140 lines
6.6 KiB
R
140 lines
6.6 KiB
R
library(tidyverse)
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library(lpSolve)
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##Value from table C-2 of Holtec report, cost categories
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#"Initial Annual Estimated Costs and 2019 Constant Dollar Values for the Various Activities for the Proposed CISF and the No-Action Alternative"
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#########
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#CURRENT_YEAR <- 30
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#END_YEAR <- 40
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#PHASE_SIZE <- 5000
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#ST_CAP <- 8680
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#TRANSPORT_COST_RATIO <- 155462880/5000 # or 269883561/8680 since transportation cost scale linearly
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#VOLUME <- 10
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#TRANS_CONSTRAINT <- (ST_CAP+5000*19)/19
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#PHASES_ADDED <- max(ceiling((VOLUME-ST_CAP)/PHASE_SIZE),0) #Make sure added phases are not negative
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#STARTING_VOLUME=8680
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#PHASE_CONST_COST=103399272
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#DISCOUNT <- 0.05
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#VOLUME <- 8660+5000
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#PHASES_ADDED <- 1
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#DECOM_COST_PER_TON =24822656/5000
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#155462880/10^9
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OPTIMAL_COST <- function(PHASES_ADDED,VOLUME,CURRENT_YEAR,DISCOUNT=0.05,STARTING_VOLUME=8680,PHASE_SIZE=5000,END_YEAR=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){
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ADDED_VOLUME=max(VOLUME-STARTING_VOLUME,0)
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ADDED_VOLUME
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STARTING_VOLUME
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VOLUME
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if(ADDED_VOLUME/PHASE_SIZE>PHASES_ADDED){stop("Not enough capacity for the requested volume")}
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###Construction Cost to cover supplied SNF volume
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CONSTRUCT_COST <- PHASES_ADDED*PHASE_CONST_COST
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#Cost to transport SNF from reactors to the CIFS in the current year and to repository at end of project period
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SHIPPING_TIME<- VOLUME/TRANS_CONSTRAINT
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VOLUME/TRANS_CONSTRAINT
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SHIPPING_YEARS <- ceiling(SHIPPING_TIME )
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if(SHIPPING_YEARS>END_YEAR-CURRENT_YEAR){stop("Not enough time to ship the requested SNF volume")}
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AT_CAPACITY_VOLUME <- TRANS_CONSTRAINT
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UNDER_CAPACITY_VOLUME <- VOLUME-(SHIPPING_YEARS-1)*AT_CAPACITY_VOLUME
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SHIPPING_SCHEDULE_OUT <- rep(AT_CAPACITY_VOLUME,SHIPPING_YEARS)
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if(UNDER_CAPACITY_VOLUME!=0){SHIPPING_SCHEDULE_OUT[1] <- UNDER_CAPACITY_VOLUME}
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SHIPPING_SCHEDULE_OUT <- TRANSPORT_COST_RATIO*SHIPPING_SCHEDULE_OUT
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SHIPPING_SCHEDULE_IN <- rev(SHIPPING_SCHEDULE_OUT)
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SHIPPING_DISCOUNT <- (1/((1+DISCOUNT)^(1:SHIPPING_YEARS)))
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SHIPPING_IN_TOTAL_COST <- sum(SHIPPING_SCHEDULE_IN*SHIPPING_DISCOUNT)
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OUT_DISCOUNT <- 1/((1+DISCOUNT)^(END_YEAR-CURRENT_YEAR-SHIPPING_YEARS))
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SHIPPING_OUT_TOTAL_COST <- OUT_DISCOUNT*sum(SHIPPING_SCHEDULE_OUT*SHIPPING_DISCOUNT)
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SHIPPING_IN_TOTAL_COST +SHIPPING_OUT_TOTAL_COST +CONSTRUCT_COST
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##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)
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YEARS_UNTIL_DECOM <- END_YEAR-CURRENT_YEAR+1
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#Assume decom is paid by phase not average volume
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DECOM_TOTAL_COST <-(DECOM_COST_PER_TON*PHASES_ADDED*PHASE_SIZE )/((1+DISCOUNT)^YEARS_UNTIL_DECOM)
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TOTAL_COST <- CONSTRUCT_COST+SHIPPING_IN_TOTAL_COST+SHIPPING_OUT_TOTAL_COST+ DECOM_TOTAL_COST
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TOTAL_COST <- TOTAL_COST*INFLATION_ADJUST
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return(TOTAL_COST)
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}
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CHECK_FEASIBLE_SHIPPING <- function(VOLUME,ST_YEAR){
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RESULT <- try(OPTIMAL_COST(10^5,VOLUME,ST_YEAR),silent=TRUE)
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return(class(RESULT)!="try-error")
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}
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FIND_FEASIBLE_LIMIT <- function(STARTING_TIME){
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ST_BOUND <-0
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END_BOUND <-140*10^3
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MID <- ceiling((END_BOUND+ST_BOUND)/2)
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while(END_BOUND-ST_BOUND>10){
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CHECK <-CHECK_FEASIBLE_SHIPPING(MID,STARTING_TIME)
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if(CHECK){ST_BOUND <- MID} else{END_BOUND <- MID}
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MID <- ceiling((END_BOUND+ST_BOUND)/2)
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}
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MAX_CAPACITY <- ST_BOUND+max(which(sapply(ST_BOUND:END_BOUND,CHECK_FEASIBLE_SHIPPING,ST_YEAR=STARTING_TIME)))
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return(MAX_CAPACITY)
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}
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SHIPPING_CAPACITY_LIMITS <- cbind(1:40,sapply(1:40,FIND_FEASIBLE_LIMIT)) %>% as_tibble %>% rename(Year=V1,Max_Capacity=V2)
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SHIPPING_CAPACITY_LIMITS %>% print(n=100)
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MAX_REV <- function(TBL,CIFS_SIZE){
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# TBL <- TBL %>% filter(Year==YEAR,Discount==DISCOUNT,Revenue/Total_Tons>SHIPPING_COST)
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REV <- TBL %>% pull(Revenue)
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VOL <- TBL %>% pull(Total_Tons)
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RES <- lp(direction = "max", objective.in = REV, const.mat = matrix(VOL, nrow = 1,byrow=TRUE),const.dir = "<=", const.rhs = CIFS_SIZE, all.bin = TRUE)
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return(RES)
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}
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PROFIT_EST <- function(ADDED_PHASES,ST_YEAR,YEARS_AHEAD,DATA=REACTOR_VALUES,DISCOUNT_RATE=0.05,ST_CAP=8680,PHASE_SIZE=5000){
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CURRENT <- DATA%>% filter(Year==ST_YEAR+YEARS_AHEAD,Discount==DISCOUNT_RATE)
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RES <- MAX_REV(CURRENT,ST_CAP+PHASE_SIZE*ADDED_PHASES)
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REVENUE <- RES$objval
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TONS_STORED <- sum(CURRENT$Total_Tons*RES$solution)
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PROFIT <- rbind(REVENUE,OPTIMAL_COST(ADDED_PHASES,TONS_STORED,YEARS_AHEAD))
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return(PROFIT)
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}
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REACTOR_VALUES <- readRDS("Data/Cleaned_Data/Reactor_Values.Rds")
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#ADDED <- 1
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#ADD_RES <- MAX_REV(CURRENT,8680+5000*ADDED)
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#REACTOR_DATA <- CURRENT
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#STARTING_YEAR <- 2026
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#YEARS_AHEAD=20
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#STARTING_CAP=8680
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#SINGLE_PHASE_CAP=5000
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#ADDED_UNITS <- 1
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#Find the optimal profit and cost, plus if the capacity constraint of an addtion in binding.
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ADDITION_CHECK <- function(REACTOR_DATA,ADDED_UNITS,YEARS_AHEAD,Discount_Rate=0.05,STARTING_CAP=8680,SINGLE_PHASE_CAP=5000){
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OPTIM_GUESS <- MAX_REV(REACTOR_DATA,STARTING_CAP+SINGLE_PHASE_CAP*ADDED_UNITS)
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SELECTED_REACTORS <- REACTOR_DATA[which(ADD_RES$solution==1),]%>% mutate(MARGINAL_VALUE=Revenue/Total_Tons)
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FOUND_VOLUME <- OPTIM_GUESS$constraint[76]
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LOWEST_VALUE_REACTOR <-SELECTED_REACTORS[SELECTED_REACTORS$MARGINAL_VALUE== min(SELECTED_REACTORS$MARGINAL_VALUE),]
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MARGINAL_VALUE <- LOWEST_VALUE_REACTOR$MARGINAL_VALUE
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FULL_COST_AT_CAPACITY <- OPTIMAL_COST(ADDED_UNITS,FOUND_VOLUME,YEARS_AHEAD)
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MARGINAL_COST <- FULL_COST_AT_CAPACITY -OPTIMAL_COST(ADDED_UNITS,FOUND_VOLUME-1,YEARS_AHEAD)
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BOUNDED <- MARGINAL_VALUE>MARGINAL_COST
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if(BOUNDED){
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FOUND_VOLUME <- FOUND_VOLUME-STARTING_CAP
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State <- "Capacity Constrainted"
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Optimal_Rev <- OPTIM_GUESS$objval
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Optimal_Cost <- FULL_COST_AT_CAPACITY
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}
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else {
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HIGHEST_VALUE_REACTOR <-SELECTED_REACTORS[SELECTED_REACTORS$MARGINAL_VALUE== max(SELECTED_REACTORS$MARGINAL_VALUE),]
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MARGINAL_VALUE <- unique(HIGHEST_VALUE_REACTOR$MARGINAL_VALUE)
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if(MARGINAL_VALUE>=MARGINAL_COST){
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State <- "Not a Profitable Phase"
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FOUND_VOLUME <- 0
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OPTIM_STARTING <- MAX_REV(REACTOR_DATA,STARTING_CAP)
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Optimal_Rev <- OPTIM_STARTING$objval
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Optimal_Cost <- OPTIMAL_COST(0,STARTING_CAP,YEARS_AHEAD)
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}else{
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State <- "No Binding Constraints"
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FOUND_VOLUME <- NA
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Optimal_Rev <- NA
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Optimal_Cost <- NA
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}
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}
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Profit <- Optimal_Rev-Optimal_Cost
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return(c(ADDED_UNITS,State,FOUND_VOLUME,Profit,Optimal_Rev,Optimal_Cost))
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}
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#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.
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ADDITION_CHECK(CURRENT,22,1)
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