In the push for clean and renewable fuels, timber derived biomass is a promising frontier for biofuel production in the United States. This thesis approaches the established timberlands biofuel implementation problem with three different mathematical programming studies, each testing feasibility and sustainability in different economic and supply related situations. In the first study, a competitive game theory approach was utilized to provide new insights into the behavior within a timberlands supply chain. We utilized Stackelberg game theory modeled with bilevel programming to represent the competing harvesting and manufacturing sectors. In the second study, the initial bilevel model was utilized in a larger two stage multiperiod model with parameter uncertainty. In this more realistic model, the first stage contained logistical decisions around biorefinery investments, such as location and capacity, while the second stage was composed of multiple discrete bilevel scenarios representing potential situations in the timberlands system. The final study focused on long term land management strategies for the timberlands supply chain. Introduction of a new biorefinery investment meant that management strategies must be altered to ensure consistent material flows to manufacturers as well as sustain the new production facility. A modified cyclic scheduling formulation was used to model a timberlands system and its planting and harvesting schedule to accommodate a new biorefinery. This cyclic model added an initial startup period to initiate biofuel production and provide time to adapt land management. The overall contribution of these studies was to analyze a biorefinery's impact on the established behavior in a timberlands supply chain. In particular, the goals of these models were to develop introductory decision making tools for timberlands supply chain managers.

Most of the cellular tra c (voice and data) is generated indoors. Due to attenuation from walls, quality of service (QoS) of di erent applications degrades for indoor tra c. Thus in order to provide QoS for such users the Macro base station (MBS) has to transmit at high power. This increases recurring costs to the service provider and contributes to green house emissions. Hence, Femtocells (FC) are considered as an option. Femto Access Points (FAP) are low cost, low powered, small base stations deployed indoors by customers. A substantial part of indoor tra c is diverted from the Macrocell (MC) through the FAP. Since the FCs also use the same channels as the MC, deployment of FCs causes interference to not only its neighbouring FCs but also to the users in the MC. Thus, we need better interference management techniques for this system. In this thesis, we consider a system with multiple Femtocells operating in a Macrocell. FCs and MC use same set of multiple channels and support multiple users. Each user may have a minimum rate requirement. To limit interference to the MC, there is a peak power constraint on each channel. In the rst part of the thesis, we consider sparsely deployed FCs where the interference between the FCs is negligible. For this we formulate the problem of channel allocation and power control in each FC. We develop computationally e cient, suboptimal algorithms to satisfy QoS of each user in the FC. If QoS of each user is not satis ed, we provide solutions which are fair to all the users. In the second part of the thesis, we consider the case of densely deployed FCs where we formulate the problem of channel allocation and power control in each Femtocell as a noncooperative Game. We develop e cient decentralized algorithms to obtain a Nash equilibrium (NE) at which QoS of each user is satis ed. We also obtain e cient decentralized algorithms to obtain fair NE when it may not be feasible to satisfy the QoS of all the users in the FC. Finally, we extend our algorithms to the case where there may be voice and data users in the system. In the third part of the thesis, we continue to study the problem setup in the second part, where we develop algorithms which can simultaneously consider the cases where QoS of users can be satis ed or not. We provide algorithms to compute Coarse Correlated Equilibrium (CCE), Pareto optimal points and Nash bargaining solutions. In the nal part of the thesis, we consider interference limit at the MBS and model FCs as sel sh nodes. The MBS protects itself via pricing subchannels per usage. We obtain a Stackelberg equilibrium (SE) by considering MBS as a leader and FCs as followers.