Limiting the impact of supply chain disruptions in the face of distributional uncertainty in demand

Abstract

Service‐level requirements play a crucial role in eliminating stock‐outs in a production pipeline. However, delivering a specific service level can become an unattainable goal given the various uncertainties influencing both the production pipeline and customer demand and causing the manufacturer to adapt the initial strategy in response to disruptions. Such deviations from optimality frequently result in unexpected (and potentially very high) costs and are complex to manage. On the one hand, the manufacturer can use a robust or distributionally robust approach to prepare for the worst‐case disruption, ensuring that the realized cost will be lower than the estimated cost with high probability. On the other hand, this solution may lead to overly conservative production schedules. In this article, we take a different approach and develop a bilevel stochastic optimization model with chance constraints, which allows us to make the production more predictable in the event of disruptions by driving costs and optimal schedules closer to the benchmark for each scenario considered. We introduce doubly probabilistic service‐level requirements to account for two interdependent layers of uncertainty, that is, production disruptions and distributional uncertainties in customer demand. This allows us to make high‐quality production decisions with only a limited understanding of the demand pattern. Approximating the problem for a numerical solution, we guarantee tight optimality gaps for high service levels and propose an efficient solution scheme, combining robust scenario reduction with a customized Benders decomposition procedure. In the managerial section, we use the Omega× Swatch MoonSwatches example to demonstrate that a desirable doubly probabilistic service level can be attained for disruptions with a drop in demand. In the case of disruptions followed by a peak in demand, one can tighten the optimality gaps if the service level is reduced.

Uncertainty Analysis and Optimization Modeling with Application to Supply Chain Management: A Systematic Review

“…Refs. [174][175][176][177][178][179][180] applied uncertainty methods based on probability theory. A two-layer optimization model was created by Timonina-Farkas et al [174] that took demand uncertainty and production disruptions into account.…”

“…[174][175][176][177][178][179][180] applied uncertainty methods based on probability theory. A two-layer optimization model was created by Timonina-Farkas et al [174] that took demand uncertainty and production disruptions into account. This model took into account how opportunity limitations and dual probability service level demand affected the connection between demand distribution and production disruptions.…”

Robust learning and optimization in distributionally robust stochastic variational inequalities under uncertainty

“…Real-world problems are random and ambiguous, therefore algorithms and models must be robust and optimal across a range of distributions (Osaba et al, 2021). This research will investigate efficient computing methods, theoretical foundations, and practical guidance for solving distributionally resilient stochastic variational inequalities under uncertainty (Timonina-Farkas et al, 2022). We can improve robust optimization algorithms and provide insights for decision-making by addressing this research challenge (Ning & You, 2018).…”