Answer to Question #180303 in Operations Research for Harish

Question

A company has three cement plants from which cement has to be transported to four distribution centres. With identical costs of production at the three plants, the only variable costs involved are transportation costs. The monthly demand at the four distribution centres and the distance from the plants to the distribution centres (in km) are given below: Distribution centres Plants Monthly production (tonnes) 500 1,000 150 800 10,000 200 700 500 100 12,000 600 400 100 900 8,000 Monthly demand (tonnes) 9,000 9,000 10,000 4,000 The transportation charges are ? 10 per tonne per km. Suggest optimal transportation schedule and indicate the total minimum transportation cost. Specially Structured Linear Programmes I: Transportation and Transhipment Problems • 295 If, for certain reasons, route from plant C to distribution centre X is closed down, will the transp- ortation schedule change? If so, suggest the new schedule and effect on total cost.

Answer 1

Unbalanced transportation problem.

North West Corner Method:

Add a dummy row:

Minimum transportation cost:

$10\cdot(500\cdot9000+1000\cdot1000+700\cdot8000+500\cdot4000+900\cdot2000)=$

$=149,000,000$