Reliable Facility Location Design Under Uncertain Correlated Disruptions

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.

“…We justify this compromise by pointing out that positively correlated disruptions are more commonly observed in practice, as is suggested by Lu et al. ().…”

Section: Introductionmentioning

confidence: 64%

Reliable Flexibility Design of Supply Chains Via Extended Probabilistic Expanders

Liang

Production and Operations Management

et al. 2019

Self Cite

“…consider a two-stage facility location problem with random demands and probabilistic disruptions, an extension of the work (Cui et al 2010, Lu et al 2015…”

Section: Example 1 (Reliable Facility Location Problem (Rflp) Under Pmentioning

confidence: 99%

On distributionally robust chance constrained programs with Wasserstein distance

2019

In the optimization under uncertainty, decision-makers first select a wait-and-see policy before any realization of uncertainty and then place a here-and-now decision after the uncertainty has been observed. Two-stage stochastic programming is a popular modeling paradigm for the optimization under uncertainty that the decision-makers first specifies a probability distribution, and then seek the best decisions to jointly optimize the deterministic wait-and-see and expected here-and-now costs. In practice, such a probability distribution may not be fully available but is probably observable through an empirical dataset. Therefore, this paper studies distributionally robust two-stage stochastic program (DRTSP) which jointly optimizes the deterministic wait-and-see and worst-case expected here-and-now costs, and the probability distribution comes from a family of distributions which are centered at the empirical distribution using ∞−Wasserstein metric. There have been successful developments on deriving tractable approximations of the worst-case expected here-and-now cost in DRTSP. Unfortunately, limited results on exact tractable reformulations of DRTSP. This paper fills this gap by providing sufficient conditions under which the worst-case expected here-and-now cost in DRTSP can be efficiently computed via a tractable convex program. By exploring the properties of binary variables, the developed reformulation techniques are extended to DRTSP with binary random parameters. The main tractable reformulations in this paper are projected into the original decision space and thus can be interpreted as conventional two-stage stochastic programs under discrete support with extra penalty terms enforcing the robustness. These tractable results are further demonstrated to be sharp through complexity analysis.

“…Peng et al [35] present a multiplicative cardinality-constrained uncertainty, considering a two-stage facility location problem with disruptions. Furthermore, Lu et al [36] is the first to apply the distributionally RO method to model disruption uncertainty in the context of facility location. We compare this paper with the related references in Table 1, the column "CC" stands for cardinality-constrained uncertainty and "2SRO" represents the two-stage robust optimization model.…”

Section: Literature Reviewmentioning

confidence: 99%

“…• case 1: θ j 1 0. Due to Equations (29) and (45), x ij 1 = 1, meaning only one facility j 1 is selected to serve i, only when (c ij 1 (36) and (41), α j 1 = 0, so that allc ij 1 =c ij 1 +ĉ ij 1 , j 1 ∈J, are equal. This requires allc ij 1 +ĉ ij 1 are identical, we assume this is a special case that cannot occur.…”

Section: Robustness Of the Multiple Allocation Strategymentioning

confidence: 99%

A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem

Zhou

2018

Symmetry

In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.