Mathematics of Operations Research

We propose a two-stage risk-averse stochastic optimization problem with a stochastic-order constraint on a vector-valued function of the second-stage decisions. This model is motivated by a multiobjective second-stage problem. We formulate optimality ...

The cutting plane approach to finding minimum-cost perfect matchings has been discussed by several authors over past decades. Its convergence has been an open question. We develop a cutting plane algorithm that converges in polynomial-time using only ...

We study the asymptotics of a class of two-player, zero-sum stochastic game with incomplete information on one side when the time span between two consecutive stages vanishes. The informed player observes the realization of a Markov chain on which the ...

The network revenue management (RM) problem arises in airline, hotel, media, and other industries where the sale products use multiple resources. It can be formulated as a stochastic dynamic program, but the dynamic program is computationally intractable ...

The theory of dynamic programming is formulated using finitely additive probability measures defined on sets of arbitrary cardinality. Many results from the conventional countably additive theory generalize, and the proofs are simpler.

We study a class of stochastic target games where one player tries to find a strategy such that the state process almost surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic programming ...

We study a class of games with a continuum of players for which a Cournot-Nash equilibria can be obtained by the minimisation of some cost related to optimal transport. This cost is not convex in the usual sense, in general, but it turns out to have ...

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. By contrast to the standard setting, a possibly nonconcave utility function U is ...

We propose a general discrete-time framework for deriving equilibrium prices of financial securities. It allows for heterogeneous agents, unspanned random endowments, and convex trading constraints. We give a dual characterization of equilibria and ...

We consider the problem of minimizing a general continuously differentiable function over symmetric sets under sparsity constraints. These type of problems are generally hard to solve because the sparsity constraint induces a combinatorial constraint into ...

This work is concerned with finite-state irreducible Markov decision chains satisfying continuity-compactness requirements. It is supposed that the system is driven by a decision maker with utility function U, which, aside mild conditions, is arbitrary, ...

We develop asymptotic approximations for the tail probabilities of integrals of lognormal random fields. We consider the asymptotic regime that the variance of the random field converges to zero. Under this setting, the integral converges to its limiting ...

In this paper, we study the classical no-wait flowshop scheduling problem with makespan objective (F|no-wait|C_max in the standard three-field notation). This problem is well known to be a special case of the asymmetric traveling salesman problem (ATSP) ...

We initiate the study of congestion games with variable demands in which the players strategically choose both a nonnegative demand and a subset of resources. The players’ incentives to use higher demands are stimulated by nondecreasing and concave ...

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case, all players receive zero ...

Quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry. The recent discovery that efficient simulation-based estimators can be obtained for quantile sensitivities has led to ...

The capacitated vehicle routing problem (CVRP) involves distributing identical items from a depot to a set of demand locations using a single capacitated vehicle. We introduce the heterogeneous capacitated vehicle routing problem, a generalization of CVRP ...

We present a unified framework for designing deterministic monotone polynomial time approximation schemes (PTASs) for a wide class of scheduling problems on uniformly related machines. This class includes (among others) minimizing the makespan, maximizing ...

We investigate computational and mechanism design aspects of allocating medical treatments at hospitals of different costs to patients who each value these hospitals differently. The payer wants to ensure that the total cost of all treatments is at most ...