Mid way through getting two phase optimization

Optimal_Deployments.r

@@ -21,9 +21,6 @@ library(lpSolve)
 #155462880/10^9
 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){
 	ADDED_VOLUME=max(VOLUME-STARTING_VOLUME,0)
-ADDED_VOLUME
-STARTING_VOLUME
-VOLUME
 if(ADDED_VOLUME/PHASE_SIZE>PHASES_ADDED){stop("Not enough capacity for the requested volume")}
 	###Construction Cost to cover supplied SNF volume
 	CONSTRUCT_COST <- PHASES_ADDED*PHASE_CONST_COST
@@ -52,6 +49,81 @@ if(ADDED_VOLUME/PHASE_SIZE>PHASES_ADDED){stop("Not enough capacity for the reque
 	return(TOTAL_COST)
 }
 
+################################################################
+OPTIMAL_COST2 <- function(PHASES_ADDED,VOLUME,CURRENT_YEAR,OTHER_PHASES=1,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){
+TOTAL_VOLUME_CONSTRAINT <- 	TRANS_CONSTRAINT*(END_YEAR-CURRENT_YEAR)
+	#Adjust volume constraint to include the SNF that is sent in the later phases. Find the percentage of the total possible volume that is already acounted for by the later SNF
+	TRANS_CONSTRAINT <- TRANS_CONSTRAINT*((TOTAL_VOLUME_CONSTRAINT-OTHER_PHASES*PHASES_ADDED)/TOTAL_VOLUME_CONSTRAINT)
+	ADDED_VOLUME=max(VOLUME-STARTING_VOLUME,0)
+if(ADDED_VOLUME/PHASE_SIZE>PHASES_ADDED){stop("Not enough capacity for the requested volume")}
+	###Construction Cost to cover supplied SNF volume
+	CONSTRUCT_COST <- PHASES_ADDED*PHASE_CONST_COST
+	#Cost to transport SNF from reactors to the CIFS in the current year and to repository at end of project period
+	SHIPPING_TIME<- VOLUME/TRANS_CONSTRAINT 
+	SHIPPING_YEARS <- ceiling(SHIPPING_TIME )
+	if(SHIPPING_YEARS>END_YEAR-CURRENT_YEAR){stop("Not enough time to ship the requested SNF volume")}
+	AT_CAPACITY_VOLUME <- TRANS_CONSTRAINT
+	UNDER_CAPACITY_VOLUME <- VOLUME-(SHIPPING_YEARS-1)*AT_CAPACITY_VOLUME
+	SHIPPING_SCHEDULE_OUT <- rep(AT_CAPACITY_VOLUME,SHIPPING_YEARS)
+	if(UNDER_CAPACITY_VOLUME!=0){SHIPPING_SCHEDULE_OUT[1] <- UNDER_CAPACITY_VOLUME}
+	SHIPPING_SCHEDULE_OUT <- TRANSPORT_COST_RATIO*SHIPPING_SCHEDULE_OUT
+	SHIPPING_SCHEDULE_IN <- rev(SHIPPING_SCHEDULE_OUT)
+	SHIPPING_DISCOUNT <- (1/((1+DISCOUNT)^(1:SHIPPING_YEARS)))
+	SHIPPING_IN_TOTAL_COST <- sum(SHIPPING_SCHEDULE_IN*SHIPPING_DISCOUNT)
+	OUT_DISCOUNT <- 1/((1+DISCOUNT)^(END_YEAR-CURRENT_YEAR-SHIPPING_YEARS))
+	SHIPPING_OUT_TOTAL_COST <- OUT_DISCOUNT*sum(SHIPPING_SCHEDULE_OUT*SHIPPING_DISCOUNT)
+	SHIPPING_IN_TOTAL_COST +SHIPPING_OUT_TOTAL_COST +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_YEAR-CURRENT_YEAR+1
+	#Assume decom is paid by phase not average volume
+	DECOM_TOTAL_COST <-(DECOM_COST_PER_TON*PHASES_ADDED*PHASE_SIZE )/((1+DISCOUNT)^YEARS_UNTIL_DECOM)
+	TOTAL_COST <- CONSTRUCT_COST+SHIPPING_IN_TOTAL_COST+SHIPPING_OUT_TOTAL_COST+ DECOM_TOTAL_COST 
+	TOTAL_COST <- TOTAL_COST*INFLATION_ADJUST
+	return(TOTAL_COST)
+}
+
+####
+CURRENT
+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")
@@ -99,6 +171,7 @@ REACTOR_VALUES <- readRDS("Data/Cleaned_Data/Reactor_Values.Rds")
 #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),]
@@ -134,6 +207,39 @@ else {
 	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.
-ADDITION_CHECK(CURRENT,22,1)
+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
+