The Stochastic Bilevel Continuous Knapsack Problem with Uncertain Follower's Objective

We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack, while the follower chooses a feasible packing maximizing his own profit. The leader's aim is to optimize a linear objective function in the capacity and in the follower's solution, but with respect to different item values. We address a stochastic version of this problem where the follower's profits are uncertain from the leader's perspective, and only a probability distribution is known. Assuming that the leader aims at optimizing the expected value of her objective function, we first observe that the stochastic problem is tractable as long as the possible scenarios are given explicitly as part of the input, which also allows to deal with general distributions using a sample average approximation. For the case of independently and uniformly distributed item values, we show that the problem is #P-hard in general, and the same is true even for evaluating the leader's objective function. Nevertheless, we present pseudo-polynomial time algorithms for this case, running in time linear in the total size of the items. Based on this, we derive an additive approximation scheme for the general case of independently distributed item values, which runs in pseudo-polynomial time.Comment: A preliminary version of parts of this article can be found in Section 8 of arXiv:1903.02810v

Robust optimization methods for chance constrained, simulation-based, and bilevel problems

The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques

A bilevel framework for decision-making under uncertainty with contextual information

In this paper, we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically tailored to maximizing the decision value, while accounting for possible feasibility constraints. From a mathematical point of view, our framework translates into a bilevel program, for which we provide both a fast regularization procedure and a big-M-based reformulation that can be solved using off-the-shelf optimization solvers. We showcase the benefits of moving from the traditional scheme for model estimation (based on statistical quality metrics) to decision-guided prediction using three different practical problems. We also compare our approach with existing ones in a realistic case study that considers a strategic power producer that participates in the Iberian electricity market. Finally, we use these numerical simulations to analyze the conditions (in terms of the firm’s cost structure and production capacity) under which our approach proves to be more advantageous to the producer.This work was supported in part by the European Research Council (ERC) under the EU Horizon 2020 research and innovation program (grant agreement No. 755705), in part by the Spanish Ministry of Science and Innovation (AEI/10.13039/501100011033) through project PID2020-115460GB-I00, and in part by the Junta de Andalucía (JA), the Universidad de Málaga and the European Regional Development Fund (FEDER) through the research projects P20_00153 and UMA2018‐FEDERJA‐001. M. Á. Muñoz is also funded by the Spanish Ministry of Science, Innovation and Universities through the State Training Subprogram 2018 of the State Program for the Promotion of Talent and its Employability in R&D&I, within the framework of the State Plan for Scientific and Technical Research and Innovation 2017-2020 and by the European Social Fund. Finally, the authors thankfully acknowledge the computer resources, technical expertise, and assistance provided by the SCBI (Supercomputing and Bioinformatics) center of the University of Malaga

Viability and value of behind-the-meter battery storage

Behind-the-meter (BTM) battery storage is a distributed, flexible technology that can support the integration of renewable generation in low-carbon power systems. This research addresses three main challenges related to the integration of BTM battery storage systems: their financial viability from the local perspective, identifying a suitable approach to account for BTM battery storage systems as autonomous decision makers in the power system and quantifying the value of BTM battery storage within low-carbon power systems. The viability of BTM battery storage was investigated from the local perspective, stacking up to three revenue streams simultaneously and accounting for battery degradation. The results indicate that single applications of BTM battery storage are unlikely to be an attractive investment but stacking more than one revenue stream improves investment viability and battery lifetime. Two approaches were compared for their suitability to account for BTM battery storage as autonomous decision makers in the power system. Additionally, the impact of retail contracts on the value of BTM battery storage to the power system was investigated. The result identifies and justifies the most suitable approach and provides insights into which retail contracts are the most beneficial from the power system perspective. The interactions between the power system and autonomous BTM batteries were studied in detail, to assess the value of BTM battery storage from the power system perspective. The results reveal BTM battery storage can have a positive or negative impact on the power system. Therefore, contract design and market structures are crucial to ensure the adoption of this technology benefits the power system

PLATFORM-DRIVEN CROWDSOURCED MANUFACTURING FOR MANUFACTURING AS A SERVICE

Platform-driven crowdsourced manufacturing is an emerging manufacturing paradigm to instantiate the adoption of the open business model in the context of achieving Manufacturing-as-a-Service (MaaS). It has attracted attention from both industries and academia as a powerful way of searching for manufacturing solutions extensively in a smart manufacturing era. In this regard, this work examines the origination and evolution of the open business model and highlights the trends towards platform-driven crowdsourced manufacturing as a solution for MaaS. Platform-driven crowdsourced manufacturing has a full function of value capturing, creation, and delivery approach, which is fulfilled by the cooperation among manufacturers, open innovators, and platforms. The platform-driven crowdsourced manufacturing workflow is proposed to organize these three decision agents by specifying the domains and interactions, following a functional, behavioral, and structural mapping model. A MaaS reference model is proposed to outline the critical functions and inter-relationships. A series of quantitative, qualitative, and computational solutions are developed for fulfilling the outlined functions. The case studies demonstrate the proposed methodologies and can pace the way towards a service-oriented product fulfillment process. This dissertation initially proposes a manufacturing theory and decision models by integrating manufacturer crowds through a cyber platform. This dissertation reveals the elementary conceptual framework based on stakeholder analysis, including dichotomy analysis of industrial applicability, decision agent identification, workflow, and holistic framework of platform-driven crowdsourced manufacturing. Three stakeholders require three essential service fields, and their cooperation requires an information service system as a kernel. These essential functions include contracting evaluation services for open innovators, manufacturers' task execution services, and platforms' management services. This research tackles these research challenges to provide a technology implementation roadmap and transition guidebook for industries towards crowdsourcing.Ph.D