We analytically investigate the impacts of several efficient carbon emissions allocation schemes in a cap-and-trade carbon trading system. Subject to each firm’s allowances restriction, a policy maker accumulates all remaining and exceeding carbon emission allowances over the industry at the end of the accounting year. We develop three new allocation schemes for allocating these total carbon emissions to each firm: Separate Payment (SP), Deterministic Equal Splitting (DES) and Allocation proportion to unit Carbon Emission (ACE). Using a Stackelberg framework based on a newsvendor non-cooperative game, we show that our suggested allocation schemes reduce total carbon emissions by aligning the firms with a single and common objective of “reducing total emissions”, not merely “meeting individual’s allowances”. We characterize the conditions under which SP and DES can equally generate fewer total carbon emissions than ACE. Moreover, we identify the condition in which DES can dominate SP in terms of a firm’s profit while DES and SP generate the same total carbon emissions. Our numerical studies further demonstrate that DES outperforms SP in terms of a firm’s financial performance depending on the gap between the firms’ unit emission rates. This study provides a useful guideline to enhance the firms’ profit while reducing total carbon emissions in the industry.

Wind power scenarios from individual wind farms are synthesized using given sample paths of wind power from these same wind farms through the generalized dynamic factor model (GDFM), where wind power scenarios are represented as the multiplication of a fixed polynomial matrix and time varying dynamic shocks, which are white noise. The stochastic structure among wind power outputs is nested in the polynomial matrix, but inherent wind power intermittency is nested in the dynamic shocks. We can generate an arbitrary number of scenarios by changing the dynamic shocks. Since the dimension of dynamic shocks is generally less than the dimension of wind farms, we can reduce the number of random variables. Synthesized sample paths of wind power from candidate wind farms might be used as scenarios to plan the wind power generation and transmission expansion.

We design a simulator in order to seek a surface warship’s survivability against a torpedo attack using MATLAB GUI. Assuming that a torpedo chases a warship in an acoustic-homing way, we model its mobility and detection mechanism according to passive sonar equation. A surface warship manoeuvres into a specified evasive course while deploying static and mobile decoys when a torpedo is detected. Taking a warship’s survival probability as a measure of effectiveness, we perform Monte Carlo simulation by changing four main factors, which include the decoy deployment plan, the torpedo’s initial location, the torpedo’s maximum target detection range, and the mobile decoy’s speed. The simulation results show that using both mobile decoys and static decoys guarantees a higher survival probability than using only static decoys, which depends on their deployment locations and speeds. We further investigate which factors are more likely to affect the survivability via regression analysis, which was based on the simulation results. The regression model results show that torpedo’s detection ability and the speed of mobile decoys highly affect the warship’s survival probability.