Mid way through getting two phase optimization
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Alex Gebben Work
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71af838e03
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df25529980
@ -21,9 +21,6 @@ library(lpSolve)
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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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@ -52,6 +49,81 @@ if(ADDED_VOLUME/PHASE_SIZE>PHASES_ADDED){stop("Not enough capacity for the reque
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return(TOTAL_COST)
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}
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################################################################
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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){
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TOTAL_VOLUME_CONSTRAINT <- TRANS_CONSTRAINT*(END_YEAR-CURRENT_YEAR)
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#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
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TRANS_CONSTRAINT <- TRANS_CONSTRAINT*((TOTAL_VOLUME_CONSTRAINT-OTHER_PHASES*PHASES_ADDED)/TOTAL_VOLUME_CONSTRAINT)
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ADDED_VOLUME=max(VOLUME-STARTING_VOLUME,0)
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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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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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####
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CURRENT
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TBL2 <- REACTOR_VALUES %>% filter(Discount==0.05,Year==2046)
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MAX_REV2 <- function(TBL,TBL2,CIFS_SIZE,LATER_PHASE_SIZE,LATER_PHASE_YEARS_AHEAD,DISCOUNT){
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REV1 <- TBL %>% pull(Revenue)
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REV2 <- TBL2 %>% pull(Revenue)
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REV2 <- REV2/((1+DISCOUNT)^LATER_PHASE_YEARS_AHEAD)
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REV_ALL <- c(REV1,REV2)
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VOL <- TBL %>% pull(Total_Tons)
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VOL_CONST <- c(VOL,rep(0,length(VOL)))
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ONLY_ONE_CONST <- cbind(diag(length(VOL)),diag(length(VOL)))
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CONSTRAINTS <- rbind(VOL_CONST,rev(VOL_CONST),ONLY_ONE_CONST)
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MAX_SIZE <- c(CIFS_SIZE,LATER_PHASE_SIZE,rep(1,length(VOL)))
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RES <- lp(direction = "max", objective.in = REV_ALL, const.mat =CONSTRAINTS,const.dir = "<=", const.rhs = MAX_SIZE, all.bin = TRUE)
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#TBL[RES$solution[1:(length(RES$solution)/2)]==1,]
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#RES$solution[(length(RES$solution)/2+1):length(RES$solution)]
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return(RES)
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}
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PROFIT_EST2 <- function(ADDED_PHASES,ST_YEAR,YEARS_AHEAD,NEXT_PHASE_YEARS_AHEAD,DATA=REACTOR_VALUES,DISCOUNT_RATE=0.05,ST_CAP=8680,PHASE_SIZE=5000,NEXT_PHASE_AHEAD_NUM=1){
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CURRENT <- DATA%>% filter(Year==ST_YEAR+YEARS_AHEAD,Discount==DISCOUNT_RATE)
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LATER <- DATA%>% filter(Year==ST_YEAR+NEXT_PHASE_YEARS_AHEAD,Discount==DISCOUNT_RATE)
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RES <- MAX_REV2(CURRENT,LATER,ST_CAP+PHASE_SIZE*ADDED_PHASES,PHASE_SIZE*NEXT_PHASE_AHEAD_NUM,NEXT_PHASE_YEARS_AHEAD,DISCOUNT_RATE)
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return(RES)
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}
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CURRENT <- REACTOR_VALUES %>% filter(Year==2042,Discount==0.05)
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LATER <- REACTOR_VALUES %>% filter(Year==2043,Discount==0.05)
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function(TBL,TBL2,CIFS_SIZE,LATER_PHASE_SIZE,LATER_PHASE_YEARS_AHEAD,DISCOUNT){
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MAX_REV2(CURRENT,LATER,8680+10000,5000,1,0.05)
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#####################
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PROFIT_EST <- function(ADDED_PHASES,ST_YEAR,YEARS_AHEAD,DATA=REACTOR_VALUES,DISCOUNT_RATE=0.05,ST_CAP=8680,PHASE_SIZE=5000){
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CURRENT <- DATA%>% filter(Year==ST_YEAR+YEARS_AHEAD,Discount==DISCOUNT_RATE)
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RES <- MAX_REV(CURRENT,ST_CAP+PHASE_SIZE*ADDED_PHASES)
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REVENUE <- RES$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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################################
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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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@ -99,12 +171,13 @@ REACTOR_VALUES <- readRDS("Data/Cleaned_Data/Reactor_Values.Rds")
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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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ADD_RES <- MAX_REV(CURRENT,STARTING_CAP+5000*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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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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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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@ -134,6 +207,39 @@ else {
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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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ST_YEAR <- 2026
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CONSTRAINED <- matrix(NA,nrow=30,ncol=40)
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PROFIT <- matrix(NA,nrow=30,ncol=40)
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for(i in ST_YEAR:(ST_YEAR+40)){
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COL <- i-ST_YEAR
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CURRENT <- REACTOR_VALUES %>% filter(Year==i,Discount==0.05)
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for(n in 1:30){
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C_RES <- try(ADDITION_CHECK(CURRENT,n,COL))
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CONSTRAINED[n,COL] <- C_RES[2]
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PROFIT[n,COL] <- C_RES[6]
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}
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}
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CONSTRAINED <- CONSTRAINED %>% as_tibble
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PROFIT <- PROFIT %>% as_tibble
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colnames(CONSTRAINED) <- ST_YEAR:(ST_YEAR+40)
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colnames(PROFIT) <- ST_YEAR:(ST_YEAR+40)
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CONSTRAINED$Size <- 1:30
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PROFIT$Size <- 1:30
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CONSTRAINED <- CONSTRAINED %>% select(Size,everything()) %>% pivot_longer(-Size,names_to="Year",values_to="Status")
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PROFIT <- PROFIT%>% select(Size,everything()) %>% pivot_longer(-Size,names_to="Year",values_to="Profit")
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PROFIT_RES <- PROFIT %>% filter(!is.na(Profit)) %>% group_by(Year) %>% mutate(Profit=as.numeric(Profit)) %>% filter(Profit==max(Profit)) %>% print(n=100)
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CONSTRAINED$Status <- ifelse(grepl("Not enough time to",CONSTRAINED$Status),"Time Limited",CONSTRAINED$Status)
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CONSTRAINED$Status %>% unique
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MAX_VOLUME <- CONSTRAINED %>% group_by(Year,Status) %>% summarize(Size=max(Size)) %>% filter(Status=="Capacity Constrainted")
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ggplot(MAX_VOLUME,aes(x=Year,y=Size))+geom_point()+scale_y_continuous(breaks=1:30)
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ggplot(PROFIT_RES,aes(x=Year,y=Size))+geom_point()+scale_y_continuous(breaks=1:30)
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9*5000+8680
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