This paper analyzes and compares the life cycle environmental impacts of two major types of Li-ion batteries using process-based and integrated hybrid life-cycle assessment (LCA) approaches. The life cycle inventories (LCIs) of Li-ion battery contain component production, battery assembly, use phase, disposal and recycling and other related background processes. For process-based LCA, 17 ReCiPe midpoint environmental impact indicators and three end point environmental impact indicators are considered. As for the integrated hybrid LCA study, life cycle greenhouse gas (GHG) emissions and energy consumption are emphasized. Furthermore, we perform sensitivity analysis of life cycle GHG emissions with respect to the uncertainties in product prices, mass of BMS and cooling system, and production efficiency. The integrated hybrid LCA results show that battery cell production is the most significant contributor to the life cycle GHG emissions and the economic input-output (EIO) systems contribute the largest part in life cycle energy consumption for both types of Li-ion batteries. The most significant difference between two Li-ion batteries lies in the disposal and recycling stage. For LiMn2O4 (LMO) battery, the disposal and recycling stage only makes up a small portion of less than 10% for life cycle GHG emissions and energy consumption. However, for Li­(Ni x Co y Mn z )­O2 (NCM) battery, it contributes a significant part at more than 20%.

To addresses the design and operations of resilient supply chains under uncertain disruptions, a general framework is proposed for resilient supply chain optimization, including a quantitative measure of resilience and a holistic biobjective twostage adaptive robust fractional programming model with decision-dependent uncertainty set for simultaneously optimizing both the economic objective and the resilience objective of supply chains. The decision-dependent uncertainty set ensures that the uncertain parameters (e.g., the remaining production capacities of facilities after disruptions) are dependent on first-stage decisions, including facility location decisions and production capacity decisions. A data-driven method is used to construct the uncertainty set to fully extract information from historical data. Moreover, the proposed model takes the time delay between disruptions and recovery into consideration. To tackle the computational challenge of solving the resulting multilevel optimization problem, two solution strategies are proposed. The applicability of the proposed approach is illustrated through applications on a location-transportation problem and on a spatially-explicit biofuel supply chain optimization problem. Figure 3. Pseudo code of solution strategy 1: Combination of affine decision rule and parametric algorithm.

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately.Distributionally robust chance constrained programming takes into consideration ambiguous probability distributions of uncertain parameters. To tackle the computational challenges, sample average approximation method is adopted, and the required data samples are generated by GAN in an end-to-end way through the differentiable networks. The proposed framework is then applied to supply chain optimization under demand uncertainty. The applicability of the proposed approach is illustrated through a county-level case study of a spatially explicit biofuel supply chain in Illinois.

When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor twist on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of iterative algorithms, with a focus on algorithms designed for convex optimization. We propose several notions of what it means for two algorithms to be equivalent, and provide computationally tractable means to detect equivalence. Our main definition, oracle equivalence, states that two algorithms are equivalent if they result in the same sequence of calls to the function oracles (for suitable initialization). Borrowing from control theory, we use state-space realizations to represent algorithms and characterize algorithm equivalence via transfer functions. Our framework can also identify and characterize some algorithm transformations including permutations of the update equations, repetition of the iteration, and conjugation of some of the function oracles in the algorithm. To support the paper, we have developed a software package named Linnaeus that implements the framework to identify other iterative algorithms that are equivalent to an input algorithm. More broadly, this framework and software advances the goal of making mathematics searchable.

This paper presents GeNI-ADMM, a framework for large-scale composite convex optimization, that facilitates theoretical analysis of both existing and new approximate ADMM schemes. GeNI-ADMM encompasses any ADMM algorithm that solves a first-or second-order approximation to the ADMM subproblem inexactly. GeNI-ADMM exhibits the usual O(1/t)-convergence rate under standard hypotheses and converges linearly under additional hypotheses such as strong convexity. Further, the GeNI-ADMM framework provides explicit convergence rates for ADMM variants accelerated with randomized linear algebra, such as NysADMM and sketchand-solve ADMM, resolving an important open question on the convergence of these methods. This analysis quantifies the benefit of improved approximations and can inspire the design of new ADMM variants with faster convergence.