Operations Research practice problems in Transportation Problem

1. A firm has 3 plants A, B & C and 4 warehouses W1, W2, W3 W4. Plant capacities are 1100, 1300 & 1900 units. Warehouse demands are 600, 1000, 1200 & 1500 units. Using cost data given below, find Optimal transportation cost. Find IFS by VAM.

2. Transportation unit cost matrix –

Find Initial Feasible solution by VAM & Optimal solution by Modified Distribution method. Is there an alternate optimal solution? Comment.

3. Following table shows supply and demand (In thousand units). Find IFS by VAM and Optimal solution by MODI method.

4. There are three plants A, B, and C with capacities of 120, 80 and 200 units. They supply to four warehouses P, Q, R, and S with demand of 60, 50, 140 & 50 units. Find IFS by VAM and Optimal solution by MODI method.

Transportation unit cost matrix –

5. Transportation unit cost matrix –

Find IFS by VAM and Optimal solution by MODI method.

Does degeneracy occur during any stage of the solution? If yes, comment on it.

6. Transportation unit cost matrix –

Find IFS by NWCR and Optimal solution by MODI method. Does degeneracy occur during any stage of the solution? If yes, comment on it.

7. Transportation unit cost matrix –

Find initial solution by NWCR & Optimal solution by MODI.

8. There are four factories & three sales depots. Production, raw material & transportation costs (per unit) along with sales prices are given. Find IFS by VAM and Optimal allocation.

9. Following data refers to unit profit for transportation from each plant to each warehouse. There are three plants P1, P2 and P3 with capacities of 2000 units each. They supply to three market locations M1, M2 and M3 where demand is 1500, 3000 and 1500 units.

Find IFS by VAM and Optimal solution by MODI method.

10. Four warehouses with capacities of 85, 35, 50 and 45 tons were receiving the materials from 3 factories, with their supply capacity as 70, 55 and 90 tons on regular basis. The transportation costs per ton from factories to warehouses are given in the following table:

(Apr 2004)

A feasible solution states that from Factory I, 25 tons have to be transported to warehouse 3 and 45 tons to Warehouse 4.  Similarly 30 tons and 25 tons were transported from Factory II to warehouse 1 and Warehouse 3 respectively.  However, from Factory III, 55 tons and 35 tones were transported to warehouse 1 and warehouse 2 respectively.

Is this transportation schedule optimum? If not, modify it and obtain optimum solution and optimum cost.

11. From three warehouses W1, W2, and W3 the stocks are to be transported to four markets M1, M2, and M4. The supplies from warehouses are 300, 200, and 250 tons respectively. Whereas the requirements of markets are 325, 175, 100, 150 tons respectively.

The cost matrix and initial solution is a given in the following table.

Perform the Post Optimality Analysis on the above table and answer the following:

Is he above solution feasible?

• Is the solution optimal? Is there more than one solution?
• Is it degenerate?
• Calculate the opportunity cost of transport ting one unit from W1 to M4.
• The manager is forced to transport one unit from W2 to M4, find the rate of increase in the cost per unit.
• If a transport carrier offers 20% discount on route W2 to M4 provided at least 20 units are transported from this route, should the management accept the offer?
• Due to some problem at W1 its supply is reduced by 2 units. To compensate for the loss it is decided to increase the supply by 2 units from W2. Will such a decision lead to increase the cost?  If yes what is the increase/

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