This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many p...This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.展开更多
Background:The double sampling method known as“big BAF sampling”has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume.A well-known method for variance ...Background:The double sampling method known as“big BAF sampling”has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume.A well-known method for variance determination,Bruce’s method,is customarily used because the volume estimator takes the form of a product of random variables.However,the genesis of Bruce’s method is not known to most foresters who use the method in practice.Methods:We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method.Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product.Additionally,two alternative estimators for the variance of individual tree volume-basal area ratios,which are part of the estimation process,were compared within the overall variance estimation procedure.Results:The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method.The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy,which had not been shown previously for Big BAF sampling.Conclusions:A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method.In most settings,there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used.A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.展开更多
In order to further improve the accuracy and reliability and reduce uncertainties in the national GHG inventories for Pakistan,this study call for using 2006 IPCC Guidelines,to help to identify the national targets fo...In order to further improve the accuracy and reliability and reduce uncertainties in the national GHG inventories for Pakistan,this study call for using 2006 IPCC Guidelines,to help to identify the national targets for GHG mitigation with respect to the nationally determined contributions(NDCs).GHG(CO2,CH4,and N20)inventories for Pakistan have been developed by conducting a detailed sectoral assessment of IPCC source sectors,energy,industrial processes and product use(IPPU),agriculture,forestry and other land use(AFOLU),and the waste sector.Further,sector wise comparative analysis of GHG inventories(1994-2017)based on the 2006 and 1996 IPCC Guidelines have also been presented.Results indicated an average relative difference of 4%in total GHG emissions(CO2 equivalent)from energy sector between 2006 and 1996 IPCC Guidelines.With 3.6%average annual growth rate based on 2006 IPCC Guidelines,CO2 from energy sector remained the most abundant GHG emitted,followed by CH4 and N2O.While the average absolute difference in emissions of CH4 and N20 from the energy sector is notable,the total estimated GHG emissions by 2006 IPCC Guidelines duplicate those by 1996 IPCC Guidelines.In the mineral industry with 2006 IPCC Guidelines,an average annual growth rate of 6.7%is observed,contributing 64%of total IPPU sector CO2 emissions.Nevertheless,the relative difference between the two Guidelines in overall IPPU sector emissions remained negligible.There might be a need for switching to 2006 IPCC Guidelines to consider more parameters such as additional source sectors and new default emission factors that fit into national circumstances.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71201027,71272085,71390334,and 11271356973 Project under Grant No.2010CB731400+3 种基金Humanity and Social Science Youth Foundation of Ministry of Education of China under Grant No.12YJC630260Guangdong Natural Science Foundation under Grant No.S2012040007919Foundation for Distinguished Young Talents in Higher Education of Guangdong under Grant No.LYM11121the Open Fund of Chongqing Key Laboratory of Logistics under Grant No.CQKLL12003
文摘This paper considers a firm that sells a durable product with a given market potential.The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.
基金Research Joint Venture Agreement 17-JV-11242306045,“Old Growth Forest Dynamics and Structure,”between the USDA Forest Service and the University of New Hampshire.Additional support to MJD was provided by the USDA National Institute of Food and Agriculture McIntire-Stennis Project Accession Number 1020142,“Forest Structure,Volume,and Biomass in the Northeastern United States.”TBL:This work was supported by the USDA National Institute of Food and Agriculture,McIntire-Stennis project OKL02834 and the Division of Agricultural Sciences and Natural Resources at Oklahoma State University.
文摘Background:The double sampling method known as“big BAF sampling”has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume.A well-known method for variance determination,Bruce’s method,is customarily used because the volume estimator takes the form of a product of random variables.However,the genesis of Bruce’s method is not known to most foresters who use the method in practice.Methods:We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method.Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product.Additionally,two alternative estimators for the variance of individual tree volume-basal area ratios,which are part of the estimation process,were compared within the overall variance estimation procedure.Results:The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method.The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy,which had not been shown previously for Big BAF sampling.Conclusions:A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method.In most settings,there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used.A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.
文摘In order to further improve the accuracy and reliability and reduce uncertainties in the national GHG inventories for Pakistan,this study call for using 2006 IPCC Guidelines,to help to identify the national targets for GHG mitigation with respect to the nationally determined contributions(NDCs).GHG(CO2,CH4,and N20)inventories for Pakistan have been developed by conducting a detailed sectoral assessment of IPCC source sectors,energy,industrial processes and product use(IPPU),agriculture,forestry and other land use(AFOLU),and the waste sector.Further,sector wise comparative analysis of GHG inventories(1994-2017)based on the 2006 and 1996 IPCC Guidelines have also been presented.Results indicated an average relative difference of 4%in total GHG emissions(CO2 equivalent)from energy sector between 2006 and 1996 IPCC Guidelines.With 3.6%average annual growth rate based on 2006 IPCC Guidelines,CO2 from energy sector remained the most abundant GHG emitted,followed by CH4 and N2O.While the average absolute difference in emissions of CH4 and N20 from the energy sector is notable,the total estimated GHG emissions by 2006 IPCC Guidelines duplicate those by 1996 IPCC Guidelines.In the mineral industry with 2006 IPCC Guidelines,an average annual growth rate of 6.7%is observed,contributing 64%of total IPPU sector CO2 emissions.Nevertheless,the relative difference between the two Guidelines in overall IPPU sector emissions remained negligible.There might be a need for switching to 2006 IPCC Guidelines to consider more parameters such as additional source sectors and new default emission factors that fit into national circumstances.
