# Implements North-West Corner Algorithm to solve transportation problem

### Description

This function implements North-West Corner Algorithm to solve transportation problem by optimized cost matrix and total optimized cost

### Usage

1 2 | ```
# Get optimized cost matrix for input matrix ex_matrix
nwc(ex_matrix)
``` |

### Arguments

`ex_matrix` |
A cost matrix where last column must be the supply and last row must be the demand. Input matrix should not have any missing values (NA), otherwise function will throw an error. |

### Details

This function takes a cost matrix (with Supply and Demand) and using North-West Corner approach gives the cost allocation matrix as well as the calcualted optimized cost. This function checks for degenerated problem but it can't resolve it. User need to resolve by seeing the cost allocation matrix.

### Value

A List which contrains the Cost allocation matrix and the total optimized cost.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
## Not run:
#Input matrix where last row is the Demand and last column is the Supply
ex_matrix=data.frame(M1=c(13,10,25,17,210),M2=c(25,19,10,24,240),
M3=c(8,18,15,18,110),M4=c(13,5,14,13,80),M5=c(20,12,18,19,170),
Supply=c(430,150,100,130,810),
row.names = c("W1","W2","W3","W4","Demand"))
ex_matrix
M1 M2 M3 M4 M5 Supply
W1 13 25 8 13 20 430
W2 10 19 18 5 12 150
W3 25 10 15 14 18 100
W4 17 24 18 13 19 130
Demand 210 240 110 80 170 810
nwc(ex_matrix)
$Alloc_Matrix
M1 M2 M3 M4 M5
W1 210 220 0 0 0
W2 0 20 110 20 0
W3 0 0 0 60 40
W4 0 0 0 0 130
$Total_Cost
[1] 14720
## End(Not run)
``` |

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