UC Berkeley

This dissertation studies the data-driven approaches to flexible systems design problems under uncertainty. We discuss real applications in various contexts with flexibility: the capability to satisfy different types of customer demands (e.g. one-way and round trips in the context of car sharing systems); the geographical demand distribution estimation and associated inventory allocation; and the freedom in production plans to fulfill uncertain customer demands (e.g. flexible recipes in continuous production process).

The problems we consider have different objectives and more importantly several degrees of richness in data availability. We develop data-driven optimization models accordingly. Specifically, in the case of new market expansion for example, the firm has to make one-shot decision with limited or side information. The focus of data-driven approach in this case is on the portability of information. Distributionally-robust optimization methodologies are applied to derive strategic decisions that hedge the risks. At the tactical level, e.g. resource planning, the firm deploys planning with ample historical data. For online retailers, geographical demand distributions need to be estimated from historical sales and serve as key input to their regular inventory allocation decisions. Furthermore, operational decisions generally require more detailed data, especially the continuous data for real-time decisions. We study the problem where routine production plans are chosen together with raw material investment decisions when periodic demand data may be available.

In the first part of the dissertation, we study the planning problem faced by urban electric vehicle (EV) sharing systems, that offer both one-way and round trips, in designing the geographical service region. This decision encompasses the trade-off between maximizing customer adoption by covering travel needs, and controlling fleet operations costs. We develop a mathematical programming model that incorporates details of both customer adoption behavior and fleet management (including EV repositioning and charging) operations under spatially-imbalanced and time-varying travel patterns. To address uncertainty in customer adoption, we employ a distributionally-robust optimization framework that informs robust decisions to avoid possible ambiguity (or lack) of data. Mathematically, the problem is approximated by a mixed integer second-order cone program (MISOCP), which is computationally-tractable. Applying this approach to the case of Car2Go's service in San Diego, California, with real operations data, we investigate several planning questions and suggest potential for future development of the service.

To make better inventory allocation to distribution centers, understanding of the geographical demand distribution is essential to online retailers who possess historical sales data that might be contaminated and/or with missing data. The second part of the dissertation presents two models: the first model estimates the geographical demand distribution; the second model integrates the demand estimation together with inventory optimization. In the first model, we study the missing geo-demand data completion problem for a national online retailer. We formulate the problem as a low-rank tensor recover problem in a convex optimization framework. An alternating direction augmented Lagrangian (ADAL) method has been developed and tailored for solving the tensor recovery problem with partial observations. We first discuss efficiency and effectiveness of the algorithm via experiments with synthetic data. We then apply the framework with observed geo-demand from the online retailer. Finally, the benefits of the missing geo-demand data completion are summarized based on computational experiment results. We have shown that the recovered geo-demand distributions possesses more smoothness over time and rendered better generalization performance than the observed geo-demand upon integrated into the existing learning framework. We also integrate the missing data recovery with the data-driven newsvendor model which provides estimation of demands as well as optimal order quantity. A preliminary analysis shows that the proposed model preserves the condition for optimal order quantity as it is in the data-driven newsvendor model. Future work directions are also discussed.

The last part of this dissertation focuses on the inventory investment, recipe selection and resource allocation decisions in continuous process systems with flexible recipes under demand uncertainty. Due to variations in both raw material quality and market conditions, variations in the recipes are used in continuous production processes. Such flexibility is not on design but on the operation that allows adjustments of recipe items aiming to achieve better input utilization than traditionally fixed recipes. We develop a two-stage stochastic mixed integer program formulation and propose a heuristic to the second stage allocation optimization problem. In the first stage, the model determines inventory levels for each period based on past demand data. After demand arrivals are realized, the second stage recourse makes recipe selection and allocation decisions in production. With available historical demand data, a simulation-based approach based on SAA algorithm is developed to solve the stochastic program. The results of numerical study show the performance of the approach on various cost settings as well as the benefits of flexible recipes over fixed recipes. In the proposed approach, we focus on the application of the sample average approximation (SAA) algorithm and use Bootstrap sampling as the default in demand simulation. A direction of future improvement is to incorporate better techniques in the simulation of future demand arrivals based on historical demand data. Those techniques may consider some properties of the demand, such as seasonality and autocorrelation. Also, with limited demand information, a robust optimization model might be developed that considers the worst cases. Moreover, since our model assumes any inventory leftover at the end of each period is disposed, the extension that relaxes this assumption and introduces inventory holding cost in multi-period setting should also be investigated.