Transportation model

TRANSPORTATION MODELLeast Cost Method (LCM)

BY-Swapnil(26),sagar(02) &

dwarkesh(05)

Transportation Model•The problem of finding the minimum-cost distribution of a given commodity from a group of supply centers (sources) i=1,…,mto a group of receiving centers (destinations) j=1,…,n

•Each source has a certain supply (si)

•Each destination has a certain demand (dj)

•The cost of shipping from a source to a destination is directly proportional to the number of units shipped

Priyanshu enterprise has 3 plants at location P1,P2 & P3 which supplies 3 warehouses located at W1,W2,W3 monthly plant capacities are 20,28,17 units respectively Monthly warehouse requirments are 21,25,19 units respectively .Unit shipping cost (in Rs.) are given in the following table and determine the lowest cost

W1 W2 W3 Supply

P1 7 6 9 20

P2 5 7 3 28

P3 4 5 8 17

Demand 21 25 19 65

CASE STUDY

LCM and application in real life

Case studyA company is spending Rs. 1000 on transportation of its units from these plants P1,P2,P3 to four distribution centers D1,D2,D3,D4. The supply and requirement of units, with unity cost of transportation are given as: Find the optimum solution of the model.

The solution is basic feasible as there are m + n – 1, i.e., 4 + 3 – 1 = 6 allocations in independent solutions.

Initial basic feasible solution: 12 * 7 + 70 * 3 + 40 * 7 + 40 * 2 + 10 * 8 + 20 * 8 = Rs. 894.

Application Can be used to resolve distribution and location decisions

• The Cost of shipping one unit

The destination points and the demand per period at each

• Rational decisions in urban infrastructure projects

For making rational decisions about investments in transportation

Application of Transportation Model

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