# Why i receive an error from R while i knit it to pdf

``````---
title: 'Homework 2 for Metra Potential Method '
author: "Nikos Matsavelas"
date: "3/26/2020"
output:
pdf_document: default
word_document: default
bibliography: bibliography.bib
html_document: default
---
## Operational Research Homework
This homework is from Dr.Ioannis Coletsos exercises assignment in NTUA MSc in Applied Mathematical Sciences (Flow C:Probability & Statistics)

```{r}

library(igraph)
library(ProjectManagement)
library(projmanr)
```

##  Precedence Design Matrix

There are four types of precedence between two activities \$i,j\$:
Type 1:(Finish-Start) the activity \$j\$ cannot start until activity \$i\$ has finished.
Type 2:(Start-Start) the activity \$j\$ cannot start until activity \$i\$ has started.
Type 3:(Finish-Finish) the activity \$j\$ cannot end until activity \$i\$ has ended.
Type 4:(Start-Finish) the activity \$j\$ cannot end until activity \$i\$ has started.

All these precedences can be written only as type 1. It should be noted that precedence type 1 implies type 2, and type 2 implies type 4. On the other hand, precedence type 1 implies type 3, and type 3 implies type 4.

## Constructing the PDM

We willconstruct a matrix which indicates the order of precedence type 1 and 2 between the activities (Default=matrix(0)). If value \$(i, j)\$ = 1 then activity \$i\$ precedes type 1 to \$j\$, and if \$(i, j)\$ = 2 then activity \$i\$ precedes type 2 to \$j\$.As we know ycles cannot exist in a project, i.e. if an activity \$i\$ precedes \$j\$ then \$j\$ cannot precede \$i\$.

For precedence type 3 and 4 between the activities (Default=matrix(0)). If value \$(i, j) = 3\$ then activity \$i\$ precedes type 3 to \$j\$, and if \$(i, j) = 4\$ then activity \$i\$ precedes type 4 to \$j\$

So there are 4 types of indicating an activity in a precedence matrix:
Type 1 : \$FS_{ij}\$
Type 2 : \$SS_{ij}\$
Type 3 : \$FF_{ij}\$
Type 4 : \$SF_{ij}\$

## Matrix of Problem 6

For our problem all the activities are of Type 1 :\$FS_{ij}\$.So we have:

```{r}

D = matrix(c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0),19,19,byrow =TRUE)

colnames(D) = c("A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S")
rownames(D) = c("A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S")
D
```

##  Vector with elements the duration of each activity

Here we have added two slack activities \$P_{1},P_{2}\$ with duration both 0
```{r}
duration = c(0,1,1,2,1,2,1,1,2,3,2,3,3,3,3,2,2,0,0)
```

## Earliest Time of the Project

```{r}
earliest = early.time(prec1and2=D,duration=duration)
earliest
max(earliest)
```

## Latest Time of the Project

```{r}
latest = last.time(prec1and2=D,duration=duration,early.times=earliest)
latest
max(latest)

```

```{r}
ID6       = c(1:19)
names     = c("T1","T2","T3","T4","T5","T6","T7","T8","T9","T10","T11","T12","T13","T14","T15","T16","T17","P1","P2")
duration  = c(0,1,1,2,1,2,1,1,2,3,2,3,3,3,3,2,2,0,0)
pred      = c(" ","1","1","2,3","4","4,5","6","5","6","7","8,18","10","11","12","13","14","14,19","7,9","15,16")
pred      = as.factor(pred);class(pred)
data6     = data.frame(ID6,names,duration,pred);data6
res6      = critical_path(data6)
```

## Critical Path of the Project

```{r}
res6\$critical_path
```

## Duration of the Project

```{r}
res6\$total_duration
```

## Gannt Chart of the Project

```{r}
gantt(data6,bar_size = 5, text_size = 3)
gantt(res6,bar_size = 5, text_size = 3)
```

## Network Diagram

```{r}
network_diagram(data6)
```

```{r}
network_diagram(res6)
```
``````

! Package inputenc Error: Unicode character Μ (U+039C)
(inputenc) not set up for use with LaTeX.

Try other LaTeX engines instead (e.g., xelatex) if you are using pdflatex. For R Markdown users, see https://bookdown.org/yihui/rmarkdown/pdf-document.html
Error: LaTeX failed to compile Untitled.tex. See https://yihui.org/tinytex/r/#debugging for debugging tips. See Untitled.log for more info.
In addition: There were 50 or more warnings (use warnings() to see the first 50)
Execution halted

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