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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… (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)

We visit the following fundamental problem: For a 'generic' model of consumer choice (namely, distributions over preference lists) and a limited amount of data on how consumers actually make decisions (such as marginal preference information), how may one predict revenues from offering a particular assortment of choices? This problem is central to areas… (More)

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract We study a problem of dynamic pricing faced by a vendor with limited inventory, uncertain about demand, aiming to maximize expected discounted revenue over an infinite time horizon. The vendor learns from purchase data, so his… (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)

Mainstream queueing models are frequently employed in modeling healthcare delivery in a number of settings, and further are used in making operational decisions for the same. The vast majority of these queueing models ignore the effects of delay experienced by a patient awaiting care. However, long delays may have adverse effects on patient outcomes and can… (More)

We develop an approximation algorithm for a dynamic capacity allocation problem with Markov modulated customer arrival rates. For each time period and each state of the modulating process, the algorithm approximates the dynamic programming value function using a concave function that is separable across resource inventory levels. We establish via… (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 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)

This paper presents a general class of dynamic stochastic optimization problems we refer to as Stochastic Depletion Problems. A number of challenging dynamic optimization problems of practical interest are stochastic depletion problems. Optimal solutions for such problems are difficult to obtain, both from a pragmatic computational perspective as also from… (More)