Distribuition and Logistics
Transportation Task
Solve the following exercises, commenting all results.
1. The company Home Sweet Home produces pots and pans, which are distributed via two deposits of goods - the big four retail stores that represent their unique customers.
The unit costs of transportation, from the deposits to the warehouses for resale suggest the following average values.
Additionally, the daily limits for supply of the deposits (which present an area somewhat reduced), and the estimated daily demand of retail stores are also presented in the following table:
|
|
Warehouse 1
|
Warehouse 2
|
Warehouse 3
|
Warehouse 4
|
Supply
|
|
Deposit 1
|
4
|
12
|
14
|
14
|
70
|
|
Deposit 2
|
8
|
12
|
6
|
12
|
20
|
|
Demand
|
10
|
10
|
15
|
25
|
|
The Home Sweet Home aims to determine how best to distribute the articles deposited in two distribution centers in order to minimize transportation costs incurred with these business operations day to day.
a) Formulate the problem in linear programming.
b) Determine the optimal solution through the 3 methods studied.
2. A distributor of soft drinks has 3 warehouses (Lisbon, Oporto and Coimbra) and 3 markets to supply.
The annual availability of soft drinks in the warehouses of Lisbon, Porto and Coimbra is 12000, 15000, and 8000 liters respectively.
The quantities that can be sold in markets 1, 2 and 3 are 6, 14 and 10 thousand liters, respectively.
Traditionally, the company makes the distribution of its shipments via road. However, is being investigated an alternative to sending shipments by train.
Costs in thousands of euros per thousand liters of soda by rail, are as follows:
|
|
M1 |
M2
|
M3
|
|
Warehouse in Lisbon
|
12 |
-
|
12
|
|
Warehouse in Oporto
|
6 |
8
|
10
|
|
Warehouse in Coimbra
|
- |
16
|
12
|
There are no rail links from Lisbon to the market 2, neither of Coimbra to market 1.
a) Formulate the problem in linear programming.
b) Determine the optimal solution using the method of Vogel.