Operations & Supply Chain Management

We consider importance sampling simulation for estimating rare event probabilities in the presence of heavy-tailed distributions that have polynomial-like tails. In particular, we prove the following negative result: there does not exist an asymptotically optimal state-independent change-of-measure for estimating the probability that a random walk (respectively, queue length for a single server queue) exceeds a "high" threshold before going below zero (respectively, becoming empty).

In a decentralized supply chain, with long-term competition between independent retailers facing random demands and buying from a common supplier, how should wholesale and retail prices be specified in an attempt to maximize supply-chain-wide profits? We show what types of coordination mechanisms allow the decentralized supply chain to generate aggregate expected profits equal to the optimal profits in a centralized system, and how the parameters of these (perfect) coordination schemes can be determined.

We review queueing-theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long-run steady-state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time-dependent performance is captured and staffing requirements can be set.

In this note we present algorithms that compute, exactly or approximately, time-dependent waiting time tail probabilities and the time-dependent expected waiting time in M(t)/M/s(t) queuing systems.

We consider a family of N items that are produced in, or obtained from, the same production facility. Demands are deterministic for each item and each period within a given horizon of T periods. If in a given period an order is placed, setup costs are incurred. The aggregate order size is constrained by a capacity limit. The objective is to find a lot-sizing strategy that satisfies the demands for all items over the entire horizon without backlogging, and that minimizes the sum of inventory-carrying costs, fixed-order costs, and variable-order costs.

We characterize supply chain settings in which perfect coordination can be achieved with simple wholesale pricing schemes: either retailer-specific constant unit wholesale prices or retailer-specific volume discount schemes. We confine ourselves to two-echelon supply chains with a single supplier servicing a network of retailers who compete with each other by selecting sales quantities.

Consider a make-to-order manufacturer that offers multiple products to a market of price and delay sensitive users.

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered.

Hospital diagnostic facilities, such as magentic resonance imaging centers, typically provide service to several diverse patient groups: outpatients, who are scheduled in advance; inpatients, whose demands are generated randomly during the day; and emergency patients, who must be served as soon as posssible. Our analysis focuses on two inter-related tasks: designing the outpatient appoitnment schedule, and establishing dynamic priority rules for admitting patients into service.