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