Economic-mathematical methods

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Examination EMM

We formulate the problem as follows. Three farms (A1, A2, A3) supply products to three plants (B1, B2, B3). These plants have at three depots sites (D1, D2, D3) which are arranged at a distance from farms and factories are designed to receive products, short storage and subsequent shipment to its plants. The volume of deliveries of production farms, warehouses opportunities, power plants and distances between farms, warehouses and factories are shown in the following table.
Availability of cargo from suppliers Consumer demand storage capacity Distance between points
D1 D2 D3 B1 B2 B3
A1 B1 105 90 400 A1 D1 10 D1 September 6 5 8 February
A2 170 A2 380 260 B2 A2 A2 5 5 4 3 7 5
250 A3 B3 A3 360 A3 330 6 7 5 6 4 June D3

Requires a plan of transporting products from the farms to the warehouses, then points to the plants, which would have a minimum total ton-kilometer performance.

Additional information

Task 2 - production problems
The purpose of scheduling is to allocate four varieties of bread production between furnaces four systems so that their capacities are used more fully, and thus the production costs are the lowest
In order to solve the economic problems of production and in which the ratio of performance of different machines with the release of different products can not be established, special methods of distribution and checking it for optimality. One such method is the method lambda (lambda algorithm). Initial data:
Number 28 types of products and the demand for it potential line
Types of equipment and fund working time B1, B2, B3, B4 Bf
400 270 250 300
A1 50 12 3 10 2 15 5 8 1 1 0
A2 30 8 8 10 5 10 5 20 5 1 0
A3 90 6 3 10 8 8 2 15 3 1 0
A4 80 5 5 7 1 10 5 10 2 1 0
Potential column vj


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