Testing new function for cost
This commit is contained in:
Alex Gebben Work
parent
df25529980
commit
520f79ddd7
237
Update.r
Normal file
237
Update.r
Normal file
@ -0,0 +1,237 @@
|
||||
library(tidyverse)
|
||||
library(lpSolve)
|
||||
##Value from table C-2 of Holtec report, cost categories
|
||||
#"Initial Annual Estimated Costs and 2019 Constant Dollar Values for the Various Activities for the Proposed CISF and the No-Action Alternative"
|
||||
|
||||
#########
|
||||
NUM_PHASES1 <- 1
|
||||
NUM_PHASES2 <- 5
|
||||
STAGE1_YEAR <-10
|
||||
STAGE2_YEAR <- 20
|
||||
ST_VOLUME=8680
|
||||
VOLUME1<- 5000
|
||||
VOLUME2 <-1000
|
||||
DISCOUNT <- 0.05
|
||||
STARTING_CAPACITY=8680
|
||||
PHASE_SIZE <- 5000
|
||||
END_TIME <- 40
|
||||
PHASE_CONST_COST=103399272
|
||||
TRANSPORT_COST_RATIO=155462880/5000
|
||||
TRANS_CONSTRAINT =(8680+5000*19)/19
|
||||
DECOM_COST_PER_TON =24822656/5000
|
||||
INFLATION_ADJUST=1.2874
|
||||
|
||||
|
||||
################################################################
|
||||
OPTIMAL_COST <- function(NUM_PHASES1,NUM_PHASES2,STAGE1_YEAR,STAGE2_YEAR,ST_VOLUME,VOLUME1,VOLUME2,DISCOUNT=0.05,STARTING_CAPACITY=8680,PHASE_SIZE=5000,END_TIME=40,PHASE_CONST_COST=103399272,TRANSPORT_COST_RATIO=155462880/5000,TRANS_CONSTRAINT =(8680+5000*19)/19,DECOM_COST_PER_TON =24822656/5000,INFLATION_ADJUST=1.2874){
|
||||
#Total volume not being analyzed, Other capacity is the capacity known in the future no in these two phases
|
||||
|
||||
VOLUME <- ST_VOLUME+VOLUME1+VOLUME2
|
||||
OTHER_CAPACITY <- NUM_PHASES2*PHASE_SIZE+STARTING_CAPACITY
|
||||
TIME_BETWEEN_PHASES <- STAGE2_YEAR-STAGE1_YEAR
|
||||
TIME_LEFT <- END_TIME-STAGE1_YEAR
|
||||
####Check if there is enough capacity to store the requested SNF
|
||||
TOTAL_CAPACITY <- STARTING_CAPACITY+PHASE_SIZE*(NUM_PHASES1+NUM_PHASES2)
|
||||
if(TOTAL_CAPACITY<VOLUME){stop("Not enough capacity for the requested volume")}
|
||||
if(STARTING_CAPACITY>ST_VOLUME){stop("Not enough capacity for the requested volume in the starting phase")}
|
||||
if(NUM_PHASES1*PHASE_SIZE<VOLUME1){stop("Not enough capacity for the requested volume in phase 1")}
|
||||
if(NUM_PHASES2*PHASE_SIZE<VOLUME2){stop("Not enough capacity for the requested volume in phase 2")}
|
||||
####Check if there is enough time to ship SNF into phase 1 before phase 2 starts
|
||||
if(ceiling(VOLUME1/TRANS_CONSTRAINT)>TIME_BETWEEN_PHASES){stop("Not enough time to ship SNF to the CIFS")}
|
||||
####Check if there is enough time to ship all SNF for disposal.
|
||||
SHIPPING_YEARS <- ceiling(VOLUME/TRANS_CONSTRAINT)
|
||||
if(TIME_LEFT<SHIPPING_YEARS){stop("Not enough time to ship the requested SNF volume for disposal")}
|
||||
###Construction Cost to cover supplied SNF volume
|
||||
CONSTRUCT_COST <- NUM_PHASES1*PHASE_CONST_COST+NUM_PHASES2*PHASE_CONST_COST/((1+DISCOUNT)^TIME_BETWEEN_PHASES)
|
||||
#Cost to transport SNF from reactors to the CIFS in the current year and to repository at end of project period
|
||||
UNDER_CAPACITY_VOLUME <- VOLUME-(SHIPPING_YEARS-1)*TRANS_CONSTRAINT
|
||||
SHIPPING_SCHEDULE_OUT <- rep(TRANS_CONSTRAINT,SHIPPING_YEARS)
|
||||
if(UNDER_CAPACITY_VOLUME!=0){SHIPPING_SCHEDULE_OUT[1] <- UNDER_CAPACITY_VOLUME}
|
||||
SHIPPING_SCHEDULE_OUT <- TRANSPORT_COST_RATIO*SHIPPING_SCHEDULE_OUT
|
||||
SHIPPING_OUT_COST <- sum(SHIPPING_SCHEDULE_OUT*(1/((1+DISCOUNT)^(1:SHIPPING_YEARS))))*(1/((1+DISCOUNT)^(END_TIME-STAGE1_YEAR)))
|
||||
|
||||
|
||||
SHIPPING_YEARS1 <- ceiling(VOLUME1/TRANS_CONSTRAINT)
|
||||
SHIPPING_YEARS2 <- ceiling(VOLUME2/TRANS_CONSTRAINT)
|
||||
UNDER_CAPACITY_VOLUME_PHASE1 <- VOLUME1-(SHIPPING_YEARS1-1)*TRANS_CONSTRAINT
|
||||
UNDER_CAPACITY_VOLUME_PHASE2 <- VOLUME2-(SHIPPING_YEARS1-2)*TRANS_CONSTRAINT
|
||||
PHASE_ONE_IN <- rep(TRANS_CONSTRAINT,SHIPPING_YEARS1)
|
||||
PHASE_TWO_IN <- rep(TRANS_CONSTRAINT,SHIPPING_YEARS2)
|
||||
UNDER_CAPACITY_VOLUME_PHASE1
|
||||
if(UNDER_CAPACITY_VOLUME_PHASE1!=0){PHASE_ONE_IN[SHIPPING_YEARS1] <- UNDER_CAPACITY_VOLUME_PHASE1}
|
||||
if(UNDER_CAPACITY_VOLUME_PHASE2 !=0){PHASE_TWO_IN[SHIPPING_YEARS2] <- UNDER_CAPACITY_VOLUME_PHASE2 }
|
||||
SHIPPING_COST_IN1 <- sum(TRANSPORT_COST_RATIO*PHASE_ONE_IN*(1/((1+DISCOUNT)^(1:SHIPPING_YEARS1))))
|
||||
SHIPPING_COST_IN2 <- sum((TRANSPORT_COST_RATIO*PHASE_TWO_IN*(1/((1+DISCOUNT)^(1:SHIPPING_YEARS2))))/((1+DISCOUNT)^(TIME_BETWEEN_PHASES )))
|
||||
|
||||
|
||||
# SHIPPING_COST_IN1+SHIPPING_COST_IN2+CONSTRUCT_COST
|
||||
|
||||
##Decommsioning cost: See Holtec Report, the NRC applies a adjustment factor for the larger capacity which we apply also to the small capacity this is in Section C-2 (just after the table and above section C-3)
|
||||
YEARS_UNTIL_DECOM <- END_TIME-STAGE1_YEAR+1
|
||||
#Assume decom is paid by phase not average volume
|
||||
DECOM_TOTAL_COST <-(DECOM_COST_PER_TON*(NUM_PHASES1+NUM_PHASES2)*PHASE_SIZE )/((1+DISCOUNT)^YEARS_UNTIL_DECOM)
|
||||
TOTAL_COST <- SHIPPING_COST_IN1+SHIPPING_COST_IN2+CONSTRUCT_COST + DECOM_TOTAL_COST
|
||||
TOTAL_COST <- TOTAL_COST*INFLATION_ADJUST
|
||||
return(TOTAL_COST)
|
||||
}
|
||||
|
||||
####
|
||||
TBL2 <- REACTOR_VALUES %>% filter(Discount==0.05,Year==2046)
|
||||
MAX_REV2 <- function(TBL,TBL2,CIFS_SIZE,LATER_PHASE_SIZE,LATER_PHASE_YEARS_AHEAD,DISCOUNT){
|
||||
REV1 <- TBL %>% pull(Revenue)
|
||||
REV2 <- TBL2 %>% pull(Revenue)
|
||||
REV2 <- REV2/((1+DISCOUNT)^LATER_PHASE_YEARS_AHEAD)
|
||||
REV_ALL <- c(REV1,REV2)
|
||||
VOL <- TBL %>% pull(Total_Tons)
|
||||
VOL_CONST <- c(VOL,rep(0,length(VOL)))
|
||||
ONLY_ONE_CONST <- cbind(diag(length(VOL)),diag(length(VOL)))
|
||||
CONSTRAINTS <- rbind(VOL_CONST,rev(VOL_CONST),ONLY_ONE_CONST)
|
||||
MAX_SIZE <- c(CIFS_SIZE,LATER_PHASE_SIZE,rep(1,length(VOL)))
|
||||
RES <- lp(direction = "max", objective.in = REV_ALL, const.mat =CONSTRAINTS,const.dir = "<=", const.rhs = MAX_SIZE, all.bin = TRUE)
|
||||
#TBL[RES$solution[1:(length(RES$solution)/2)]==1,]
|
||||
#RES$solution[(length(RES$solution)/2+1):length(RES$solution)]
|
||||
return(RES)
|
||||
}
|
||||
PROFIT_EST2 <- function(ADDED_PHASES,ST_YEAR,YEARS_AHEAD,NEXT_PHASE_YEARS_AHEAD,DATA=REACTOR_VALUES,DISCOUNT_RATE=0.05,ST_CAP=8680,PHASE_SIZE=5000,NEXT_PHASE_AHEAD_NUM=1){
|
||||
CURRENT <- DATA%>% filter(Year==ST_YEAR+YEARS_AHEAD,Discount==DISCOUNT_RATE)
|
||||
LATER <- DATA%>% filter(Year==ST_YEAR+NEXT_PHASE_YEARS_AHEAD,Discount==DISCOUNT_RATE)
|
||||
|
||||
RES <- MAX_REV2(CURRENT,LATER,ST_CAP+PHASE_SIZE*ADDED_PHASES,PHASE_SIZE*NEXT_PHASE_AHEAD_NUM,NEXT_PHASE_YEARS_AHEAD,DISCOUNT_RATE)
|
||||
return(RES)
|
||||
}
|
||||
CURRENT <- REACTOR_VALUES %>% filter(Year==2042,Discount==0.05)
|
||||
LATER <- REACTOR_VALUES %>% filter(Year==2043,Discount==0.05)
|
||||
function(TBL,TBL2,CIFS_SIZE,LATER_PHASE_SIZE,LATER_PHASE_YEARS_AHEAD,DISCOUNT){
|
||||
MAX_REV2(CURRENT,LATER,8680+10000,5000,1,0.05)
|
||||
|
||||
#####################
|
||||
PROFIT_EST <- function(ADDED_PHASES,ST_YEAR,YEARS_AHEAD,DATA=REACTOR_VALUES,DISCOUNT_RATE=0.05,ST_CAP=8680,PHASE_SIZE=5000){
|
||||
CURRENT <- DATA%>% filter(Year==ST_YEAR+YEARS_AHEAD,Discount==DISCOUNT_RATE)
|
||||
RES <- MAX_REV(CURRENT,ST_CAP+PHASE_SIZE*ADDED_PHASES)
|
||||
REVENUE <- RES$objval
|
||||
TONS_STORED <- sum(CURRENT$Total_Tons*RES$solution)
|
||||
PROFIT <- rbind(REVENUE,OPTIMAL_COST(ADDED_PHASES,TONS_STORED,YEARS_AHEAD))
|
||||
return(PROFIT)
|
||||
}
|
||||
|
||||
|
||||
################################
|
||||
CHECK_FEASIBLE_SHIPPING <- function(VOLUME,ST_YEAR){
|
||||
RESULT <- try(OPTIMAL_COST(10^5,VOLUME,ST_YEAR),silent=TRUE)
|
||||
return(class(RESULT)!="try-error")
|
||||
}
|
||||
FIND_FEASIBLE_LIMIT <- function(STARTING_TIME){
|
||||
ST_BOUND <-0
|
||||
END_BOUND <-140*10^3
|
||||
MID <- ceiling((END_BOUND+ST_BOUND)/2)
|
||||
while(END_BOUND-ST_BOUND>10){
|
||||
CHECK <-CHECK_FEASIBLE_SHIPPING(MID,STARTING_TIME)
|
||||
if(CHECK){ST_BOUND <- MID} else{END_BOUND <- MID}
|
||||
MID <- ceiling((END_BOUND+ST_BOUND)/2)
|
||||
}
|
||||
MAX_CAPACITY <- ST_BOUND+max(which(sapply(ST_BOUND:END_BOUND,CHECK_FEASIBLE_SHIPPING,ST_YEAR=STARTING_TIME)))
|
||||
return(MAX_CAPACITY)
|
||||
}
|
||||
SHIPPING_CAPACITY_LIMITS <- cbind(1:40,sapply(1:40,FIND_FEASIBLE_LIMIT)) %>% as_tibble %>% rename(Year=V1,Max_Capacity=V2)
|
||||
SHIPPING_CAPACITY_LIMITS %>% print(n=100)
|
||||
MAX_REV <- function(TBL,CIFS_SIZE){
|
||||
# TBL <- TBL %>% filter(Year==YEAR,Discount==DISCOUNT,Revenue/Total_Tons>SHIPPING_COST)
|
||||
REV <- TBL %>% pull(Revenue)
|
||||
VOL <- TBL %>% pull(Total_Tons)
|
||||
RES <- lp(direction = "max", objective.in = REV, const.mat = matrix(VOL, nrow = 1,byrow=TRUE),const.dir = "<=", const.rhs = CIFS_SIZE, all.bin = TRUE)
|
||||
return(RES)
|
||||
}
|
||||
|
||||
PROFIT_EST <- function(ADDED_PHASES,ST_YEAR,YEARS_AHEAD,DATA=REACTOR_VALUES,DISCOUNT_RATE=0.05,ST_CAP=8680,PHASE_SIZE=5000){
|
||||
CURRENT <- DATA%>% filter(Year==ST_YEAR+YEARS_AHEAD,Discount==DISCOUNT_RATE)
|
||||
RES <- MAX_REV(CURRENT,ST_CAP+PHASE_SIZE*ADDED_PHASES)
|
||||
REVENUE <- RES$objval
|
||||
TONS_STORED <- sum(CURRENT$Total_Tons*RES$solution)
|
||||
PROFIT <- rbind(REVENUE,OPTIMAL_COST(ADDED_PHASES,TONS_STORED,YEARS_AHEAD))
|
||||
return(PROFIT)
|
||||
}
|
||||
|
||||
REACTOR_VALUES <- readRDS("Data/Cleaned_Data/Reactor_Values.Rds")
|
||||
#ADDED <- 1
|
||||
#ADD_RES <- MAX_REV(CURRENT,8680+5000*ADDED)
|
||||
#REACTOR_DATA <- CURRENT
|
||||
#STARTING_YEAR <- 2026
|
||||
#YEARS_AHEAD=20
|
||||
#STARTING_CAP=8680
|
||||
#SINGLE_PHASE_CAP=5000
|
||||
#ADDED_UNITS <- 1
|
||||
#Find the optimal profit and cost, plus if the capacity constraint of an addtion in binding.
|
||||
ADDITION_CHECK <- function(REACTOR_DATA,ADDED_UNITS,YEARS_AHEAD,Discount_Rate=0.05,STARTING_CAP=8680,SINGLE_PHASE_CAP=5000){
|
||||
OPTIM_GUESS <- MAX_REV(REACTOR_DATA,STARTING_CAP+SINGLE_PHASE_CAP*ADDED_UNITS)
|
||||
ADD_RES <- MAX_REV(CURRENT,STARTING_CAP+5000*ADDED_UNITS)
|
||||
SELECTED_REACTORS <- REACTOR_DATA[which(ADD_RES$solution==1),]%>% mutate(MARGINAL_VALUE=Revenue/Total_Tons)
|
||||
FOUND_VOLUME <- OPTIM_GUESS$constraint[76]
|
||||
LOWEST_VALUE_REACTOR <- SELECTED_REACTORS[SELECTED_REACTORS$MARGINAL_VALUE== min(SELECTED_REACTORS$MARGINAL_VALUE),]
|
||||
MARGINAL_VALUE <- LOWEST_VALUE_REACTOR$MARGINAL_VALUE
|
||||
FULL_COST_AT_CAPACITY <- OPTIMAL_COST(ADDED_UNITS,FOUND_VOLUME,YEARS_AHEAD)
|
||||
MARGINAL_COST <- FULL_COST_AT_CAPACITY - OPTIMAL_COST(ADDED_UNITS,FOUND_VOLUME-1,YEARS_AHEAD)
|
||||
BOUNDED <- MARGINAL_VALUE>MARGINAL_COST
|
||||
if(BOUNDED){
|
||||
FOUND_VOLUME <- FOUND_VOLUME-STARTING_CAP
|
||||
State <- "Capacity Constrainted"
|
||||
Optimal_Rev <- OPTIM_GUESS$objval
|
||||
Optimal_Cost <- FULL_COST_AT_CAPACITY
|
||||
}
|
||||
else {
|
||||
HIGHEST_VALUE_REACTOR <-SELECTED_REACTORS[SELECTED_REACTORS$MARGINAL_VALUE== max(SELECTED_REACTORS$MARGINAL_VALUE),]
|
||||
MARGINAL_VALUE <- unique(HIGHEST_VALUE_REACTOR$MARGINAL_VALUE)
|
||||
if(MARGINAL_VALUE>=MARGINAL_COST){
|
||||
State <- "Not a Profitable Phase"
|
||||
FOUND_VOLUME <- 0
|
||||
OPTIM_STARTING <- MAX_REV(REACTOR_DATA,STARTING_CAP)
|
||||
Optimal_Rev <- OPTIM_STARTING$objval
|
||||
Optimal_Cost <- OPTIMAL_COST(0,STARTING_CAP,YEARS_AHEAD)
|
||||
}else{
|
||||
State <- "No Binding Constraints"
|
||||
FOUND_VOLUME <- NA
|
||||
Optimal_Rev <- NA
|
||||
Optimal_Cost <- NA
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
Profit <- Optimal_Rev-Optimal_Cost
|
||||
return(c(ADDED_UNITS,State,FOUND_VOLUME,Profit,Optimal_Rev,Optimal_Cost))
|
||||
}
|
||||
#Note for self: By running addition's from 1 to 20 (Roughly) at the same number of years ahead the number of 5000 unit addtions which maximizes profit in that year can be found. It looks like at least 22 units will be built which is enough for the whole US, but the timing of addtions needs to be worked out by backwards induction using the years.
|
||||
ST_YEAR <- 2026
|
||||
CONSTRAINED <- matrix(NA,nrow=30,ncol=40)
|
||||
PROFIT <- matrix(NA,nrow=30,ncol=40)
|
||||
|
||||
for(i in ST_YEAR:(ST_YEAR+40)){
|
||||
COL <- i-ST_YEAR
|
||||
CURRENT <- REACTOR_VALUES %>% filter(Year==i,Discount==0.05)
|
||||
for(n in 1:30){
|
||||
C_RES <- try(ADDITION_CHECK(CURRENT,n,COL))
|
||||
|
||||
CONSTRAINED[n,COL] <- C_RES[2]
|
||||
PROFIT[n,COL] <- C_RES[6]
|
||||
|
||||
}
|
||||
}
|
||||
CONSTRAINED <- CONSTRAINED %>% as_tibble
|
||||
PROFIT <- PROFIT %>% as_tibble
|
||||
colnames(CONSTRAINED) <- ST_YEAR:(ST_YEAR+40)
|
||||
colnames(PROFIT) <- ST_YEAR:(ST_YEAR+40)
|
||||
|
||||
CONSTRAINED$Size <- 1:30
|
||||
PROFIT$Size <- 1:30
|
||||
|
||||
|
||||
CONSTRAINED <- CONSTRAINED %>% select(Size,everything()) %>% pivot_longer(-Size,names_to="Year",values_to="Status")
|
||||
PROFIT <- PROFIT%>% select(Size,everything()) %>% pivot_longer(-Size,names_to="Year",values_to="Profit")
|
||||
PROFIT_RES <- PROFIT %>% filter(!is.na(Profit)) %>% group_by(Year) %>% mutate(Profit=as.numeric(Profit)) %>% filter(Profit==max(Profit)) %>% print(n=100)
|
||||
CONSTRAINED$Status <- ifelse(grepl("Not enough time to",CONSTRAINED$Status),"Time Limited",CONSTRAINED$Status)
|
||||
|
||||
CONSTRAINED$Status %>% unique
|
||||
MAX_VOLUME <- CONSTRAINED %>% group_by(Year,Status) %>% summarize(Size=max(Size)) %>% filter(Status=="Capacity Constrainted")
|
||||
ggplot(MAX_VOLUME,aes(x=Year,y=Size))+geom_point()+scale_y_continuous(breaks=1:30)
|
||||
ggplot(PROFIT_RES,aes(x=Year,y=Size))+geom_point()+scale_y_continuous(breaks=1:30)
|
||||
|
||||
9*5000+8680
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user