We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have one-dimensional approximating Brownian control problems. We propose a simple discrete review policy for controlling such networks. Assuming 2 + ε moments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy. Contents

In this paper we present a canonical setting that illustrates the need for explicitly modeling interactions between manufacturing and marketing/sales decisions in a firm. We consider a firm that sells an innovative product with a given market potential. The firm may not be able to meet demand due to capacity constraints. For such firms, we present a new model of demand, modified from the original model of Bass, to capture the effect of unmet past demand on future demand. We use this model to find production and sales plans that maximize profit during the lifetime of the product in a firm with a fixed production capacity. We conduct an extensive numerical study to establish that the trivial, myopic sales plan that sells the maximal amount possible at each time instant is not necessarily optimal. We show that a heuristic “build-up” policy, in which the firm does not sell at all for a period of time and builds up enough inventory to never lose sales once it begins selling, is a robust approximation to the optimal policy. Specializing to a lost-sales setting, we prove that the optimal sales plan is indeed of the “build-up” type. We explicitly characterize the optimal build-up period and analytically derive the optimal initial inventory and roll-out delay. Finally, we show that the insights obtained in the fixed capacity case continue to hold when the firm is able to dynamically change capacity.

We consider a network revenue management problem with customer choice and exogenous prices. We study the performance of a class of certainty equivalent heuristic control policies. These heuristics periodically re-solve the deterministic Linear Program (DLP) that results when all future random variables are replaced by their average values and implement the solutions in a probabilistic manner. We provide an upper bound for the expected revenue loss under such policies when compared to the optimal policy. Using this bound, we construct a schedule of re-solving times such that the resulting expected revenue loss, obtained by re-solving the DLP at these times and implementing the solution as a probabilistic scheme, is bounded by a constant that is independent of the size of the problem.Key words: revenue management; customer choice; asymptotic optimality; reoptimization MSC2000 Subject Classification: Primary: 90C40 , 90C59 ; Secondary: 90B50, 90B36OR/MS subject classification: Primary: Inventory/production ; Secondary: Probability 1. Introduction. We consider a finite-horizon Revenue Management (RM) problem where a decision maker offers collections of products over a finite period at pre-determined prices for customers to choose from. The sale of products consumes resources whose inventories are pre-determined. Meeting a customer request for a product can require multiple resources simultaneously, as in an itinerary that requires a seat on each of multiple flight legs in the airline context. That is, we consider a Network RM problem with customer choice. Uncertainty in our setting arises from both the arrival of potential customers, modeled via Poisson processes, as well as their choices. The objective is to design a dynamic control policy that offers a collection of products, or simply an offer each time a customer arrives so as to maximize expected revenue earned over the entire duration of the problem. Our setting includes, but is not limited to, the classical application of seat allocation in airline RM with customer choice.

We provide a computational study of the problem of optimally allocating wealth among multiple stocks and a bank account, to maximize the infinite horizon discounted utility of consumption. We consider the situation where the transfer of wealth from one asset to another involves transaction costs that are proportional to the amount of wealth transferred. Our model allows for correlation between the price processes, which in turn gives rise to interesting hedging strategies. This results in a stochastic control problem with both drift-rate and singular controls, which can be recast as a free boundary problem in partial differential equations. Adapting the finite element method and using an iterative procedure that converts the free boundary problem into a sequence of fixed boundary problems, we provide an efficient numerical method for solving this problem. We present computational results that describe the impact of volatility, risk aversion of the investor, level of transaction costs, and correlation among the risky assets on the structure of the optimal policy. Finally we suggest and quantify some heuristic approximations.

We consider a GI/GI/1 queue with impatient customers in heavy traffic. We use the solution of an approximating singular diffusion control problem to construct an admission control policy for the queue. The approximating control problem does not admit a so-called pathwise solution. Hence, the resulting admission control policy depends on second-moment data. We prove asymptotic optimality of the constructed policy using weak-convergence methods.