Three essays on multi-level optimization models and applications

The general form of a multi-level mathematical programming problem is a set of nested optimization problems, in which each level controls a series of decision variables independently. However, the value of decision variables may also impact the objective function of other levels. A two-level model is called a bilevel model and can be considered as a Stackelberg game with a leader and a follower. The leader anticipates the response of the follower and optimizes its objective function, and then the follower reacts to the leader\u27s action. The multi-level decision-making model has many real-world applications such as government decisions, energy policies, market economy, network design, etc. However, there is a lack of capable algorithms to solve medium and large scale these types of problems. The dissertation is devoted to both theoretical research and applications of multi-level mathematical programming models, which consists of three parts, each in a paper format. The first part studies the renewable energy portfolio under two major renewable energy policies. The potential competition for biomass for the growth of the renewable energy portfolio in the United States and other interactions between two policies over the next twenty years are investigated. This problem mainly has two levels of decision makers: the government/policy makers and biofuel producers/electricity generators/farmers. We focus on the lower-level problem to predict the amount of capacity expansions, fuel production, and power generation. In the second part, we address uncertainty over demand and lead time in a multi-stage mathematical programming problem. We propose a two-stage tri-level optimization model in the concept of rolling horizon approach to reducing the dimensionality of the multi-stage problem. In the third part of the dissertation, we introduce a new branch and bound algorithm to solve bilevel linear programming problems. The total time is reduced by solving a smaller relaxation problem in each node and decreasing the number of iterations. Computational experiments show that the proposed algorithm is faster than the existing ones

Public evaluation of large projects : variational inequialities, bilevel programming and complementarity. A survey

Large projects evaluation rises well known difficulties because -by definition- they modify the current price system; their public evaluation presents additional difficulties because they modify too existing shadow prices without the project. This paper analyzes -first- the basic methodologies applied until late 80s., based on the integration of projects in optimization models or, alternatively, based on iterative procedures with information exchange between two organizational levels. New methodologies applied afterwards are based on variational inequalities, bilevel programming and linear or nonlinear complementarity. Their foundations and different applications related with project evaluation are explored. As a matter of fact, these new tools are closely related among them and can treat more complex cases involving -for example- the reaction of agents to policies or the existence of multiple agents in an environment characterized by common functions representing demands or constraints on polluting emissions

Hierarchical decision making with supply chain applications

Hierarchical decision making is a decision system, where multiple decision makers are involved and the process has a structure on the order of levels. It gains interest not only from a theoretical point of view but also from real practice. Its wide applications in supply chain management are the main focus of this dissertation.The first part of the work discusses an application of continuous bilevel programming in a remanufacturing system. Under intense competitive pressures to lower production costs, coupled with increasing environmental concerns, used products can often be collected via customer returns to retailers in supply chains and remanufactured by producers, in orderto bring them back into “as-new” condition for resale. In this part, hierarchical models are developed to determine optimal decisions involving inventory replenishment, retail pricingand collection price for returns. Based on the simplified assumption of a single manufacturer and a single retailer dealing with a single recoverable item under deterministic conditions,all of these decisions are examined in an integrated manner. Models depicting decentralized, as well as centralized policies are explored. Analytical results are derived and detailed sensitivity analysis is performed via an extensive set of numerical computations.In the second part of this dissertation, a discrete bilevel problem is illustrated by investigating a biofuel production problem. The issues of governmental incentives, industry decisions of price, and farm management of land are incorporated. While fixed costs are natural components of decision making in operations management, such discrete phenomena have not received sufficient research attention in the current literature on bilevel programming, due to a variety of theoretical and algorithmic difficulties. When such costs are taken into account, it is not easy to derive optimality conditions and explore convergence properties due to discontinuities and the combinatorial nature of this problem, which is NP-hard. In order to solve this problem, a derivative-free search technique is used to arrive at a solution to this bilevel problem. A new heuristic methodology is developed, which integrates sensitivity analysis and warm-starts to improve the efficiency of the algorithm.Ph.D., Decision Sciences -- Drexel University, 201

Fuzzy multilevel programming with a hybrid intelligent algorithm

AbstractIn order to model fuzzy decentralized decision-making problem, fuzzy expected value multilevel programming and chance-constrained multilevel programming are introduced. Furthermore, fuzzy simulation, neural network, and genetic algorithm are integrated to produce a hybrid intelligent algorithm for finding the Stackelberg-Nash equilibrium. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm

Analyzing the Impacts of Policy Supports and Incentive Programs on Resource Management

Feedstock-based renewable fuels, and ecosystem restoration practices such as afforestation are long-term solutions to mitigating greenhouse gas (GHG) emissions. This dissertation aligns with assessing the effects of policy supports and voluntary incentive programs on renewable fuel production and forest-based carbon sequestration.Higher investment risks and novelty of the feedstock-based conversion technologies hinder large-scale deployment of renewable fuels at present. In the first essay, a two-stage stochastic model is employed to evaluate the impact of federal subsidies in designing a switchgrass-based bioethanol supply chain in west Tennessee wherein decisions driven by minimized expected and Conditional Value-at-Risk of system cost reflected the risk-neutral and risk-averse perspective of the biofuel sector, respectively. Major contribution of this study is the impact assessment of Biomass Crop Assistance Program (BCAP) on investment decisions (including land allocation) of a risk-sensitive biofuel industry under feedstock supply uncertainty.In the second essay, impacts of renewable jet fuel (RJF) production from switchgrass on farmland allocation, processing facility configuration, and GHG emissions are estimated in response to fulfilling the RJF demand at the Memphis International Airport in Tennessee. Importantly, a potential carbon market is used to explore the impact of hypothetical carbon credits on the GHG emissions reduction and net supply-chain welfare while addressing the economic motives of the supply-chain participants. Considering the attention paid by the Unites States aviation sector with respect to GHG emissions, this study highlights the importance of Renewable Identification Number (RIN) credits and tradable carbon credits in achieving the desired economic viability and emission abatement goals through a Stackelberg interaction between the feedstock suppliers and the feedstock processor.In the third essay, discriminatory-price auction and agent-based model are used to examine the cost-efficiency of cost-ranked and cost-benefit-ranked auction-based payment designs for forest-based carbon sequestration with varying degree of correlation between opportunity costs of afforestation and carbon sequestration capacities, when bidders learn in multi-round procurement auctions. Simulation outcomes are expected to guide decision makers in choosing an optimal payment design that ensures efficiency gains for auction-based payments compared to fixed-rate payments, and more importantly ensures minimal loss in cost-efficiency in a dynamic setting

When Nash Meets Stackelberg

Motivated by international energy trade between countries with profit-maximizing domestic producers, we analyze Nash games played among leaders of Stackelberg games (\NASP). We prove it is both $\Sigma^p_2$-hard to decide if the game has a pure-strategy (\PNE) or a mixed-strategy Nash equilibrium (\MNE). We then provide a finite algorithm that computes exact \MNEs for \NASPs when there is at least one, or returns a certificate if no \MNE exists. To enhance computational speed, we introduce an inner approximation hierarchy that increasingly grows the description of each Stackelberg leader feasible region. Furthermore, we extend the algorithmic framework to specifically retrieve a \PNE if one exists. Finally, we provide computational tests on a range of \NASPs instances inspired by international energy trades.Comment: 40 Pages and a computational appendix. Code is available on gitHu

Fuzzy Random Noncooperative Two-level Linear Programming through Absolute Deviation Minimization Using Possibility and Necessity

This paper considers fuzzy random two-level linear programming problems under noncooperative behaviorof the decision makers. Having introduced fuzzy goals of decision makers together with the possibiliy and necessity measure, following absolute deviation minimization, fuzzy random two-level programin problems are transformed into deterministic ones. Extended Stackelberg solutions are introduced andcomputational methods are also presented

Carbon Tax Based on the Emission Factor

In response to growing concerns about the negative impact of GHG emissions, several countries such as the European Union have adopted a cap-and-trade policy to limit the overall emissions levels. Alternatively, other countries including Argentina, Canada, the United Kingdom, and United States have proposed an intensity-based cap-and-trade system that targets emission intensities, measured in emissions per dollars or unit of output. Arguably,intensity regulations can accommodate future economic growth, reduce cost uncertainty, engage developing countries in international efforts to mitigate climate change, and provide incentives to improve energy efficiency and to use less carbon-intensive fuels. This work models and studies a carbon tax scheme where policy makers set a target emission factor, which is used as an intensity measure, for a specific industry and tax firms if they exceed that limit. The policy aims to promote energy efficiency, alleviate the impact on low emitters, and allow high emitters some flexibility to comply. We examine the effectiveness of the policy in reducing the emission factor due to manufacturing and transportation. The major objective of this research is to provide policy makers with a decision support tool that can aid in investigating the impact of an intensity-based carbon tax on regulated sectors and in finding the tax rate that achieves a target reduction. Therefore, we first propose a social-welfare maximizing model that can serve as a tool to evaluate the economic and environmental impacts of the policy. We compare the outcomes of the intensity-based tax and other existing environmental policies; namely, carbon tax imposed on overall emissions, cap-and-trade systems, and mandatory caps using case studies that are built within the context of the cement industry. The effectiveness of the policy is measured by achieving a balance between the target emission factor and the social welfare. To find the optimal tax rate that achieves a target reduction, we propose a bilevel programming model where at the upper level, the government sets a target emission factor for the industry and taxes firms if they exceed that target, and at the lower level, the industry sets output levels that maximize social welfare. In the design of the policy, the government takes into account the decisions of the producers regarding fuel types and production quantities as well as the decisions of the market regarding demand. To evaluate the effectiveness of the policy, we build case studies in the context of cement industry. The policy is found to be effective in reducing the CO2 emissions by opting for a less carbon-intensive fuel with a little impact on social welfare. To examine the effectiveness of the intensity-based carbon tax on reducing CO2 emissions from transportation, which is a major supply chain activity, we finally propose a bilevel program where at the upper level the government decides on the tax rate and at the lower level firms decide on the design of their supply chain and truck types. The policy is found to be effective in inducing firms to reduce their emission factors and consequently reducing the overall emissions

Determining a subsidy rate for Taiwan's recycling glass industry: an application of bi-level programming

[[abstract]]This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the R.O.C. Government (on Taiwan), through the decision of a subsidy rate for the domestic glass recycling industry. The hierarchical and interactive nature between the two parties is modelled by bi-level programming, where the RFMB plays the upper-level decision unit while the recycling industry is the lower-level counterpart. In order to solve the problem by optimization software, the bi-level formulation is transformed to a single-level problem via Karush-Kuhn-Tucker optimality conditions and is further transformed to a 0—1 mixed integer programming problem by variable substitution. The problem is solved with real-world data, and the obtained solutions are analysed and compared with the RFMB's current operations. The results suggest that the proposed approach can improve the operations of the RFMB.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[countrycodes]]GB