# Optimal Allocation - Minimum Sum of Relative Variances Allocation of the overall sample size n to the strata for the following purpose: A weighted sum of variances (or relative variances) of the estimates of totals for the m survey variables is minimized. ```r BSSM_FD(Nh,Sh2j,Yj,Cust,nmin,ch,w,certain) ``` ## Arguments - `Nh`: Vector with total number of population units in each stratum (h=1,...,H) - `Sh2j`: Matrix (or vector) mxH (m = number of variables and H =number of strata) with Population variance for each variable of the hth stratum - `Yj`: Vector with population total Yj for the jth survey variable - `Cust`: Corresponds to the overall variable cost budget for the survey C - `nmin`: Smallest possible sample size in any stratum - `ch`: Vector with the unit level survey costs for sampling from stratum h - `w`: Vector with Variable-specific weights, set a priori to represent the relative importance of the survey variables - `certain`: if (nH=NH) => certain=TRUE else certain=FALSE ## Details Function that uses an integer programming formulation ## Returns - **n**: Sample size - **nh**: Sample of size by stratum - **cvs**: Coefficients of variation for the estimators of totals of the survey variables considered - **time_cpu**: Time consumed by the algorithm (seconds) ## References Brito, J.A.M, Silva, P.L.N.,Semaan, G.Srogramming Formulations Applied to Optimal Allocation in Stratified Sampling. Survey Methodology, 41, No.2, pp.427-442. ## Author(s) Jose Brito (jambrito@gmail.com), Pedro Silva, Gustavo Semaan and Nelson Maculan ## See Also BSSM_FC ## Examples ```r #Example1 #Unit level survey costs for sampling from the strata are assumed to be the same. #Number of survey variables (m=2) and seven strata (H=7) #ch=1 ==> Cust = n Nh<-c(49,78,20,39,73,82,89) Yj<-c(542350,56089251) Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505), c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806)) n<-200 #sample size result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n) #Example2 #Unit level survey costs for sampling from the strata are assumed to be the same. #ch=1 ==> Cust = n #nmin>2 Nh<-c(49,78,20,39,73,82,89) Yj<-c(542350,56089251) Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505), c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806)) nmin<-20 n<-200 result<-BSSM_FD(Nh,Sh2j,Yj,nmin,Cust=n) #Example3 #certain=TRUE Nh<-c(49,78,20,39,73,82,89) Yj<-c(542350,56089251) Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505), c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806)) n<-200 result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n,certain=TRUE) #Example4 #Relative importance of the survey variables is different w<-c(0.3,0.7) Nh<-c(49,78,20,39,73,82,89) Yj<-c(542350,56089251) Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505), c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806)) n<-200 result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n,w=w) #Example5 #Number of survey variables m=1 Nh<-c(49,78,20,39,73,82,89) Yj<-542350 Sh2j<-c(4436978,5581445,33454902,5763294,8689167,3716130,13938505) n<-100 result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n) ```

BSSM_FD function