---
title: "Scheduling with MILP"
output: 
  flexdashboard::flex_dashboard:
    orientation: columns
    vertical_layout: fill
    social: menu
    source_code: embed
    theme: simplex
    css: www/css/custom.css
runtime: shiny
editor_options: 
  markdown: 
    wrap: 72
---

```{r setup, global, include=FALSE}
rm(list = ls())
library(shiny)
library(magrittr)
library(leaflet) # devtools::install_github('rstudio/leaflet')
library(highcharter) # devtools::install_github('jbkunst/highcharter')
library(plotly) # devtools::install_github('ropensci/plotly')
library(ggplot2) # devtools::install_github('hadley/ggplot2')
library(sp)
library(dplyr)
library(flexdashboard) # devtools::install_github('rstudio/flexdashboard')
library(rgeos)
library(mapproj)
library(maptools)
library(readr)
library(ggthemes)
library(knitr)
library(viridis)
library(formattable)
library(ggrepel)
library(ompr)
library(ompr.roi)
library(ROI.plugin.glpk)
source(file = "helper.R")
```

# Flight Scheduling Problem {data-vertical_layout="scroll"}

## Sidebar5 {.sidebar}

```{r}
hr()
  strong("Parameters")
  hr()
  br()
  sliderInput(inputId = "num_flights", label = "Number of Flights:",min = 1, max = 100, value = 60)
  sliderInput(inputId = "runway_capacity[1]", label = "R1 Capacity:", min = 1, max = 50, value = 30)
  sliderInput(inputId = "runway_capacity[2]", label = "R2 Capacity:", min = 1, max = 100,value =15)
  sliderInput(inputId = "runway_capacity[3]", label = "R3 Capacity:", min = 1, max = 100,value =17)
  br()
  actionButton(inputId = "solve_it5", label = "Schedule flights")
  hr()
  
```

## ##Row {data-width="1100"}

### Flight Scheduling Problem

```{r}



renderTable({
  input$solve_it5 
  if(input$solve_it5 == 0){num_flights <- input$num_flights
        runway_capacity <- c(input$`runway_capacity[1]`, input$`runway_capacity[2]`, input$`runway_capacity[3]`)
        # print(runway_capacity)  # Debugging statement
        return(solve_flight_scheduling(num_flights, runway_capacity))
  } else {
  isolate({
    withProgress(message = 'Scheduling in Progress', value = 0, {
      incProgress(0.5)
      if(input$solve_it5 > 0){
        num_flights <- input$num_flights
        runway_capacity <- c(input$`runway_capacity[1]`, input$`runway_capacity[2]`, input$`runway_capacity[3]`)
        # print(runway_capacity)  # Debugging statement
        return(solve_flight_scheduling(num_flights, runway_capacity))
      }
    })
  })
  }
})

  
```

## Row {data-width="1100"}

### Problem Background: Flight Scheduling Problem

<h4>The Warehouse Location Problem:</h4>

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# Staff Scheduling Problem {data-vertical_layout="scroll"}

## Sidebar2 {.sidebar}

```{r}
hr()
strong("Application Parameters")
hr()
br()
sliderInput(inputId = "num_physicians", label = "Number of Physicians:",min = 1, max = 30, value = 10)
sliderInput(inputId = "num_nurses", label = "Number of Nurses:", min = 1, max = 50, value = 30)
sliderInput(inputId = "num_assistants", label = "Number of Assistants:", min = 1, max = 100,value =60)
    br()
    actionButton(inputId = "solve_it4", label = "Schedule staff")
    hr()

```

## Row {data-width="1100"}

### Hospital Staff Scheduling Problem

```{r}
renderTable({
  input$solve_it4
  if(input$solve_it4 == 0){
     num_physicians <- input$num_physicians
        num_nurses <-  input$num_nurses
        num_assistants <- input$num_assistants
        optimize_result <- optimize_staffing(num_physicians, num_nurses, num_assistants)
        # print(runway_capacity)  # Debugging statement
        return(optimize_result)
  } else {
  isolate({
    withProgress(message = 'Scheduling in Progress', value = 0, {
      incProgress(0.5)
      if(input$solve_it4 > 0){
        num_physicians <- input$num_physicians
        num_nurses <-  input$num_nurses
        num_assistants <- input$num_assistants
        optimize_result <- optimize_staffing(num_physicians, num_nurses, num_assistants)
        
        return(optimize_result)
      }
    })
  })
  }
})

```

## Row {data-width="1100"}

### Problem Background: Hospital Staff Scheduling Problem

<h4>The mTSP vehicle routing problem:</h4>

<font size="2"> A hospital manager should plan the working timetable for
the hospital staff. Determine the minimum weekly cost associated with
the staff of this hospital if</font> - <font size="2">The daily working
time is structured in 3 shifts.</font> - <font size="2">In every shift
there should be at least 1 physician, 2 (male) nurses, and 3
assistants.</font> - <font size="2">The maximum total number of
employees needed on every shift is 10.</font> - <font size="2">The
salaries are: \$50/shift for a physician, \$20/shift for a nurse, and
\$10/shift for an assistant.</font> - <font size="2">The total number of
employees is: 15 physicians, 36 nurses, and 49 assistants.</font> -
<font size="2">Each employee should rest during at least two consecutive
shifts.<br> </font> <font size="2"> Formulate a mixed integer
programming problem <br> Decision Variables: $\small x_{ijk}$: Binary
variable indicating whether employee $\small i$ works in shift
$\small j$ on day $\small k$, where: $\small i$ represents each employee
(physician, male nurse, assistant), $\small j$ represents each shift
(1st shift, 2nd shift, 3rd shift), $\small k$ represents each day of the
week (Monday, Tuesday, ..., Sunday).<br> Objective Function:
$$\small \min \sum_{i}\sum_{j}\sum_{k} (50x_{ijk} + 20x_{ijk} + 10x_{ijk})$$
Subject to:<br> 1. Each shift should have at least 1 physician, 2 male
nurses, and 3 assistants:<br> $\small \sum_{i}x_{ijk} \geq 1$ B for
physicians,<br> $\small \sum_{i}x_{ijk} \geq 2$ B for male nurses,<br>
$\small \sum_{i}x_{ijk} \geq 3$ B for assistants,<br> 2. The maximum
total number of employees on every shift is 10:<br>
$\small \sum_{i}x_{ijk} \leq 10$ B ,<br> 3. Each employee should rest
during at least two consecutive shifts:<br>
$\small x_{ijk} + x_{i(j+1)k} + x_{i(j+2)k} \leq 1$<br> for all
employees and days of the week