SIAM Journal on Scientific and Statistical Computing
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Lower bounds for multi-echelon stochastic inventory systems
Management Science
Stock Positioning and Performance Estimation in Serial Production-Transportation Systems
Manufacturing & Service Operations Management
Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem
Transportation Science
Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains
Management Science
Application of the Fast Gauss Transform to Option Pricing
Management Science
Fill Rates of Single-Stage and Multistage Supply Systems
Manufacturing & Service Operations Management
A Series System with Returns: Stationary Analysis
Operations Research
Optimal Control of a High-Volume Assemble-to-Order System
Mathematics of Operations Research
A Numerical Method for Solving Singular Stochastic Control Problems
Operations Research
Queueing Systems: Theory and Applications
Newsvendor equations for optimal reorder levels of serial inventory systems with fixed batch sizes
Operations Research Letters
A new algorithm and a new heuristic for serial supply systems
Operations Research Letters
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A supply stream is a continuous version of a supply chain. It is like a series inventory system, but stock can be held at any point along a continuum, not just at discrete stages. We assume stationary parameters and aim to minimize the long-run average total cost. We show that a stationary continuous-stage echelon base-stock policy is optimal. That is, at each geographic point along the supply stream, there is a target echelon inventory level, and the optimal policy at all times is to order and dispatch material so as to move the echelon inventory position as close as possible to this target. We establish this result by showing that the solutions to certain discrete-stage systems converge monotonically to a limit, as the distances between the stages become small, and this limit solves the continuous-stage system. With demand approximated by a Brownian motion, we show that, in the continuous-stage limit, the supply stream model is equivalent to one describing first-passage times. This linkage leads to some interesting and useful results. Specifically, we obtain a partial differential equation that characterizes the optimal cost function, and we find a closed-form expression for the optimal echelon base-stock levels in a certain special case, the first in the inventory literature. These expressions demonstrate that the well-known square-root law for safety stock does not apply in this context.