# 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.

 W1 W2 W3 W4 Capacity A 20 16 25 13 1100 B 17 18 14 23 1300 C 32 27 18 41 1900 Demand 600 1000 1200 1500

1. Transportation unit cost matrix –

 D1 D2 D3 D4 Capacity P1 110 120 90 60 700 P2 70 30 70 70 600 P3 60 60 90 110 900 Demand 600 400 600 200

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

1. Following table shows supply and demand (In thousand units). Find IFS by VAM and Optimal solution by MODI method.
 W1 W2 W3 W4 Capacity P1 18 30 50 12 7 P2 70 30 40 60 10 P3 40 10 60 20 18 Demand 5 8 7 15

1. 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 –

 Warehouse   Plant P Q R S A 3 5 2 5 B 3 8 4 8 C 7 4 7 4

1. Transportation unit cost matrix –

 Warehouse   Plant W1 W2 W3 W4 Capacity A 49 150 70 60 50 B 80 70 90 10 60 C 15 87 79 81 40 Demand 20 70 50 10

Find IFS by VAM and Optimal solution by MODI method.

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

1. Transportation unit cost matrix –

 W1 W2 W3 W4 Capacity P1 4 6 9 11 40 P2 11 9 14 13 30 P3 15 18 26 20 30 Demand 5 15 35 45

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

1. Transportation unit cost matrix –
 D1 D2 D3 Capacity P1 15 14 11 50 P2 13 18 17 40 P3 14 14 12 60 Demand 20 95 35

Find initial solution by NWCR & Optimal solution by MODI.

1. 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.

 F1 F2 F3 F4 Demand S1 2 9 5 4 80 S2 1 7 4 5 120 S3 5 8 3 6 150 Capacity 10 150 50 100

 F1 F2 F3 F4 Prod. Cost 15 18 14 13 Raw mat. cost 10 9 12 9

 S1 S2 S3 Sales Price 34 32 31

1. 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.
 M1 M2 M3 P1 28 28 30 P2 25 27 23 P3 35 37 38

Find IFS by VAM and Optimal solution by MODI method.

1. 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)

 Factory Warehouse 1 2 3 4 I 6 1 9 3 II 11 5 2 8 III 10 12 4 7

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.

1. 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.

 Warehouses Markets M1 M2 M3 M4 W1 300 10 10 16 20 W2 15 175 6 25 17 25 W3 25 8 21 75 10 150 15

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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#### vipin0785

Education Qualification: BMS- N M College (University Rank Holder) PGDBM- Sydenham College M Com- College topper Mr Vipin Saboo has been associated with the following institutes as a visiting faculty Lords college, Malad Patkar College, Goregoan Saraf college, Malad Dalmia college, Malad St Andrews College, Bandra Wilson College, Grant Road Thakur college, Kandivili L N College, Kandivili N K College, Malad Dhanukar College, Vile Parle St Xaviers College, Marine Lines Shroff College, Kandivili KES College, Khar Mr.Vipin Saboo also has more than 5 years of industry expertise with corporate like CRISIL, Motilal Oswal Investment Banking and Yes Bank. Mr. Saboo has also published a text book on Logistics and Supply Chain Management for TYBMS Students.

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