| Title: | Implementation of Transportation Problem Algorithm |
|---|---|
| Description: | Implementation of two transportation problem algorithms. 1. North West Corner Method 2. Minimum Cost Method or Least cost method. For more technical details about the algorithms please refer below URLs. <http://www.universalteacherpublications.com/univ/ebooks/or/Ch5/nw.htm>. <http://personal.maths.surrey.ac.uk/st/J.F/chapter7.pdf>. |
| Authors: | Somenath Sit |
| Maintainer: | Somenath Sit <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1 |
| Built: | 2024-10-29 05:46:23 UTC |
| Source: | https://github.com/somenath24/transp |
This function implements Minimum Cost Algorithm to resolve transportation problem and get optimized allocation matrix
mincost(ex_matrix)mincost(ex_matrix)
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. |
This function takes a cost matrix (with Supply and Demand) and using North-West Corner approach gives the 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 final allocation matrix. If Supply and Demand are not equal Balance Supply/Demand will be stored in Dummy variable.
A List which contrains the allocation matrix and the total optimized cost.
## 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 mincost(ex_matrix) $Alloc_Matrix M1 M2 M3 M4 M5 W1 140 140 110 0 40 W2 70 0 0 80 0 W3 0 100 0 0 0 W4 0 0 0 0 130 $Total_Cost [1] 11570 ## End(Not run)## 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 mincost(ex_matrix) $Alloc_Matrix M1 M2 M3 M4 M5 W1 140 140 110 0 40 W2 70 0 0 80 0 W3 0 100 0 0 0 W4 0 0 0 0 130 $Total_Cost [1] 11570 ## End(Not run)
This function implements North-West Corner Algorithm to solve transportation problem by optimized cost matrix and total optimized cost
# Get optimized cost matrix for input matrix ex_matrix nwc(ex_matrix)# Get optimized cost matrix for input matrix ex_matrix nwc(ex_matrix)
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. |
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.
A List which contrains the Cost allocation matrix and the total optimized cost.
## 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)## 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)