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Vogel's approximation Method is an application developed for an assignment of a Linear Programming class, with the goal of determine solutions for linear problems using the Vogel's approximation method to the Transport Problem.
A company received orders for Silver Carburetors from its traveling salesmen to different cities in the states of the Southeast region of Brazil.
| Orders | |
|---|---|
| Cities | Quantity |
| Angra dos Reis | 289 |
| Belford Roxo | 335 |
| Campos dos Goytacazes | 319 |
| Cariacica | 268 |
| Contagem | 314 |
| Duque de Caxias | 812 |
| Guarulhos | 1253 |
| Linhares | 276 |
| Mauá | 345 |
| Niterói | 482 |
| Nova Iguaçu | 831 |
| Osasco | 630 |
| Ribeirão Preto | 833 |
| Rio de Janeiro | 1461 |
| Santo André | 962 |
| São Bernardo do Campo | 605 |
| São Gonçalo | 829 |
| São José dos Campos | 572 |
| São Paulo | 1959 |
| Serra | 481 |
| Sorocaba | 333 |
| Uberaba | 998 |
| Vila Velha | 390 |
| Vitória | 251 |
The company has 5 distribution centers, where its products are stored:
| Offer | |
|---|---|
| Distribution Center | Inventory |
| Belo Horizonte | 6500 |
| Governador Valadares | 2100 |
| Juiz de Fora | 4400 |
| Montes Claros | 2300 |
| Uberlândia | 1700 |
Carburettor delivery is outsourced. The Largest Names of Alternative Transport charge to carry out each delivery the unit price that varies according to the distance traveled:
| Transport Cost Table (unit) | |||||
|---|---|---|---|---|---|
| Belo Horizonte | Gov. Valadares | Juiz de Fora | Montes Claros | Uberlândia | |
| Angra dos Reis | 27,65 | 35,4 | 14,95 | 48,6 | 47,5 |
| Belford Roxo | 21,7 | 29,4 | 9 | 42,6 | 47,9 |
| Campinas | 29 | 4,8 | 26,4 | 48,65 | 24,9 |
| Campos dos Goytacazes | 23,8 | 23,1 | 15,15 | 44,3 | 50 |
| Cariacica | 25,75 | 18,3 | 23,7 | 26,75 | 41,85 |
| Contagem | 1 | 17,75 | 13,2 | 20,45 | 26,1 |
| Duque de Caxias | 20,95 | 28,7 | 8,25 | 33,75 | 48,5 |
| Guarulhos | 28,6 | 43,95 | 23,1 | 48,5 | 30,1 |
| Linhares | 29,05 | 14,7 | 29,85 | 39,2 | 55,85 |
| Mauá | 30,6 | 46,25 | 24,25 | 50,6 | 31,65 |
| Niterói | 22,3 | 30 | 9,5 | 43,1 | 49,8 |
| Nova Iguaçu | 22,05 | 29,8 | 9,25 | 42,85 | 47,6 |
| Osasco | 30,05 | 45,45 | 24,65 | 50,05 | 19,3 |
| Ribeirão Preto | 25,8 | 41,2 | 31,5 | 41,05 | 14 |
| Rio de Janeiro | 22,2 | 29,25 | 9,1 | 42,8 | 49,5 |
| Santo André | 30 | 35,75 | 25,15 | 50,1 | 30,45 |
| São Bernardo do Campo | 29,95 | 45 | 25,3 | 49,9 | 30,35 |
| São Gonçalo | 22,85 | 29 | 9,9 | 43,45 | 50,15 |
| São José dos Campos | 30,4 | 31,75 | 19,5 | 50,35 | 32,45 |
| São Paulo | 29,25 | 24 | 23,9 | 49,25 | 29,5 |
| Serra | 27,2 | 51 | 24,4 | 40,95 | 27,4 |
| Sorocaba | 33,6 | 23,55 | 28,5 | 53,35 | 28,85 |
| Uberaba | 24 | 39,4 | 36,5 | 32,9 | 4,9 |
| Vila Velha | 25,45 | 17,6 | 22,8 | 42,45 | 52,9 |
| Vitória | 25,95 | 17,9 | 23,8 | 42,15 | 52,75 |
The purpose of this case study is to determine the lowest total transport cost for orders to be delivered to the ordering cities, also indicating which CD will be left over after all deliveries.