Time and Temperature Profiles Generator.Rmd

---
title: "Time and Temperature Profiles Milk"
output: html_document
date: "2023-04-24"
---

#This document is used to create the milk time and temperature profiles.


## Run this chunk for libraries
```{r}
library(tidyverse)
library(reshape2)
```


##Functions to get temperature profiles

```{r}
#Function to get the h (heat transfer coefficient)
get_h<-function(Neg_slope, rho = 1.033, C = 4.2 , V = 0.236, A = 0.004275){
  #Neg slope for each condition
  neg_h =  ((Neg_slope*rho*C*V)/A)
  return(-neg_h)
} 


#This function gets temperature after some time. Based on Tinf and To
get_temp<-function(h, To, Tinf, time,  A =0.004275,rho =1.033, C= 4.2, V = 0.236 ){
  #Time in minutes
  #Tinf = External Temp
  #To = Initial temperature of the milk
  # h = convection trans coeff for that codition
  return (exp(-(h*A/rho*C*V)*(time))*(To-Tinf)+Tinf)
}

#Function to get the temperature profile from an external temperature vector (Time and Temperature Profile)
predict_temp_fromProf<-function(Time_Temp_Prof, Initial_Temp, h_condition){
  Time_Temp_Profile<-Time_Temp_Prof
  Temp_Initial = Initial_Temp
  Temp_V<-c()
  for (i in 1:length(Time_Temp_Profile)){
    T_inf<-Time_Temp_Profile[i]
    if (i == 1){
      New_Temp = Temp_Initial
    }else if (i == 2){
      New_Temp = get_temp(h = h_condition, To = Temp_Initial, Tinf =  T_inf, time = 1)
    }else{
      New_Temp = get_temp(h = h_condition, To = New_Temp, Tinf =  T_inf, time = 1)
    }
    Temp_V<-c(Temp_V, New_Temp)
  }
  return(Temp_V)
}

#Generate Temperature Conditions (Simulated Condition)
#Temperatures are a normal distribution
#tot time =minutes
#Iterval = minutes
Time_Temp_Creation_Var<-function(Total_Time, Interval, Mean_Temperature, SD_Temperature){
  Time_Temp_df<-rnorm(n =Total_Time+1, mean = Mean_Temperature, sd= SD_Temperature)
  return (Time_Temp_df)
}



#First cpnd = "Room Temp" , "Refrigeration", ....
#Second Cond= Same
#Total Time minutes - 1
#Interval = 1 minute
#Cycles = number of days

#Main function to create the time and temp profiles
Create_Temperature_Profile_days<-function(First_Cond, 
                                          Second_Cond, 
                                          First_Cond_Total_Time,
                                          Second_Cond_Total_Time,
                                          First_Cond_Mean_Temperature, 
                                          First_Cond_SD_Temperature,
                                          Second_Cond_Mean_Temperature, 
                                          Second_Cond_SD_Temperature,
                                          Interval, 
                                          Cycles){
  
    First_Cond_Temps<-Time_Temp_Creation_Var(Total_Time = First_Cond_Total_Time, Interval = Interval , 
                           Mean_Temperature = First_Cond_Mean_Temperature, 
                           SD_Temperature = First_Cond_SD_Temperature)
    Second_Cond_Temps<-Time_Temp_Creation_Var(Total_Time = Second_Cond_Total_Time, Interval = Interval , 
                                        Mean_Temperature = Second_Cond_Mean_Temperature, 
                                        SD_Temperature = Second_Cond_SD_Temperature)
    
    
    First_Cond_Temps_Desc<-rep(First_Cond,length(First_Cond_Temps))
    Second_Cond_Temps_Desc<-rep(Second_Cond,length(Second_Cond_Temps))
    
    Temp_Vector<-c()
    Cond_Vec<-c()
    for (i in 1:Cycles){
      Temp_Vector<-c(Temp_Vector,First_Cond_Temps,Second_Cond_Temps)
      Cond_Vec<-c(Cond_Vec,First_Cond_Temps_Desc,Second_Cond_Temps_Desc)
    }
    
    
    Simulated_Conditions<-data.frame("Rtemp" = Temp_Vector,
                                      "Condition" = Cond_Vec)
    return(Simulated_Conditions)
}



Create_Temperature_Profile_var<-function(Service_Cond,
                                         Break_Cond,
                                         Overnight_Cond,
                                         Service_Time,
                                         Break_Time,
                                         Overnight_Time,
                                         Service_Cond_Mean_Temperature,
                                         Service_Cond_SD_Temperature,
                                         Break_Cond_Mean_Temperature,
                                         Break_Cond_SD_Temperature,
                                         Overnight_Cond_Mean_Temperature,
                                         Overnight_Cond_SD_Temperature,
                                         services,
                                         Cycles,
                                         Interval) {
  Service_Condition<-Time_Temp_Creation_Var(Total_Time = Service_Time, Interval = Interval , 
                       Mean_Temperature = Service_Cond_Mean_Temperature, 
                       SD_Temperature = Service_Cond_SD_Temperature)

  Break_Condition<-Time_Temp_Creation_Var(Total_Time = Break_Time, Interval = Interval , 
                         Mean_Temperature = Break_Cond_Mean_Temperature, 
                         SD_Temperature = Break_Cond_SD_Temperature)
  
  Overnight_Condition<-Time_Temp_Creation_Var(Total_Time = Overnight_Time, Interval = Interval , 
                         Mean_Temperature = Overnight_Cond_Mean_Temperature, 
                         SD_Temperature = Overnight_Cond_SD_Temperature)
  
  Service_Cond_Temps_Desc<-rep(Service_Cond,length(Service_Condition))
  Break_Cond_Temps_Desc<-rep(Break_Cond,length(Break_Condition))
  Overnight_Cond_Temps_Desc<-rep(Overnight_Cond,length(Overnight_Condition))
  
  Vector_services<-c()
  condition_vector_services<-c()
  for (i in 1:services){
    if (i<services){
      Vector_services<-c(Vector_services,Service_Condition,Break_Condition)
      condition_vector_services<-c(condition_vector_services,Service_Cond_Temps_Desc,Break_Cond_Temps_Desc)
    } else if (i == services){
      Vector_services<-c(Vector_services,Service_Condition)
      condition_vector_services<-c(condition_vector_services,Service_Cond_Temps_Desc)
    }
  }
  
  Temp_Vector<-c()
  Cond_Vec<-c()
  for (i in 1:Cycles){
    Temp_Vector<-c(Temp_Vector,Vector_services,Overnight_Condition)
    Cond_Vec<-c(Cond_Vec,condition_vector_services,Overnight_Cond_Temps_Desc)
  }
  
  Simulated_Conditions<-data.frame("Rtemp" = Temp_Vector,
                                    "Condition" = Cond_Vec)
  return(Simulated_Conditions)
}



#Function to predict all milk based on the conditions...
#df = Milk df
#Temp_Initial = Milk's initial temperature. (Refrigeration)
predict_full_milk_temp<-function(df, Temp_Initial){
  Temp_Milk_Vectors<-c()
  Temp_Milk_Vectors<-c(Temp_Initial)
  T_inf = df$Rtemp[1]
  New_Temp = Temp_Initial
  for (i in 2:length(df$Rtemp)){
    #Selecting the condition that applies
    if (df$Condition[i] == "Room Temp"){
      h_condition = h_RTB
    } else if (df$Condition[i] == "Refrigeration"){
      h_condition = h_ref
    } else if (df$Condition[i] == "Refrigerated Tray"){
      h_condition = h_RT
    } else if (df$Condition[i] == "Tray With Ice Packs"){
      h_condition = h_TIP
    } else if (df$Condition[i] == "Tray With Ice"){
      h_condition = h_TIC
    } else if (df$Condition[i] == "Cooler with Ice"){
      h_condition = h_CI
    }
    #Checking if condition changed
    if(df$Condition[i] != df$Condition[i-1]){
      Condition_Change = 1
      T_inf = df$Rtemp[i]
    } else {
      Condition_Change = 0
    }
    
    #Predicting the new temperature
    New_Temp = get_temp(h = h_condition, To = New_Temp, Tinf =  T_inf, time = 1)
    Temp_Milk_Vectors<-c(Temp_Milk_Vectors,New_Temp)
  }
  return(Temp_Milk_Vectors)
}

```


## Generating H, temperature transfer coefficients
```{r}
#Negative Slopes
#Negative Slopes
Neg_Slope_RTB<-(-0.01293) #Room Temperature
Neg_Slope_Ref<-(-0.01620) #Refrigeration
Neg_Slope_RT<-(-0.01183) #Refrigerated Tray
Neg_Slope_TIC<-(-0.006528) #Tray with Ice 
Neg_Slope_TIP<-(-0.006007) #Tray with Ice Packs
Neg_Slope_CI<-(-0.002103) #Cooler with Ice

#Getting the Heat Transfer Coefficients for each Temp
h_RTB = get_h(Neg_slope = Neg_Slope_RTB)
h_ref = get_h(Neg_slope = Neg_Slope_Ref)
h_RT = get_h(Neg_slope = Neg_Slope_RT)
h_TIC = get_h(Neg_slope = Neg_Slope_TIC)
h_TIP = get_h(Neg_slope = Neg_Slope_TIP)
h_CI = get_h(Neg_slope = Neg_Slope_CI)

```


## Generating Specific Time and Temperature profiles for study

### Room Temp B 
```{r}
#Worst case scenario 124, 1314.125 min Room Temp - 21 hr 55 min Refrigerated Overnight"
Time_Temp_Df_RTB<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_RTB<-predict_full_milk_temp(df = Time_Temp_Df_RTB, Temp_Initial = 4.2)

Df_RT_MT_RTB<-data.frame("RoomTemp" = Time_Temp_Df_RTB$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_RTB,
                     "Time" = 1:length(Temp_Milk_Vectors_RTB))
Df_RT_MT_RTB_melted<-melt(Df_RT_MT_RTB, id.vars = "Time")
Df_RT_MT_RTB_melted$Condition = "Ambient Temperature 72°F (22.1°C)"
Df_RT_MT_RTB_melted$Scenario = "Condition Scenario"


#Saving as CSV
write.csv(Df_RT_MT_RTB, file = "Pedicted Time and Temp Profiles/Df_RT_MT_RTB.csv")
```

Plotting it 

```{r}
ggplot(data = Df_RT_MT_RTB_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "125 min Refrigerated Tray - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

#Unhash to save. 
#ggsave("Pedicted Time and Temp Profiles/PredictedRefTray.png", height = 3, width = 8, dpi = 300)

```

### Refrigerated Tray

```{r}
Time_Temp_Df_RT<-Create_Temperature_Profile_days(First_Cond = "Refrigerated Tray", 
                                              Second_Cond = "Refrigeration", 
                                              First_Cond_Total_Time = 124,
                                              Second_Cond_Total_Time = 1314,
                                              First_Cond_Mean_Temperature = 22.1, 
                                              First_Cond_SD_Temperature = 0,#0.77,
                                              Second_Cond_Mean_Temperature= 3.71, 
                                              Second_Cond_SD_Temperature = 0,#1.04,
                                              Interval  =1, 
                                              Cycles = 5)




Temp_Milk_RT<-predict_full_milk_temp(Time_Temp_Df_RT, Temp_Initial = 4)

Df_RT_MT_RT<-data.frame("RoomTemp" = Time_Temp_Df_RT$Rtemp,
                     "MilkTemp" = Temp_Milk_RT,
                     "Time" = 1:length(Temp_Milk_RT))
Df_RT_MT_RT_melted<-melt(Df_RT_MT_RT, id.vars = "Time")
Df_RT_MT_RT_melted$Condition = "Refrigerated Tray"
Df_RT_MT_RT_melted$Scenario = "Condition Scenario"


write.csv(Df_RT_MT_RT, file = "Pedicted Time and Temp Profiles/Df_RT_MT_RT.csv")
```

Plotting it 
```{r}
ggplot(data = Df_RT_MT_RT_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "125 min Refrigerated Tray - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedRefTray.png", height = 3, width = 8, dpi = 300)
```


### Tray with Ice Packs
```{r}
#Worst case scenario 124, 1314.125 min Tray with ice packs - 21 hr 55 min Refrigerated Overnight"
Time_Temp_Df_TIP<-Create_Temperature_Profile_days(First_Cond = "Tray With Ice Packs", 
                                                 Second_Cond = "Refrigeration", 
                                                 First_Cond_Total_Time = 124,
                                                 Second_Cond_Total_Time = 1314,
                                                 First_Cond_Mean_Temperature = 22.1, 
                                                 First_Cond_SD_Temperature = 0,#0.77,
                                                 Second_Cond_Mean_Temperature= 3.71, 
                                                 Second_Cond_SD_Temperature = 0,#1.04,
                                                 Interval  =1, 
                                                 Cycles = 5)




Temp_Milk_TIP<-predict_full_milk_temp(Time_Temp_Df_TIP, Temp_Initial = 4.2)

Df_RT_MT_TIP<-data.frame("RoomTemp" = Time_Temp_Df_TIP$Rtemp,
                        "MilkTemp" = Temp_Milk_TIP,
                        "Time" = 1:length(Temp_Milk_TIP))
Df_RT_MT_TIP_melted<-melt(Df_RT_MT_TIP, id.vars = "Time")
Df_RT_MT_TIP_melted$Condition = "Tray with Ice Packs"
Df_RT_MT_TIP_melted$Scenario = "Condition Scenario"


write.csv(Df_RT_MT_TIP, file = "Pedicted Time and Temp Profiles/Df_RT_MT_TIP.csv")

```

Plotting it
```{r}
ggplot(data = Df_RT_MT_TIP_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "125 min Tray with Ice Packs - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedTIP.png", height = 3, width = 8, dpi = 300)
```

### Tray with Ice 

```{r}
Time_Temp_Df_TIC<-Create_Temperature_Profile_days(First_Cond = "Tray With Ice", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_TIC<-predict_full_milk_temp(Time_Temp_Df_TIC, Temp_Initial = 4.2)

Df_RT_MT_TIC<-data.frame("RoomTemp" = Time_Temp_Df_TIC$Rtemp,
                         "MilkTemp" = Temp_Milk_TIC,
                         "Time" = 1:length(Temp_Milk_TIC))

Df_RT_MT_TIC_melted<-melt(Df_RT_MT_TIC, id.vars = "Time")
Df_RT_MT_TIC_melted$Condition = "Tray with Ice"
Df_RT_MT_TIC_melted$Scenario = "Condition Scenario"


write.csv(Df_RT_MT_TIC, file = "Pedicted Time and Temp Profiles/Df_RT_MT_TIC.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_TIC_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "125 min Tray with Ice - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedTIC.png", height = 3, width = 8, dpi = 300)
```

### Cooler with Ice

```{r}
Time_Temp_Df_CI<-Create_Temperature_Profile_days(First_Cond = "Cooler with Ice", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)




Temp_Milk_CI<-predict_full_milk_temp(Time_Temp_Df_CI, Temp_Initial = 4.2)

Df_RT_MT_CI<-data.frame("RoomTemp" = Time_Temp_Df_CI$Rtemp,
                         "MilkTemp" = Temp_Milk_CI,
                         "Time" = 1:length(Temp_Milk_CI))

Df_RT_MT_CI_melted<-melt(Df_RT_MT_CI, id.vars = "Time")
Df_RT_MT_CI_melted$Condition = "Cooler with Ice"
Df_RT_MT_CI_melted$Scenario = "Condition Scenario"



write.csv(Df_RT_MT_CI, file = "Pedicted Time and Temp Profiles/Df_RT_MT_CI.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_CI_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "125 min Cooler with Ice - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedCI.png", height = 3, width = 8, dpi = 300)
```

### Room Temp with Intermediate Ref
```{r}

Time_Temp_Df_RTB_refB<-Create_Temperature_Profile_var(Service_Cond = "Room Temp",
                                         Break_Cond ="Refrigeration",
                                         Overnight_Cond = "Refrigeration",
                                         Service_Time = 49,
                                         Break_Time = 24,
                                         Overnight_Time = 1314,
                                         Service_Cond_Mean_Temperature = 22.1,
                                         Service_Cond_SD_Temperature = 0,
                                         Break_Cond_Mean_Temperature = 3.71,
                                         Break_Cond_SD_Temperature = 0,
                                         Overnight_Cond_Mean_Temperature = 3.71,
                                         Overnight_Cond_SD_Temperature = 0,
                                         services = 2,
                                         Cycles = 5,
                                         Interval = 1)

Temp_Milk_RTB_refB<-predict_full_milk_temp(Time_Temp_Df_RTB_refB, Temp_Initial = 4.2)

Df_RT_MT_RTB_refB<-data.frame("RoomTemp" = Time_Temp_Df_RTB_refB$Rtemp,
                         "MilkTemp" = Temp_Milk_RTB_refB,
                         "Time" = 1:length(Temp_Milk_RTB_refB))

Df_RT_MT_RTB_refB_melted<-melt(Df_RT_MT_RTB_refB, id.vars = "Time")
Df_RT_MT_RTB_refB_melted$Condition = "Ambient with Intermediate Refrigeration"
Df_RT_MT_RTB_refB_melted$Scenario = "Condition Scenario"


write.csv(Df_RT_MT_RTB_refB, file = "Pedicted Time and Temp Profiles/Df_RT_MT_RTB_refB.csv")


```


Plotting it

```{r}
ggplot(data = Df_RT_MT_RTB_refB_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "RTB with ref breaks - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRTB_refB.png", height = 3, width = 8, dpi = 300)
```


##### TEmperature Conditions

## Room Temp B at 18 °C

```{r}
#Worst case scenario 124, 1314.125 min Room Temp - 21 hr 55 min Refrigerated Overnight"
Time_Temp_Df_RTB_18C<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 18.3, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_RTB_18C<-predict_full_milk_temp(df = Time_Temp_Df_RTB_18C, Temp_Initial = 4.2)

Df_RT_MT_RTB_18C<-data.frame("RoomTemp" = Time_Temp_Df_RTB_18C$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_RTB_18C,
                     "Time" = 1:length(Temp_Milk_Vectors_RTB_18C))
Df_RT_MT_RTB_18C_melted<-melt(Df_RT_MT_RTB_18C, id.vars = "Time")
Df_RT_MT_RTB_18C_melted$Condition = "Ambient Temperature 65°F (18.3° C)"
Df_RT_MT_RTB_18C_melted$Scenario = "Ambient Temperature Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_RTB_18C, file = "Pedicted Time and Temp Profiles/Df_RT_MT_RTB_18C.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_RTB_18C_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "RTB at 18.3°C - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRTB_18C.png", height = 3, width = 8, dpi = 300)
```

## Room Temp B at 21 °C

```{r}
Time_Temp_Df_RTB_21C<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 21.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_RTB_21C<-predict_full_milk_temp(df = Time_Temp_Df_RTB_21C, Temp_Initial = 4.2)

Df_RT_MT_RTB_21C<-data.frame("RoomTemp" = Time_Temp_Df_RTB_21C$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_RTB_21C,
                     "Time" = 1:length(Temp_Milk_Vectors_RTB_21C))
Df_RT_MT_RTB_21C_melted<-melt(Df_RT_MT_RTB_21C, id.vars = "Time")
Df_RT_MT_RTB_21C_melted$Condition = "Ambient Temperature 70°F (21.1° C)"
Df_RT_MT_RTB_21C_melted$Scenario = "Ambient Temperature Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_RTB_21C, file = "Pedicted Time and Temp Profiles/Df_RT_MT_RTB_21C.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_RTB_21C_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "RTB at 21.1°C - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRTB_21C.png", height = 3, width = 8, dpi = 300)
```

## Room Temp B at 23 °C

```{r}
Time_Temp_Df_RTB_23C<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 23.8, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_RTB_23C<-predict_full_milk_temp(df = Time_Temp_Df_RTB_23C, Temp_Initial = 4.2)

Df_RT_MT_RTB_23C<-data.frame("RoomTemp" = Time_Temp_Df_RTB_23C$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_RTB_23C,
                     "Time" = 1:length(Temp_Milk_Vectors_RTB_23C))
Df_RT_MT_RTB_23C_melted<-melt(Df_RT_MT_RTB_23C, id.vars = "Time")
Df_RT_MT_RTB_23C_melted$Condition = "Ambient Temperature 75°F (23.8° C)"
Df_RT_MT_RTB_23C_melted$Scenario = "Ambient Temperature Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_RTB_23C, file = "Pedicted Time and Temp Profiles/Df_RT_MT_RTB_23C.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_RTB_23C_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "RTB at 23.8°C - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRTB_23C.png", height = 3, width = 8, dpi = 300)
```


## Refrigeration Temp 2 C

```{r}
Time_Temp_Df_Ref_2C<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 2, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_Ref_2C<-predict_full_milk_temp(df = Time_Temp_Df_Ref_2C, Temp_Initial = 2)

Df_RT_MT_Ref_2C<-data.frame("RoomTemp" = Time_Temp_Df_Ref_2C$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_Ref_2C,
                     "Time" = 1:length(Temp_Milk_Vectors_Ref_2C))
Df_RT_MT_Ref_2C_melted<-melt(Df_RT_MT_Ref_2C, id.vars = "Time")
Df_RT_MT_Ref_2C_melted$Condition = "Overnight Refrigeration 36°F (2°C)"
Df_RT_MT_Ref_2C_melted$Scenario = "Overnight Refrigeration Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_Ref_2C, file = "Pedicted Time and Temp Profiles/Df_RT_MT_Ref_2C.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_Ref_2C_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 2°C ")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRef_2C.png", height = 3, width = 8, dpi = 300)
```


## Refrigeration Temp 7 C

```{r}
Time_Temp_Df_Ref_7C<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 7, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_Ref_7C<-predict_full_milk_temp(df = Time_Temp_Df_Ref_7C, Temp_Initial = 7)

Df_RT_MT_Ref_7C<-data.frame("RoomTemp" = Time_Temp_Df_Ref_7C$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_Ref_7C,
                     "Time" = 1:length(Temp_Milk_Vectors_Ref_7C))
Df_RT_MT_Ref_7C_melted<-melt(Df_RT_MT_Ref_7C, id.vars = "Time")
Df_RT_MT_Ref_7C_melted$Condition = "Overnight Refrigeration 45°F (7°C)"
Df_RT_MT_Ref_7C_melted$Scenario = "Overnight Refrigeration Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_Ref_7C, file = "Pedicted Time and Temp Profiles/Df_RT_MT_Ref_7C.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_Ref_7C_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 7°C ")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRef_7C.png", height = 3, width = 8, dpi = 300)
```

## Refrigeration Temp 4 C

```{r}
Time_Temp_Df_Ref_4C<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 4, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_Ref_4C<-predict_full_milk_temp(df = Time_Temp_Df_Ref_4C, Temp_Initial = 4)

Df_RT_MT_Ref_4C<-data.frame("RoomTemp" = Time_Temp_Df_Ref_4C$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_Ref_4C,
                     "Time" = 1:length(Temp_Milk_Vectors_Ref_4C))
Df_RT_MT_Ref_4C_melted<-melt(Df_RT_MT_Ref_4C, id.vars = "Time")
Df_RT_MT_Ref_4C_melted$Condition = "Overnight Refrigeration 39°F (4°C)"
Df_RT_MT_Ref_4C_melted$Scenario = "Overnight Refrigeration Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_Ref_4C, file = "Pedicted Time and Temp Profiles/Df_RT_MT_Ref_4C.csv")
```

Plotting it

```{r}
ggplot(data = Df_RT_MT_Ref_4C_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 4°C ")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRef_4C.png", height = 3, width = 8, dpi = 300)
```



## 5s4b

```{r}
Time_Temp_Df_s5b4<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 266,
                                                  Second_Cond_Total_Time = 1174,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_s5b4<-predict_full_milk_temp(df = Time_Temp_Df_s5b4, Temp_Initial = 4)

Df_RT_MT_s5b4<-data.frame("RoomTemp" = Time_Temp_Df_s5b4$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_s5b4,
                     "Time" = 1:length(Temp_Milk_Vectors_s5b4))
Df_RT_MT_s5b4_melted<-melt(Df_RT_MT_s5b4, id.vars = "Time")
Df_RT_MT_s5b4_melted$Condition = "5 Lunch (50 min) with 4 breaks (4 min)"
Df_RT_MT_s5b4_melted$Scenario = "Bell Schedule Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_s5b4, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s5b4.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s5b4_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 4°C ")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRef_4C.png", height = 3, width = 8, dpi = 300)
```


## 4b3b

```{r}
Time_Temp_Df_s4b3<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 221,
                                                  Second_Cond_Total_Time = 1219,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_s4b3<-predict_full_milk_temp(df = Time_Temp_Df_s4b3, Temp_Initial = 4)

Df_RT_MT_s4b3<-data.frame("RoomTemp" = Time_Temp_Df_s4b3$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_s4b3,
                     "Time" = 1:length(Temp_Milk_Vectors_s4b3))
Df_RT_MT_s4b3_melted<-melt(Df_RT_MT_s4b3, id.vars = "Time")
Df_RT_MT_s4b3_melted$Condition = "4 Lunch (50 min) with 3 breaks (7 min)"
Df_RT_MT_s4b3_melted$Scenario = "Bell Schedule Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_s4b3, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s4b3.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s4b3_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 4°C ")+
  scale_color_discrete(name = "Temperature Profile")

ggsave("Pedicted Time and Temp Profiles/PredictedRef_4C.png", height = 3, width = 8, dpi = 300)
```


## 1b

```{r}
Time_Temp_Df_s1b0<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 40,
                                                  Second_Cond_Total_Time = 1400,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_s1b0<-predict_full_milk_temp(df = Time_Temp_Df_s1b0, Temp_Initial = 4)

Df_RT_MT_s1b0<-data.frame("RoomTemp" = Time_Temp_Df_s1b0$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_s1b0,
                     "Time" = 1:length(Temp_Milk_Vectors_s1b0))
Df_RT_MT_s1b0_melted<-melt(Df_RT_MT_s1b0, id.vars = "Time")
Df_RT_MT_s1b0_melted$Condition = "1 Lunch (40 min) with 0 breaks"
Df_RT_MT_s1b0_melted$Scenario = "Bell Schedule Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_s1b0, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s1b0.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s1b0_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 4°C ")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedRef_4C.png", height = 3, width = 8, dpi = 300)
```

## 2s1b-short

```{r}
Time_Temp_Df_s2b1<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 74,
                                                  Second_Cond_Total_Time = 1366,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_s2b1<-predict_full_milk_temp(df = Time_Temp_Df_s2b1, Temp_Initial = 4)

Df_RT_MT_s2b1<-data.frame("RoomTemp" = Time_Temp_Df_s2b1$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_s2b1,
                     "Time" = 1:length(Temp_Milk_Vectors_s2b1))
Df_RT_MT_s2b1_melted<-melt(Df_RT_MT_s2b1, id.vars = "Time")
Df_RT_MT_s2b1_melted$Condition = "2 Lunches (30 min) with 1 break (14 min)"
Df_RT_MT_s2b1_melted$Scenario = "Bell Schedule Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_s2b1, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s2b1.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s2b1_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 4°C ")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedRef_4C.png", height = 3, width = 8, dpi = 300)
```

## 3s2b-short

```{r}
Time_Temp_Df_s3b2<-Create_Temperature_Profile_days(First_Cond = "Room Temp", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 124,
                                                  Second_Cond_Total_Time = 1314,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_Vectors_s3b2<-predict_full_milk_temp(df = Time_Temp_Df_s3b2, Temp_Initial = 4)

Df_RT_MT_s3b2<-data.frame("RoomTemp" = Time_Temp_Df_s3b2$Rtemp,
                     "MilkTemp" = Temp_Milk_Vectors_s3b2,
                     "Time" = 1:length(Temp_Milk_Vectors_s3b2))
Df_RT_MT_s3b2_melted<-melt(Df_RT_MT_s3b2, id.vars = "Time")
Df_RT_MT_s3b2_melted$Condition = "3 Lunches (31 min) with 2 break (16 min)"
Df_RT_MT_s3b2_melted$Scenario = "Bell Schedule Scenarios"


#Saving as CSV
write.csv(Df_RT_MT_s3b2, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s3b2.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s2b1_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "Overnight Refrigeration at 4°C ")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/PredictedRef_4C.png", height = 3, width = 8, dpi = 300)
```

##s4b3TIC
```{r}
Time_Temp_Df_s4b3TIC<-Create_Temperature_Profile_days(First_Cond = "Tray With Ice", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 221,
                                                  Second_Cond_Total_Time = 1219,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_s4b3TIC<-predict_full_milk_temp(Time_Temp_Df_s4b3TIC, Temp_Initial = 4.2)

Df_RT_MT_s4b3TIC<-data.frame("RoomTemp" = Time_Temp_Df_s4b3TIC$Rtemp,
                         "MilkTemp" = Temp_Milk_s4b3TIC,
                         "Time" = 1:length(Temp_Milk_s4b3TIC))

Df_RT_MT_s4b3TIC_melted<-melt(Df_RT_MT_s4b3TIC, id.vars = "Time")
Df_RT_MT_s4b3TIC_melted$Condition = "4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice"
Df_RT_MT_s4b3TIC_melted$Scenario = "Longer Bell Schedules Plus Storage System"


write.csv(Df_RT_MT_s4b3TIC, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s4b3TIC.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s4b3TIC_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/Predicteds4b3TIC.png", height = 3, width = 8, dpi = 300)
```

##s4b3TIP
```{r}
Time_Temp_Df_s4b3TIP<-Create_Temperature_Profile_days(First_Cond = "Tray With Ice Packs", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 221,
                                                  Second_Cond_Total_Time = 1219,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_s4b3TIP<-predict_full_milk_temp(Time_Temp_Df_s4b3TIP, Temp_Initial = 4.2)

Df_RT_MT_s4b3TIP<-data.frame("RoomTemp" = Time_Temp_Df_s4b3TIP$Rtemp,
                         "MilkTemp" = Temp_Milk_s4b3TIP,
                         "Time" = 1:length(Temp_Milk_s4b3TIP))

Df_RT_MT_s4b3TIP_melted<-melt(Df_RT_MT_s4b3TIP, id.vars = "Time")
Df_RT_MT_s4b3TIP_melted$Condition = "4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice Packs"
Df_RT_MT_s4b3TIP_melted$Scenario = "Longer Bell Schedules Plus Storage System"


write.csv(Df_RT_MT_s4b3TIP, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s4b3TIP.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s4b3TIP_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice Packs")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/Predicteds4b3TIP.png", height = 3, width = 8, dpi = 300)
```



##s5b4TIC
```{r}
Time_Temp_Df_s5b4TIC<-Create_Temperature_Profile_days(First_Cond = "Tray With Ice", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 266,
                                                  Second_Cond_Total_Time = 1174,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_s5b4TIC<-predict_full_milk_temp(Time_Temp_Df_s5b4TIC, Temp_Initial = 4.2)

Df_RT_MT_s5b4TIC<-data.frame("RoomTemp" = Time_Temp_Df_s5b4TIC$Rtemp,
                         "MilkTemp" = Temp_Milk_s5b4TIC,
                         "Time" = 1:length(Temp_Milk_s5b4TIC))

Df_RT_MT_s5b4TIC_melted<-melt(Df_RT_MT_s5b4TIC, id.vars = "Time")
Df_RT_MT_s5b4TIC_melted$Condition = "5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice"
Df_RT_MT_s5b4TIC_melted$Scenario = "Longer Bell Schedules Plus Storage System"


write.csv(Df_RT_MT_s5b4TIC, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s5b4TIC.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s5b4TIC_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/Predicteds5b4TIC.png", height = 3, width = 8, dpi = 300)
```


##s5b4TIP
```{r}
Time_Temp_Df_s5b4TIP<-Create_Temperature_Profile_days(First_Cond = "Tray With Ice Packs", 
                                                  Second_Cond = "Refrigeration", 
                                                  First_Cond_Total_Time = 266,
                                                  Second_Cond_Total_Time = 1174,
                                                  First_Cond_Mean_Temperature = 22.1, 
                                                  First_Cond_SD_Temperature = 0,#0.77,
                                                  Second_Cond_Mean_Temperature= 3.71, 
                                                  Second_Cond_SD_Temperature = 0,#1.04,
                                                  Interval  =1, 
                                                  Cycles = 5)


Temp_Milk_s5b4TIP<-predict_full_milk_temp(Time_Temp_Df_s5b4TIP, Temp_Initial = 4.2)

Df_RT_MT_s5b4TIP<-data.frame("RoomTemp" = Time_Temp_Df_s5b4TIP$Rtemp,
                         "MilkTemp" = Temp_Milk_s5b4TIP,
                         "Time" = 1:length(Temp_Milk_s5b4TIP))

Df_RT_MT_s5b4TIP_melted<-melt(Df_RT_MT_s5b4TIP, id.vars = "Time")
Df_RT_MT_s5b4TIP_melted$Condition = "5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice Packs"
Df_RT_MT_s5b4TIP_melted$Scenario = "Longer Bell Schedules Plus Storage System"


write.csv(Df_RT_MT_s5b4TIP, file = "Pedicted Time and Temp Profiles/Df_RT_MT_s5b4TIP.csv")
```

Plotting it
```{r}
ggplot(data = Df_RT_MT_s5b4TIP_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)", title= "5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice Packs")+
  scale_color_discrete(name = "Temperature Profile")

#ggsave("Pedicted Time and Temp Profiles/Predicteds5b4TIP.png", height = 3, width = 8, dpi = 300)
```




### Plotting all of them together

```{r}

All_6_melted<-rbind(Df_RT_MT_RTB_melted,
                    Df_RT_MT_RT_melted,
                    Df_RT_MT_TIC_melted,
                    Df_RT_MT_TIP_melted,
                    Df_RT_MT_CI_melted,
                    Df_RT_MT_RTB_refB_melted,
                    Df_RT_MT_RTB_18C_melted,
                    Df_RT_MT_RTB_21C_melted,
                    Df_RT_MT_RTB_23C_melted,
                    Df_RT_MT_Ref_2C_melted,
                    Df_RT_MT_Ref_4C_melted,
                    Df_RT_MT_Ref_7C_melted,
                    Df_RT_MT_s5b4_melted,
                    Df_RT_MT_s4b3_melted,
                    Df_RT_MT_s2b1_melted,
                    Df_RT_MT_s1b0_melted,
                    Df_RT_MT_s3b2_melted,
                    Df_RT_MT_s4b3TIC_melted,
                    Df_RT_MT_s4b3TIP_melted,
                    Df_RT_MT_s5b4TIC_melted,
                    Df_RT_MT_s5b4TIP_melted
                    )

#All_6_melted$Condition<-str_replace(All_6_melted$Condition, pattern = "Room Temp B", replacement = "Baseline")

All_6_melted$Condition<-factor(All_6_melted$Condition, levels = c("Ambient Temperature 72°F (22.1°C)", "Refrigerated Tray", "Tray with Ice Packs", "Tray with Ice", "Cooler with Ice", "Ambient with Intermediate Refrigeration","Ambient Temperature 65°F (18.3° C)","Ambient Temperature 70°F (21.1° C)","Ambient Temperature 75°F (23.8° C)", "Overnight Refrigeration 36°F (2°C)","Overnight Refrigeration 39°F (4°C)","Overnight Refrigeration 45°F (7°C)","5 Lunch (50 min) with 4 breaks (4 min)","4 Lunch (50 min) with 3 breaks (7 min)","2 Lunches (30 min) with 1 break (14 min)","1 Lunch (40 min) with 0 breaks", "3 Lunches (31 min) with 2 break (16 min)","4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice","4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice Packs","5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice","5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice Packs" ))

Max_RTB<-round(max(Df_RT_MT_RTB$MilkTemp),1)
Max_RT<-round(max(Df_RT_MT_RT$MilkTemp),1)
Max_TIC<-round(max(Df_RT_MT_TIC$MilkTemp),1)
Max_TIP<-round(max(Df_RT_MT_TIP$MilkTemp),1)
Max_CI<-round(max(Df_RT_MT_CI$MilkTemp),1)
Max_RTB_refB<-round(max(Df_RT_MT_RTB_refB$MilkTemp),1)
Max_RTB_18C<-round(max(Df_RT_MT_RTB_18C$MilkTemp),1)
Max_RTB_21C<-round(max(Df_RT_MT_RTB_21C$MilkTemp),1)
Max_RTB_23C<-round(max(Df_RT_MT_RTB_23C$MilkTemp),1)
Max_Ref_2C<-round(max(Df_RT_MT_Ref_2C$MilkTemp),1)
Max_Ref_4C<-round(max(Df_RT_MT_Ref_4C$MilkTemp),1)
Max_Ref_7C<-round(max(Df_RT_MT_Ref_7C$MilkTemp),1)
Max_s5b4<-round(max(Df_RT_MT_s5b4$MilkTemp),1)
Max_s4b3<-round(max(Df_RT_MT_s4b3$MilkTemp),1)
Max_s2b1<-round(max(Df_RT_MT_s2b1$MilkTemp),1)
Max_s1b0<-round(max(Df_RT_MT_s1b0$MilkTemp),1)
Max_s3b2<-round(max(Df_RT_MT_s3b2$MilkTemp),1)
Max_s4b3TIC<-round(max(Df_RT_MT_s4b3TIC$MilkTemp),1)
Max_s4b3TIP<-round(max(Df_RT_MT_s4b3TIP$MilkTemp),1)
Max_s5b4TIC<-round(max(Df_RT_MT_s5b4TIC$MilkTemp),1)
Max_s5b4TIP<-round(max(Df_RT_MT_s5b4TIP$MilkTemp),1)


#Text SHOWING THE MAX TEMP
dat_text <- data.frame(
label = c(paste("Milk Peak:",Max_RTB,"°C"), 
          paste("Milk Peak:",Max_RT,"°C"), 
          paste("Milk Peak:",Max_TIC,"°C"), 
          paste("Milk Peak:",Max_TIP,"°C"), 
          paste("Milk Peak:",Max_CI,"°C"),
          paste("Milk Peak:",Max_RTB_refB,"°C"),
          paste("Milk Peak:",Max_RTB_18C,"°C"),
          paste("Milk Peak:",Max_RTB_21C,"°C"),
          paste("Milk Peak:",Max_RTB_23C,"°C"),
          paste("Milk Peak:",Max_Ref_2C,"°C"),
          paste("Milk Peak:",Max_Ref_4C,"°C"),
          paste("Milk Peak:",Max_Ref_7C,"°C"),
          paste("Milk Peak:",Max_s5b4,"°C"),
          paste("Milk Peak:",Max_s4b3,"°C"),
          paste("Milk Peak:",Max_s2b1,"°C"),
          paste("Milk Peak:",Max_s1b0,"°C"),
          paste("Milk Peak:",Max_s3b2,"°C"),
          paste("Milk Peak:",Max_s4b3TIC,"°C"),
          paste("Milk Peak:",Max_s4b3TIP,"°C"),
          paste("Milk Peak:",Max_s5b4TIC,"°C"),
          paste("Milk Peak:",Max_s5b4TIP,"°C")
          ),
Condition   = c("Ambient Temperature 72°F (22.1°C)", "Refrigerated Tray", "Tray with Ice", "Tray with Ice Packs", "Cooler with Ice", "Ambient with Intermediate Refrigeration","Ambient Temperature 65°F (18.3° C)","Ambient Temperature 70°F (21.1° C)","Ambient Temperature 75°F (23.8° C)", "Overnight Refrigeration 36°F (2°C)","Overnight Refrigeration 39°F (4°C)","Overnight Refrigeration 45°F (7°C)","5 Lunch (50 min) with 4 breaks (4 min)","4 Lunch (50 min) with 3 breaks (7 min)","2 Lunches (30 min) with 1 break (14 min)","1 Lunch (40 min) with 0 breaks","3 Lunches (31 min) with 2 break (16 min)","4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice","4 Lunch (50 min) with 3 breaks (7 min) under Tray with Ice Packs","5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice","5 Lunch (50 min) with 4 breaks (4 min) Under Tray with Ice Packs"),

Scenario   = c("Condition Scenario", "Condition Scenario", "Condition Scenario", "Condition Scenario", "Condition Scenario", "Condition Scenario", "Ambient Temperature Scenarios","Ambient Temperature Scenarios","Ambient Temperature Scenarios","Overnight Refrigeration Scenarios","Overnight Refrigeration Scenarios","Overnight Refrigeration Scenarios","Bell Schedule Scenarios","Bell Schedule Scenarios","Bell Schedule Scenarios","Bell Schedule Scenarios","Bell Schedule Scenarios","Longer Bell Schedules Plus Storage System","Longer Bell Schedules Plus Storage System","Longer Bell Schedules Plus Storage System","Longer Bell Schedules Plus Storage System" ),
  x     = c(6725, 6725, 6725,6725,6725, 6725, 6725,6725, 6725, 6725, 6725,6725, 6800,6725, 6725,6725,6725,6800,6800,6800,6800),
  y     = c(23, 23, 23,23,23,23,23, 23, 23,23,23,23,23,23,23,23,23,23,23,23,23)
)


All_6_melted$Scenario<-factor(All_6_melted$Scenario, levels = c("Condition Scenario","Ambient Temperature Scenarios","Overnight Refrigeration Scenarios","Bell Schedule Scenarios","Longer Bell Schedules Plus Storage System"))

dat_text$Scenario<-factor(dat_text$Scenario, levels = c("Condition Scenario","Ambient Temperature Scenarios","Overnight Refrigeration Scenarios","Bell Schedule Scenarios","Longer Bell Schedules Plus Storage System"))

ggplot(data = All_6_melted, aes(x = Time, y = value))+
  geom_line(size = 0.6, aes(color = variable))+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)")+
  scale_color_manual(name = "Temperature Profile", values = c("#00AFBB", "#FC4E07"))+
  #scale_linetype_discrete(name = "Temperature Profile")+
  facet_wrap(Scenario~Condition, ncol=3)+
  theme(legend.position = "right")+
  geom_text(data = dat_text, mapping = aes(x = x, y = y, label = label), size =3) +
  theme(legend.position = "top",strip.text = element_text(face="bold"),strip.background = element_rect(fill="lightgrey"))

ggsave("Pedicted Time and Temp Profiles/All Temp Combined.png", height = 10, width = 16, dpi = 300)


```

```{r}
All_Temp_melted<-rbind(Df_RT_MT_RTB_18C_melted,
                       Df_RT_MT_RTB_21C_melted,
                       Df_RT_MT_RTB_23C_melted)


All_Temp_melted$Condition<-factor(All_Temp_melted$Condition, levels = c("Ambient Temperature 65°F (18.3° C)","Ambient Temperature 70°F (21.1° C)","Ambient Temperature 75°F (23.8° C)"))

ggplot(data = All_Temp_melted, aes(x = Time, y = value, color = variable))+
  geom_line(size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "Temperature (°C)")+
  scale_color_discrete(name = "Temperature Profile")+
  facet_wrap(~Condition, ncol= 1)+
  theme(legend.position = "right")

ggsave("Pedicted Time and Temp Profiles/All Temp Combined Temperature.png", height = 10, width = 10, dpi = 300)
```





## Spilage Model, To create secondary plots - Not needed to Manuscript

### Spoilage Model Functions
```{r}
#Function for growth and lag phase
new_growth_rate<-function(newTemp, oldMu,oldTemp = 6, T0 = -4.15){
  newMu<-((newTemp-T0)/(oldTemp-T0))* oldMu
  return (newMu)
}

#Calculation of the new lag time.
new_lag_time <- function (newTemp, oldLag, oldTemp = 6, T0 = -4.15) {
  numerator <- oldTemp -T0
  denom <- newTemp - T0
  newLag <- ( (numerator / denom)^2) * oldLag
  return(newLag)
}

#This function calculates thee growth based on a time and temperature profile for 1 specific milk with R100084 P Paoae
Func_Growth_LagCon<-function(In_Lag_Consumed, Time_Temp_df,Interval, AF){
  #In_Lag_Consumed= Total lag time consumed
  #Time_Temp_df = dataframe with time and temperature conditions
  #Interval = time interval in the time_temp_df in hrs. 
  Total_Lag_Consumed = In_Lag_Consumed
  Total_Growth = 0
  old_lag = 0
  NMax = 8.14
  old_mumax = 0.083508
  Growth_V = c()
  for (i in 1:nrow(Time_Temp_df)){
    if (Total_Lag_Consumed <1 && old_lag!=0){
      Lag_t_interval<-new_lag_time(newTemp = Time_Temp_df$MilkTemp[i], oldLag = old_lag)
      Lag_Consumed<-Interval/Lag_t_interval
      Total_Lag_Consumed<-Total_Lag_Consumed+Lag_Consumed
      Growth = 0
    } else if (Total_Lag_Consumed>=1 | old_lag == 0){
      Growth = ((new_growth_rate(newTemp = Time_Temp_df$MilkTemp[i], oldMu = old_mumax))/2.303)* AF#0.684 #Converted log10 from log ln
      Total_Growth = Total_Growth + (Growth*Interval)
    }
    Growth_V = c(Growth_V,Total_Growth)
    #print(length(Growth_V))
  }
  return(list(Total_Growth,Total_Lag_Consumed,Growth_V))
}

#Buchanan spoilage function
Spoilage_Function_Single_Milk<-function(Cont, Pop_Max, Time_Temp_df, Interval =1/60, AF){
  Lag_Consumed = 0
  #this function provides two outputs, the total growth, and the new updated lag phase consumed. 
  Output_Milk<-Func_Growth_LagCon(In_Lag_Consumed = Lag_Consumed ,Time_Temp_df = Time_Temp_df,Interval = Interval, AF=AF)
  Lag_Consumed = Output_Milk[[2]]
  Cont<-Output_Milk[[1]]+Cont
  if( Cont>Pop_Max){
    Cont = Pop_Max
  }
  return (list(Cont,Output_Milk[[3]]))
}

```


### Spoilage prediction for Room Temp B
```{r}
#Room Temp 2 hr -----
Output_Milk<-Spoilage_Function_Single_Milk(Cont = 2.44, Pop_Max =8.14, Time_Temp_df = Df_RT_MT_RTB, Interval =1/60,AF = 1.32)

Changes_Over_Time<-2.44+Output_Milk[[2]]

Df_RT_MT_RTB_melted$Type<-"Temperature Profiles"

data_Milk_G_RTB<-data.frame("Time" = 1:length(Changes_Over_Time),
                            "variable" = "Population Change",
                            "value" = Changes_Over_Time,
                            "Type" = "Population Changes")

new_dat = rbind(Df_RT_MT_RTB_melted,data_Milk_G_RTB)

ggplot(data = new_dat, aes(x = Time))+
  geom_line(aes(y = value, color = variable),size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "", title= "125 min Room Temp - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Line Description")+
  facet_wrap(~Type, scales = "free_y", ncol= 1,labeller = as_labeller(c(`Population Changes` = "Population (log CFU/g)", `Temperature Profiles` = "Temperature (°C)") ),strip.position = "left", )

#ggsave("Pedicted Time and Temp Profiles/TempandChange_RTB.png", height = 4, width = 8, dpi = 300)
```


### Spoilage prediction for 2 hr -----
```{r}
Output_Milk<-Spoilage_Function_Single_Milk(Cont = 2.44, Pop_Max =8.14, Time_Temp_df = Df_RT_MT_RT, Interval =1/60,AF = 1.32)
Changes_Over_Time_RT<-2.44+Output_Milk[[2]]

Df_RT_MT_RT_melted$Type<-"Temperature Profiles"

data_Milk_G_RT<-data.frame("Time" = 1:length(Changes_Over_Time_RT),
                            "variable" = "Population Change",
                            "value" = Changes_Over_Time_RT,
                            "Type" = "Population Changes")

new_dat_RT = rbind(Df_RT_MT_RT_melted,data_Milk_G_RT)

ggplot(data = new_dat_RT, aes(x = Time))+
  geom_line(aes(y = value, color = variable),size = 1)+
  theme_bw()+
  labs(x = "Time (min)", y = "", title= "125 min Refrigerated Tray - 21 hr 55 min Refrigerated Overnight")+
  scale_color_discrete(name = "Line Description")+
  facet_wrap(~Type, scales = "free_y", ncol= 1,labeller = as_labeller(c(`Population Changes` = "Population (log CFU/g)", `Temperature Profiles` = "Temperature (°C)") ),strip.position = "left", )

#ggsave("Pedicted Time and Temp Profiles/TempandChange_RTB.png", height = 4, width = 8, dpi = 300)
```