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optimization.R
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optimization.R
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#updated 12/11
#summary: monthly optimization of gin trash to generate electricity and/or ammonia
#I use the lp function from lpSolve package for optimization
#There is another package called linprog (same arguments as linprog from matlab)
#but lpSolve is written in C which is a compiled language as opposed to R, which is an interpreted language
#One consequence of this is that lpsolve is much faster than linprog
#More details: http://www.noamross.net/archives/2014-04-16-vectorization-in-r-why/
#The optimization here is a monthly iteration with annual gin trash data (9 iteration in a year)
#So each iteration is dependent on the results of previous iterations
#I also have 10,000 rows of data, meaning each sequence of a full iteration is run 10,000 times, which I do using a loop
#I can use a nested loop for the iterations; but, the conditions in each iteration (obj function, constraints) are different
#So writing a nested loop may make the codes cleaner but at the expense of my readability
rm(list=ls())
library(lpSolve)
data <- read.csv("gin.csv")
#sensitivity analysis:
#(i) change eff=2/3;
#(ii) reduce lower base to 25;
#(iii) reduce ammonia marginal cost to 85 (change 17.35 to 13.23);
#(iv) change extra_fc=75000;
#(v) increase electricity price by 10%, price_inc=1.1 instead of 1.0
n=nrow(data)
U <- data$gin_medium
c=7 #electricity plant capacity
m=0 #no. of ammonia plant
#only for sensitivity analysis
eff=1
extra_fc=0
price_inc=1.1
XC=matrix(NA, nrow=n, ncol=55)
XC <- assign(paste("XC", c, m, sep = ""), matrix(NA, nrow=n, ncol=55))
#profvis
system.time(
for (i in seq_along(XC[,1])){
f.con <- matrix (c(1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1), nrow = 6, byrow = TRUE)
f.dir <- c("<=", "<=", "<=", "<=", "<=", "<=")
f.con_sum <- matrix (c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 5, byrow = TRUE)
f.dir_sum <- c("<=", "<=", "<=", "<=", "<=")
#for december
f.obj <- c((data$dec_peak[i]*price_inc-5.5), (data$dec_ubase[i]*price_inc-5.5), (data$dec_lbase[i]*price_inc-5.5), ((data$winter_crop[i]/11-17.35)))
f.rhs <- c(340*c*eff, U[i]*eff, 68*c*eff, 187*c*eff, 85*c*eff, 369*m*eff)
results_dec <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_dec$solution[1]+results_dec$solution[2]+results_dec$solution[3]+results_dec$solution[4])*1/eff
XC[i,1] <- results_dec$solution[1]
XC[i,12] <- results_dec$solution[2]
XC[i,23] <- results_dec$solution[3]
XC[i,34] <- results_dec$solution[4]
XC[i,45] <- as.numeric(format(round(U[i]-total, 3), nsmall=3))
gin <- XC[i,45]
#for january
f.obj <- c((data$jan_peak[i]*price_inc-5.5), (data$jan_ubase[i]*price_inc-5.5), (data$jan_lbase[i]*price_inc-5.5), ((data$winter_crop[i]/11-17.35)))
f.rhs <- c(620*c*eff, gin*eff, 217*c*eff, 248*c*eff, 155*c*eff, 672*m*eff)
results_jan <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_jan$solution[1]+results_jan$solution[2]+results_jan$solution[3]+results_jan$solution[4])*1/eff
XC[i,2] <- results_jan$solution[1]
XC[i,13] <- results_jan$solution[2]
XC[i,24] <- results_jan$solution[3]
XC[i,35] <- results_jan$solution[4]
XC[i,46] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,46]
#for february
f.obj <- c((data$feb_peak[i]*price_inc-5.5), (data$feb_ubase[i]*price_inc-5.5), (data$feb_lbase[i]*price_inc-5.5), ((data$winter_crop[i]/11-17.35)))
f.rhs <- c(560*c*eff, gin*eff, 196*c*eff, 224*c*eff, 140*c*eff, 640*m*eff)
results_feb <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_feb$solution[1]+results_feb$solution[2]+results_feb$solution[3]+results_feb$solution[4])*1/eff
XC[i,3] <- results_feb$solution[1]
XC[i,14] <- results_feb$solution[2]
XC[i,25] <- results_feb$solution[3]
XC[i,36] <- results_feb$solution[4]
XC[i,47] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,47]
#march divided into two parts: first part has peak electricity and second part does not
#for march first half with peak electricity
f.obj <- c((data$mar_peak[i]*price_inc-5.5), (data$mar_ubase[i]*price_inc-5.5), (data$mar_lbase[i]*price_inc-5.5), ((data$summer_crop[i]/11-17.35)))
f.rhs <- c(300*c*eff, gin*eff, 60*c*eff, 165*c*eff, 75*c*eff, 325*m*eff)
results_mar1 <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_mar1$solution[1]+results_mar1$solution[2]+results_mar1$solution[3]+results_mar1$solution[4])*1/eff
XC[i,4] <- results_mar1$solution[1]
XC[i,15] <- results_mar1$solution[2]
XC[i,26] <- results_mar1$solution[3]
XC[i,37] <- results_mar1$solution[4]
XC[i,48] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,48]
#for march second half without peak electricity
f.obj <- c((data$mar_ubase[i]*price_inc-5.5), (data$mar_lbase[i]*price_inc-5.5), ((data$summer_crop[i]/11-17.35)))
f.rhs <- c(304*c*eff, gin*eff, 224*c*eff, 80*c*eff, 347*m*eff)
results_mar2 <- lp("max", f.obj, f.con_sum, f.dir_sum, f.rhs)
total <- as.numeric(results_mar2$solution[1]+results_mar2$solution[2]+results_mar2$solution[3])*1/eff
XC[i,5] <- 0
XC[i,16] <- results_mar2$solution[1]
XC[i,27] <- results_mar2$solution[2]
XC[i,38] <- results_mar2$solution[3]
XC[i,49] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,49]
#for april
f.obj <- c((data$apr_ubase[i]*price_inc-5.5), (data$apr_lbase[i]*price_inc-5.5), ((data$summer_crop[i]/11-17.35)))
f.rhs <- c(570*c*eff, gin*eff, 420*c*eff, 150*c*eff, 672*m*eff)
results_apr <- lp("max", f.obj, f.con_sum, f.dir_sum, f.rhs)
total <- as.numeric(results_apr$solution[1]+results_apr$solution[2]+results_apr$solution[3])*1/eff
XC[i,6] <- 0
XC[i,17] <- results_apr$solution[1]
XC[i,28] <- results_apr$solution[2]
XC[i,39] <- results_apr$solution[3]
XC[i,50] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,50]
#for may
f.obj <- c((data$may_ubase[i]*price_inc-5.5), (data$may_lbase[i]*price_inc-5.5), ((data$summer_crop[i]/11-17.35)))
f.rhs <- c(589*c*eff, gin*eff, 434*c*eff, 155*c*eff, 672*m*eff)
results_may <- lp("max", f.obj, f.con_sum, f.dir_sum, f.rhs)
total <- as.numeric(results_may$solution[1]+results_may$solution[2]+results_may$solution[3])*1/eff
XC[i,7] <- 0
XC[i,18] <- results_may$solution[1]
XC[i,29] <- results_may$solution[2]
XC[i,40] <- results_may$solution[3]
XC[i,51] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,51]
#for june
f.obj <- c((data$jun_peak[i]*price_inc-5.5), (data$jun_ubase[i]*price_inc-5.5), (data$jun_lbase[i]*price_inc-5.5), ((data$roy_crop[i]/11-17.35)))
f.rhs <- c(600*c*eff, gin*eff, 150*c*eff, 150*c*eff, 300*c*eff, 672*m*eff)
results_jun <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_jun$solution[1]+results_jun$solution[2]+results_jun$solution[3]+results_jun$solution[4])*1/eff
XC[i,8] <- results_jun$solution[1]
XC[i,19] <- results_jun$solution[2]
XC[i,30] <- results_jun$solution[3]
XC[i,41] <- results_jun$solution[4]
XC[i,52] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,52]
#for july
f.obj <- c((data$jul_peak[i]*price_inc-5.5), (data$jul_ubase[i]*price_inc-5.5), (data$jul_lbase[i]*price_inc-5.5), ((data$roy_crop[i]/11-17.35)))
f.rhs <- c(620*c*eff, gin*eff, 155*c*eff, 155*c*eff, 310*c*eff, 672*m*eff)
results_jul <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_jul$solution[1]+results_jul$solution[2]+results_jul$solution[3]+results_jul$solution[4])*1/eff
XC[i,9] <- results_jul$solution[1]
XC[i,20] <- results_jul$solution[2]
XC[i,31] <- results_jul$solution[3]
XC[i,42] <- results_jul$solution[4]
XC[i,53] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,53]
#for august
f.obj <- c((data$aug_peak[i]*price_inc-5.5), (data$aug_ubase[i]*price_inc-5.5), (data$aug_lbase[i]*price_inc-5.5), ((data$roy_crop[i]/11-17.35)))
f.rhs <- c(610*c*eff, gin*eff, 150*c*eff, 150*c*eff, 300*c*eff, 672*m*eff)
results_aug <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_aug$solution[1]+results_aug$solution[2]+results_aug$solution[3]+results_aug$solution[4])*1/eff
XC[i,10] <- results_aug$solution[1]
XC[i,21] <- results_aug$solution[2]
XC[i,32] <- results_aug$solution[3]
XC[i,43] <- results_aug$solution[4]
XC[i,54] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,54]
#for september
f.obj <- c((data$sep_peak[i]*price_inc-5.5), (data$sep_ubase[i]*price_inc-5.5), (data$sep_lbase[i]*price_inc-5.5), ((data$roy_crop[i]/11-17.35)))
f.rhs <- c(300*c*eff, gin*eff, 75*c*eff, 75*c*eff, 150*c*eff, 336*m*eff)
results_sep <- lp("max", f.obj, f.con, f.dir, f.rhs)
total <- as.numeric(results_sep$solution[1]+results_sep$solution[2]+results_sep$solution[3]+results_sep$solution[4])*1/eff
XC[i,11] <- results_sep$solution[1]
XC[i,22] <- results_sep$solution[2]
XC[i,33] <- results_sep$solution[3]
XC[i,44] <- results_sep$solution[4]
XC[i,55] <- as.numeric(format(round(gin-total, 3), nsmall=3))
gin <- XC[i,55]
}
)
XC <- as.data.frame(XC)
summary(XC)
XC$extra_profit <- XC$V55*10
XC$V48 <- XC$V48-XC$V55
XC$V49 <- XC$V49-XC$V55
XC$V50 <- XC$V50-XC$V55
XC$V51 <- XC$V51-XC$V55
XC$V52 <- XC$V52-XC$V55
XC$V53 <- XC$V53-XC$V55
XC$V54 <- XC$V54-XC$V55
XC$V55 <- XC$V55-XC$V55
XC$cost <- XC$V45+XC$V46+XC$V47+XC$V48+XC$V49+XC$V50+XC$V51+XC$V52+XC$V53+XC$V54+XC$V55
price_mat <- matrix(c(c(data$dec_peak*price_inc-5.5), c(data$jan_peak*price_inc-5.5), c(data$feb_peak*price_inc-5.5), c(data$mar_peak*price_inc-5.5), c(rep(0, n)),
c(rep(0, n)), c(rep(0, n)), c(data$jun_peak*price_inc-5.5), c(data$jul_peak*price_inc-5.5), c(data$aug_peak*price_inc-5.5), c(data$sep_peak*price_inc-5.5),
c(data$dec_ubase*price_inc-5.5), c(data$jan_ubase*price_inc-5.5), c(data$feb_ubase*price_inc-5.5), c(data$mar_ubase*price_inc-5.5), c(data$mar_ubase*price_inc-5.5),
c(data$apr_ubase*price_inc-5.5), c(data$may_ubase*price_inc-5.5), c(data$jun_ubase*price_inc-5.5), c(data$jul_ubase*price_inc-5.5), c(data$aug_ubase*price_inc-5.5),
c(data$sep_ubase*price_inc-5.5),
c(data$dec_lbase*price_inc-5.5), c(data$jan_lbase*price_inc-5.5), c(data$feb_lbase*price_inc-5.5), c(data$mar_lbase*price_inc-5.5), c(data$mar_lbase*price_inc-5.5),
c(data$apr_lbase*price_inc-5.5), c(data$may_lbase*price_inc-5.5), c(data$jun_lbase*price_inc-5.5), c(data$jul_lbase*price_inc-5.5), c(data$aug_lbase*price_inc-5.5),
c(data$sep_lbase*price_inc-5.5),
c(data$winter_crop/11-17.35), c(data$winter_crop/11-17.35), c(data$winter_crop/11-17.35), c(data$summer_crop/11-17.35),
c(data$summer_crop/11-17.35), c(data$summer_crop/11-17.35), c(data$summer_crop/11-17.35), c(data$roy_crop/11-17.35),
c(data$roy_crop/11-17.35), c(data$roy_crop/11-17.35), c(data$roy_crop/11-17.35)), nrow=n, ncol=44, byrow=FALSE)
prod_mat <- as.matrix(XC[, -c(45:ncol(XC))])
XC$profit <- rowSums(price_mat*prod_mat)-37645*m-0.100385*(640000+(4000000/(1.2*c+5)))*c+XC$extra_profit-XC$cost-extra_fc
XC$electricity <- ifelse(c==0, 0, ifelse(c==1, 1285161, ifelse(c==2, 2300255, ifelse(c==3, 3233510, ifelse(c==4, 4108624,
ifelse(c==5, 4960041, ifelse(c==6, 5770701, ifelse(c==7, 6559135, ifelse(c==8, 7336343, 8104855)))))))))
XC$ammonia <- ifelse(m==0, 0, ifelse(m==1, 350000, ifelse(m==2, 700000, ifelse(m==3, 1050000, ifelse(m==4, 1400000, 1750000)))))
XC$roic <- XC$profit/((XC$electricity+XC$ammonia)*0.25)
XC$loss <- ifelse(XC$profit<0, 1, 0)
XC$roic100 <- ifelse(XC$roic>=1, 1, 0)
assign(paste("XC", c, m, sep = ""), XC)
XC %>% filter(between(profit, quantile(profit, 0.00), quantile(profit, 0.95))) -> XC_new
#profit table reporting average annual profit and ROIC
profit_table <- data.frame(Model=paste0("C=", c, ", M=", m), MWe=c, Ammonia=m, Ave_ROIC=mean(XC$roic)*100,
Prob_loss=mean(XC$loss)*100, Prob_ROIC=mean(XC$roic100)*100, Mean_profit=mean(XC$profit),
SD_profit=sd(XC$profit), Extra=mean(XC$extra_profit), Cost=mean(XC$cost),
Ave_ROIC_95=mean(XC_new$roic)*100, Prob_loss_95=mean(XC_new$loss)*100,
Prob_ROIC_95=mean(XC_new$roic100)*100, Mean_profit_95=mean(XC_new$profit), SD_profit_95=sd(XC_new$profit))
profit_table
#production table reporting average annual electricity and ammonia production
prod_table <- data.frame(dec=mean(colMeans(XC[, c(1,12,23)])), dec=mean(XC[, c(34)])/11,
jan=mean(colMeans(XC[, c(2,13,24)])), jan=mean(XC[, c(35)])/11,
feb=mean(colMeans(XC[, c(3,14,25)])), feb=mean(XC[, c(36)])/11,
mar1=mean(colMeans(XC[, c(4,15,26)])), mar1=mean(XC[, c(37)])/11,
mar2=mean(colMeans(XC[, c(5,16,27)])), mar2=mean(XC[, c(38)])/11,
apr=mean(colMeans(XC[, c(6,17,28)])), apr=mean(XC[, c(39)])/11,
may=mean(colMeans(XC[, c(7,18,29)])), may=mean(XC[, c(40)])/11,
jun=mean(colMeans(XC[, c(8,19,30)])), jun=mean(XC[, c(41)])/11,
jul=mean(colMeans(XC[, c(9,20,31)])), jul=mean(XC[, c(42)])/11,
aug=mean(colMeans(XC[, c(10,21,32)])), aug=mean(XC[, c(43)])/11,
sep=mean(colMeans(XC[, c(11,22,33)])), sep=mean(XC[, c(44)])/11)
prod_table
year <- rep(1:833, each=12)
year <- append(year, c(2,6,9,12))
set.seed(12345)
year <- sample(year)
XC$year <- year
XC_group = XC %>% group_by(year) %>%
summarise(profit = sum(profit)*0.3757,
#roic = sum(profit)*0.3757/(XC$electricity[1]*0.25+XC$ammonia[1]*0.25),
n = n())
XC_group$roic <- 100*XC_group$profit/(XC$electricity[1]*0.25+XC$ammonia[1]*0.25)
#cumulative profit table reporting average profit and ROIC over a 12-year period
agg_table <- data.frame(Model=paste0("C=", c, ", M=", m), Ave_Profit=mean(XC_group$profit), SD_Profit=sd(XC_group$profit),
Ave_ROIC=mean(XC_group$roic), ROIC0=nrow(subset(XC_group, roic<0)), ROIC100=nrow(subset(XC_group, roic>=0 & roic<250)),
ROIC200=nrow(subset(XC_group, roic>=250 & roic<500)), ROIC300=nrow(subset(XC_group, roic>=500)))
agg_table