Question

A recycling company takes various cartons and produces three different types of recycled paper. The raw material of the imported cartons is basically the same, the mixture of recycled papers is not important. These three types of recyclable paper are obtained from parcel cardboard, general use cardboard and ornamental cardboard. The first type can be made from parcels and general use cartons, the second can be made from general use and ornamental cartons, and the third one can use three types of cartons. In the production of the first type of paper, 20% of the input cardboard weight goes to waste. For the second and third types of paper, this rate is 40% and 20% respectively.. It is necessary to produce 240 tons, 207 tons from the second type of paper and 132 tons from the third type of paper. For the supply of the process and cartons.
a) Consider this information and establish an evaluation transportation model to reduce the costs of this company. Create the transport chart. b) Find a baseline feasible solution using the Vogel Approach.
The following are the data for the table of the problem
Purchase cost per ton: parcel = 10, General Usage = 9, Ornamental = 8,
Processing cost per ton: parcel for type one = 3, parcel for type three = 4, general use for type one = 4, general use for type two = 1, general use for type three= 6, ornamental for type two = 5 , ornamental for type three = 3.
Supply (Ton): parcel = 500, general use = 300, ornamental = 200

Answer 1

Solution :

Vogel's approach :

In this method, the difference between two least costs cells are noted and the difference is noted. Identify that row or column having the highest difference, and allocation is made in that particular row/column that has the the least cost.

In the image given below, the first allocation is made to type 1- dummy as, the difference for that column is high and the dummy has the least cost.

The second allocation is made to type 1-ornamental & the 3rd allocation to type 2-cardboard.

The remaining allocations are made as per the balance figures.

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