Risk-Averse Stochastic Integer Programs for Mixed-Model Assembly Line Sequencing Problems

A variety of optimization formulations have been proposed for mixed-model assembly sequencing problems with stochastic demand and task times. In the real world, however, mixed-model assembly lines are faced with more challenging uncertainties including timely part delivery, material quality, upstream sub-assembly completion and availability of other resources. In addition, sub-assembly lines must meet deadlines imposed by downstream stations. The inevitable disruptions require resequencing. We present a risk-averse stochastic mixed-integer model for mixed-model assembly line resequencing problems to increase on-time performance

Ускорение сходимости метода декомпозиции "Progressive Hedging’’

Показано як метод розв'язку багатоетапних задач стохастичного програмування «Progressive Hedging» пов'язаний із методом декомпозиції по змінним першого рівня за допомогою множників Лагранжа на прикладі двоетапної задачі. Обговорюються питання регулювання швидкості збіжності методу та відновлення змінних першого рівня.It is shown relation between «Progressive Hedging» method for solving multistage stochastic optimization problems and decomposition method using Lagrangе multipliers in case of Two Stage stochastic problem. Adjusting of convergence rate and restoring of first stage variables are discussed

Computing Wasserstein Barycenter via operator splitting: the method of averaged marginals

The Wasserstein barycenter (WB) is an important tool for summarizing sets of probabilities. It finds applications in applied probability, clustering, image processing, etc. When the probability supports are finite and fixed, the problem of computing a WB is formulated as a linear optimization problem whose dimensions generally exceed standard solvers' capabilities. For this reason, the WB problem is often replaced with a simpler nonlinear optimization model constructed via an entropic regularization function so that specialized algorithms can be employed to compute an approximate WB efficiently. Contrary to such a widespread inexact scheme, we propose an exact approach based on the Douglas-Rachford splitting method applied directly to the WB linear optimization problem for applications requiring accurate WB. Our algorithm, which has the interesting interpretation of being built upon averaging marginals, operates series of simple (and exact) projections that can be parallelized and even randomized, making it suitable for large-scale datasets. As a result, our method achieves good performance in terms of speed while still attaining accuracy. Furthermore, the same algorithm can be applied to compute generalized barycenters of sets of measures with different total masses by allowing for mass creation and destruction upon setting an additional parameter. Our contribution to the field lies in the development of an exact and efficient algorithm for computing barycenters, enabling its wider use in practical applications. The approach's mathematical properties are examined, and the method is benchmarked against the state-of-the-art methods on several data sets from the literature

Solution methods and bounds for two-stage risk-neutral and multistage risk-averse stochastic mixed-integer programs with applications in energy and manufacturing

This dissertation presents an integrated method for solving stochastic mixed-integer programs, develops a lower bounding approach for multistage risk-averse stochastic mixed-integer programs, and proposes an optimization formulation for mixed-model assembly line sequencing (MMALS) problems. It is well known that a stochastic mixed-integer program is difficult to solve due to its non-convexity and stochastic factors. The scenario decomposition algorithms display computational advantage when dealing with a large number of possible realizations of uncertainties, but each has its own advantages and disadvantages. This dissertation presents a solution method for solving large-scale stochastic mixed-integer programs that integrates two scenario-decomposition algorithms: Progressive Hedging (PH) and Dual Decomposition (DD). In this integrated method, fast progress in early iterations of PH speeds up the convergence of DD to an exact solution. In many applications, the decision makers are risk-averse and are more concerned with large losses in the worst scenarios than with average performance. The PH algorithm can serve as a time-efficient heuristic for risk-averse stochastic mixed-integer programs with many scenarios, but the scenario reformulation for time consistent multistage risk-averse models does not exist. This dissertation develops a scenario-decomposed version of time consistent multistage risk-averse programs, and proposes a lower bounding approach that can assess the quality of PH solutions and thus identify whether the PH algorithm is able to find near-optimal solutions within a reasonable amount of time. The existing optimization formulations for MMALS problems do not consider many real-world uncertainty factors such as timely part delivery and material quality. In addition, real-time sequencing decisions are required to deal with inevitable disruptions. This dissertation formulates a multistage stochastic optimization problem with part availability uncertainty. A risk-averse model is further developed to guarantee customers’ satisfaction regarding on-time performance. Computational studies show that the integration of PH helps DD to reduce the run-time significantly, and the lower bounding approach can obtain convergent and tight lower bounds to help PH evaluate quality of solutions. The PH algorithm and the lower bounding approach also help the proposed MMALS formulation to make real-time sequencing decisions

Enhancing Distribution Resilience with Mobile Energy Storage: A Progressive Hedging Approach

Electrochemical energy storage (ES) units (e.g. batteries) have been field-validated as an efficient back-up resource that enhance resilience of the distribution system in case of natural disasters. However, using these units for resilience is not sufficient to economically justify their installation and, therefore, these units are often installed in locations where they incur the greatest economic value during normal operations. Motivated by the recent progress in transportable ES technologies, i.e. ES units can be moved using public transportation routes, this paper proposes to use this spatial flexibility to bridge the gap between the economically optimal locations during normal operations and disaster-specific locations where extra back-up capacity is necessary. We propose a two-stage optimization model that optimizes investments in mobile ES units in the first stage and can re-route the installed mobile ES units in the second stage to avoid the expected load shedding caused by disaster forecasts. Since the proposed model cannot be solved efficiently with off-the-shelf solvers, even for relatively small instances, we apply a progressive hedging algorithm. The proposed model and progressive hedging algorithm are tested through two illustrative examples on a 15-bus radial distribution test system.Comment: Accepted for publication in the Proc. of the 2018 IEEE General Meeting in Portland, Orego