1.79-Approximation Algorithms for Continuous Review Single-Sourcing Lost-Sales and Dual-Sourcing Inventory Models

Stochastic inventory systems with lead times are often challenging to optimize, including single-sourcing lost-sales and dual-sourcing systems. Recent numerical results suggest that capped policies demonstrate superior performance over existing heuristics. However, the superior performance lacks a theoretical foundation. In “1.79-Approximation Algorithms for Continuous Review Single-Sourcing Lost-Sales and Dual-Sourcing Inventory Models,” the author provides a theoretical foundation for this phenomenon in two classical inventory models. First, in a continuous review lost-sales model with lead times and Poisson demand, he proves that a capped base-stock policy has a worst-case performance guarantee of 1.79 by conducting an asymptotic analysis under a large penalty cost and lead time. Second, in a more complex continuous review dual-sourcing model with general lead times and Poisson demand, he proves that a similar capped dual-index policy has a worst-case performance guarantee of 1.79 under large lead time and ordering cost differences. The results provide a deeper understanding of the superior numerical performance of capped policies and present a new approach to proving worst-case performance guarantees of simple policies in hard inventory problems.

The Window Fill Rate in a Multiple Location Inventory System with Periodic Review and Order Crossover

Deliveries in global supply chains are often made through lengthy shipping routes that are subject to many delays such as border crossings, inspections and so forth. Consequently, orders frequently crossover, that is, their order of arrival is not the same as the order that they were issued. In this paper we model a multiple location inventory system with Poisson demand and periodic review in which orders may crossover. The system’s performance measure is the window fill rate, i.e., the probability that a customer arriving to the system is served within her tolerable wait. We show that when spares are scarce the system’s overall performance decreases if spares are allotted equitably. Additionally, we show that there is a linear tradeoff between the tolerable wait and the number of spares needed to maintain a given performance level. The observations have practical implications to inventory mangers. First, that when resources are scarce it is optimal to cluster spares to only few locations. In contrast, when resources are abundant, then a more equitable solution is optimal. Second, that it is possible to design simple contracts that reward customers for their patience, or alternatively, that charge customers a premium for expedited service.