Operations & Supply Chain Management

We analyze a single-period, stochastic inventory model (newsboy-like model) in which a sequence of heterogeneous customers dynamically substitute among product variants within a retail assortment when inventory is depleted. The customer choice decisions are based on a natural and classical utility maximization criterion. Faced with such substitution behavior, the retailer must choose initial inventory levels for the assortment to maximize expected profits.

Recent papers have developed analytical models to explain and quantify the benefits of delayed differentiation and quick response programs. These models assume that while demands in each period are random, they are independent across time and their distribution is perfectly known, i.e., sales forecasts do not need to be updated as time progresses. In this paper, we characterize these benefits in more general settings, where parameters of the demand distributions fail to be known with accuracy or where consecutive demands are correlated.

This paper integrates pricing and replenishment decisions for the following prototypical two-echelon distribution system with deterministic demands. A supplier distributes a single product to multiple retailers, who in turn sell it to consumers. The retailers serve geographically dispersed, heterogeneous markets. The demand in each retail market arrives continuously at a constant rate, which is a general decreasing function of the retail price in the market. The supplier replenishes its inventory through orders (purchases, production runs) from a source with ample capacity.

This paper evaluates the practice of determining staffing requirements in service systems with random cyclic demands by using a series of stationary queueing models. We consider Markovian models with sinusoidal arrival rates and use numerical methods to show that the commonly used "stationary independent period by period" (SIPP) approach to setting staffing requirements is inaccurate for parameter values corresponding to many real situations.

Returns policies are usually thought of as being a way to insure retailers against excess inventory. The work of Pellegrini (1986), Chu (1993), Lin (1993) and Padmanabhan and Png (1997) highlights the fact that there is considerably more to returns policies than just a mechanism for insurance. Our work identifies a heretofore undocumented rationale for returns policy: its role in learning the demand for a new product. The model of manufacturer?retailer interaction assumes that the demand is uncertain but correlated across time periods.

This paper describes a general approach for dynamic control of stochastic networks based on fluid model analysis, where in broad terms, the stochastic network is approximated by its fluid analog, an associated fluid control problem is solved and, finally, a scheduling rule for the original system is defined by itnerpreting the fluid control policy.

We investigate a simple adaptive approach to optimizing seat protection levels in airline revenue management systems. The approach uses only historical observations of the relative frequencies of certain seat-filling events to guide direct adjustments of the seat protection levels in accordance with the optimality conditions of Brumelle and McGill (1993). Stochastic approximation theory is used to prove the convergence of this adaptive algorithm to the optimal protection levels.

We study the estimation of tail probabilities in a queue via a semi-parametric estimator based on the maximum value of the workload, observed over the sampled time interval. Logarithmic consistency and efficiency issues for such estimators are considered, and their performance is contrasted with the (non-parametric) empirical tail estimator. Our results indicate that in order to "successfully" estimate and extrapolate buffer overflow probabilities in regenerative queues, it is in some sense necessary to first introduce a rough model for the behavior of the tails.

Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM).When the queue is stable, we prove that the maximum of the workload process observed over an interval of length t grows like y(log t)1/(2-2H), where H > 1/2 is the self-similarity index (also known as the Hurst parameter) that characterizes the fBM and can be explicitly computed.