear program’ – relaxes this(More)
The present paper develops a simple, easy to interpret algorithm for a large class of dynamic allocation problems with unknown, volatile demand. Potential applications include ad display problems and network revenue management problems. The algorithm operates in an online fashion and relies on reoptimization and forecast updates. The algorithm is robust (as(More)