On the Design of Sparse But Efficient Structures in Operations

Production and Operations Management

2021

Section: Distribution Ambiguity When Certain Incomplete Distribution Information Ismentioning

confidence: 99%

Section: Efficient Computation For Robust Ommentioning

confidence: 99%

A Review of Robust Operations Management under Model Uncertainty

Production and Operations Management

2021

“…The work of Jordan and Graves (1995) has also been extended in other settings, such as in multistage supply chains (Graves and Tomlin 2003), queueing systems (Bassamboo et al 2012, Gurumurthi andBenjaafar 2004), queueing networks (Iravani et al 2005), and newsvendor networks (Bassamboo et al 2010). In addition, the flexibility design problems are further investigated via optimization approaches, such as stochastic programming model (Mak and Shen 2009) and distributionally robust model (Yan et al 2018).…”

Section: Literature Reviewmentioning

confidence: 99%

Reliable Flexibility Design of Supply Chains Via Extended Probabilistic Expanders

Liang

Production and Operations Management

et al. 2019

Self Cite

It is well‐known that adding a little flexibility to the right place is an effective strategy to improve the performance of operations in the face of demand uncertainties, to ensure high level of capacity utilization. However, given that system disruptions are ubiquitous, the legacy flexibility designs may perform poorly under disruptions to supply or capacity installations. In this study, we focus on the design of reliable and sparse flexibility structures that consistently meet a reasonable performance criterion under disruptions to both demand and supply. Specifically, we propose a class of structures termed as extended probabilistic expanders, based on the conjecture that the expansion property, rather than the global connectivity, is critical to good performance of the structures. We prove that for a system with n retailers, essentially only O(n) supply routes between suppliers and retailers are necessary to ensure good performance under disruption. In addition, we present an efficient randomized algorithm to construct extended probabilistic expanders, and demonstrate that the construction yields very good structure with the least number of edges asymptotically. We also investigate an extension to systems with structural constraints. Numerical results demonstrate that our design has not only a wide range of applications, but also better performance than a variety of known structures.

“…Against this backdrop, we should mention that the ADMM-type algorithms that have been progressively designed in [48,30,6] not only come with convergence guarantee but they have also been demonstrated to have superior numerical performance than the directly extended ADMM, at least for a large number of convex conic programming problems. More recently, those algorithms have found applications in various areas [1,2,9,17,27,31,53,55,56]. Among those algorithms, the most general and versatile one is the recently developed inexact majorized multi-block proximal ADMM in Chen et al [6], which we shall briefly describe in the next paragraph.…”

Section: Introductionmentioning

confidence: 99%

On the equivalence of inexact proximal ALM and ADMM for a class of convex composite programming

Chen

Sun

et al. 2019

Math. Program.

In this paper, we show that for a class of linearly constrained convex composite optimization problems, an (inexact) symmetric Gauss-Seidel based majorized multi-block proximal alternating direction method of multipliers (ADMM) is equivalent to an inexact proximal augmented Lagrangian method (ALM). This equivalence not only provides new perspectives for understanding some ADMM-type algorithms but also supplies meaningful guidelines on implementing them to achieve better computational efficiency. Even for the two-block case, a by-product of this equivalence is the convergence of the whole sequence generated by the classic ADMM with a step-length that exceeds the conventional upper bound of (1 + √ 5)/2, if one part of the objective is linear. This is exactly the problem setting in which the very first convergence analysis of ADMM was conducted by Gabay and Mercier in 1976, but, even under notably stronger assumptions, only the convergence of the primal sequence was known. A collection of illustrative examples are provided to demonstrate the breadth of applications for which our results can be used. Numerical experiments on solving a large number of linear and convex quadratic semidefinite programming problems are conducted to illustrate how the theoretical results established here can lead to improvements on the corresponding practical implementations.