Optimal Flexibility Configurations in Newsvendor Networks: Going Beyond Chaining and Pairing

Abstract

We study the classical problem of capacity and flexible technology selection with a newsvendor network model of resource portfolio investment. The resources differ by their level of flexibility, where "level-k flexibility" refers to the ability to process k different product types. We present an exact set-theoretic methodology to analyze newsvendor networks with multiple products and parallel resources. This simple approach is sufficiently powerful to prove that (i) flexibility exhibits decreasing returns and (ii) the optimal portfolio will invest in at most two, adjacent levels of flexibility in symmetric systems, and to characterize (iii) the optimal flexibility configuration for asymmetric systems as well. The optimal flexibility configuration can serve as a theoretical performance benchmark for other configurations suggested in the literature. For example, although chaining is not optimal in our setting, the gap is small and the inclusion of scale economies quickly favors chaining over pairing. We also demonstrate how this methodology can be applied to other settings such as product substitution and queuing systems with parameter uncertainty.inventory production, stochastic models, programming, linear, applications, queues, networks, flexibility, newsvendor networks

A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

“…This sharpens "a little flexibility is all you need"-not only the amount but, also the level of flexibility is small-and refines the findings in Bassamboo et al (2010).…”

“…This optimality follows if the objective function is convex in the capacity levels. Such a convexity is straightforward to show in the newsvendor setting of Jordan and Graves (1995) (see Van Mieghem 1998 andBassamboo et al 2010). In a queueing setting, however, this amounts to showing that the sum of the N queue-lengths is convex in the entire 2 N − 1-dimensional capacity portfolio.…”

“…While tailored flexibility is well understood in a two-product setting, finding desirable flexible processing systems for N > 2 products is much more difficult because the capacity portfolio can now consist of 2 N − 1 different resources, and hence grows exponentially in N . Recently, Bassamboo et al (2010) analyzed such a system in a newsvendor setting. To describe their key result, let "level-k flexibility" refer to the ability to process k ∈ 1 2 N different product types.…”

“…1423-1435, © 2012 flexibility, including N dedicated or specialized resources with k = 1 and one fully flexible resource with k = N . Bassamboo et al (2010) shows that, if the flexibility premiums are linear in the flexibility level, then the optimal capacity portfolio invests in at most two adjacent levels of flexibility. In this paper, we expand this result in a parallel queuing network and show that, with mild economies of scope (i.e., as long as capacity costs are not too concave in flexibility), the investment is in levels 1 and 2.…”

“…This expression corresponds to the performance of the asymptotically optimal symmetric configuration called "tailored pairing" (cf. Bassamboo et al 2010). Tailored pairing uses a dedicated resource for each arrival stream to serve the base demand, and a level-2 flexible resource for each pair of arrival streams to serve the variable demand.…”