The value of quality grading in remanufacturing under quality level uncertainty

In remanufacturing, variability in quality levels of available cores (end-of-life products) has an impact on both the process cost and the process time. While previous research suggests that quality grading adds value, there are also concerns raised regarding how reliably the grades can be identified. We argue that uncertainty is inherent to the grading process and investigate the value of grading by taking into account the underlying uncertainty. We develop a robust optimisation model for remanufacturing planning, where both the per-unit cost and resource requirement to remanufacture a core are uncertain parameters that are assumed to reside in two different uncertainty sets; box and ellipsoidal. We analyse both uncapacitated and capacitated cases, and based on extensive numerical analysis, conclude that while on average, there is still value in grading, it becomes significantly smaller when the inherent uncertainty is accounted for. For the capacitated case, we also consider a cost for grading and find that it may cause a significant deterioration in the value of grading, if not rendering the grading totally useless. We show the validity of our approach through extensive numerical analyses.This accepted article is published Yanıkoğlu, İ., & Denizel, M. (2020). The value of quality grading in remanufacturing under quality level uncertainty. International Journal of Production Research, 59(3), 839–859. https://doi.org/10.1080/00207543.2020.1711983. Posted with permission

Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs

We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader's problem. Both bounding problems are equivalent to explicit mixed-integer linear programs that are amenable to efficient numerical solution. The method is illustrated through a facility location problem involving sellers and customers with conflicting preferences

Robust dual-response optimization

This article presents a robust optimization reformulation of the dual-response problem developed in response surface methodology. The dual-response approach fits separate models for the mean and the variance and analyzes these two models in a mathematical optimization setting. We use metamodels estimated from experiments with both controllable and environmental inputs. These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, classic approaches assume known means, variances, or covariances and sometimes even a known distribution. We, however, develop a method that uses only experimental data, so it does not need a known probability distribution. Moreover, our approach yields a solution that is robust against the ambiguity in the probability distribution. We also propose an adjustable robust optimization method that enables adjusting the values of the controllable factors after observing the values of the environmental factors. We illustrate our novel methods through several numerical examples, which demonstrate their effectiveness

Adjustable Robust Parameter Design with Unknown Distributions

Abstract This article presents a novel combination of robust optimization developed in mathematical programming, and robust parameter design developed in statistical quality control. Robust parameter design uses metamodels estimated from experiments with both controllable and environmental inputs (factors). These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, classic robust parameter design assumes known means and covariances, and sometimes even a known distribution. We, however, develop a robust optimization approach that uses only experimental data, so it does not need these classic assumptions. Moreover, we develop `adjustable' robust parameter design which adjusts the values of some or all of the controllable factors after observing the values of some or all of the environmental inputs. We also propose a new decision rule that is suitable for adjustable integer decision variables. We illustrate our novel method through several numerical examples, which demonstrate its effectiveness.