Asymptotic Optimality of Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems

Abstract

Dual-sourcing inventory systems, in which one supplier is faster (i.e. express) and more costly, while the other is slower (i.e. regular) and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize due to the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for over 40 years. Recently, so-called Tailored Base-Surge (TBS) policies have been proposed as a heuristic for the dual-sourcing problem. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the express source follows a simple order-up-to rule. Numerical experiments by several authors have suggested that such policies perform well as the lead time difference between the two sources grows large, which is exactly the setting in which the curse of dimensionality leads to the problem becoming intractable. However, providing a theoretical foundation for this phenomenon has remained a major open problem.In this paper, we provide such a theoretical foundation by proving that a simple TBS policy is indeed asymptotically optimal as the lead time of the regular source grows large, with the lead time of the express source held fixed. Our main proof technique combines novel convexity and lower-bounding arguments, an explicit implementation of the vanishing discount factor approach to analyzing infinite-horizon Markov decision processes, and ideas from the theory of random walks and queues, significantly extending the methodology and applicability of a novel framework for analyzing inventory models with large lead times recently introduced by Goldberg and co-authors in the context of lost-sales models with positive lead times.

Optimal Policies for a Dual-Sourcing Inventory Problem with Endogenous Stochastic Lead Times

“…In Table 9, the performance of the TBS policy improves as the lead time difference between normal source and emergency source becomes larger. This is consistent with the findings of Janakiraman et al (2015) and Xin and Goldberg (2015) for deterministic lead times.…”

“…They also show that the performance of the best TBS policy improves as the lead time difference between the two sources grows. Furthermore, assuming deterministic lead times, Xin and Goldberg (2015) prove that a TBS policy is asymptotically optimal, when the lead time from the normal source grows large while the lead time from the emergency source is fixed. More recently, Arts et al (2016) study a system in which the lead time from the emergency source is deterministic while the lead time from the normal source is the sum of a phase-type random variable and the lead time from the emergency source.…”

Optimal inventory and timing decisions for emergency shipments

“…A common assumption in these studies is that the emergency shipments have a shorter lead time than the regular replenishments. We refer the interested reader to the following recent works and the references therein: Sethi et al (2003), Bylka (2005), Veeraraghavan and Scheller-Wolf (2008), Huggins and Olsen (2010), Sheopuri et al (2010), Cheaitou and van Delft (2013), Chand et al (2016), Xin and Goldberg (2017) and Johansen (2019).…”

A bibliometrics data analysis of management science

“…To be specific, there are many studies on behavioral economics (Ozer et al 2011), supplier alliances (Granot and Sosic 2005), dual-source procurement strategy (Xin and Goldberg 2018), flexible capacity in a make-to-order environment (Bish et al 2005) in the field of supply chain management (#0). The researches of strategic consumer behavior (#1) give priority to the pricing strategy, focusing on the impacts of channel coordination mechanism on product pricing (Taylor 2001), the application of strategic consumer behavior in dynamic pricing and revenue management (Yin et al 2009;Vulcano et al 2002), the structural estimation of the model containing strategic consumer behavior under stochastic dynamic game (Li et al 2014) and the price discrimination based on consumer behaviors (Chen et al 2005).…”