Transshipment Problem

TRANSHIPMENTPROBLEM

The transshipment problem is a transportation problem where shipment is possible from an origin to an origin or a destination as well as from a destination to an origin or a destination.

Shipment is also possible from a middle point called transhipment nodes.

Transshipment problem can be formulated as a transportation with ;

Increased number of origins. Increased number of destinations.

Need For Transhipment1.To achieve economy in some cases.2.More practical scenario.

PROBLEM

Table 1Factory warehouses

W1 W2 W3F1 2 6 30 150F2 6 10 50 300

150 150 150 450

Unit transportation costs, capacity at the factories and the requirement at the warehouses of Adani Group are indicated below;

Table 2

Unit Transportation Cost from Factory To Factory

From To Factory

Factory FactoryF1 F2

F1 2 6F2 6 10

Table 3

Unit Transportation Cost from Warehouse To Warehouse

From To

Warehouse warehousesW1 W2 W3

W1 0 46 2W2 2 0 6W3 130 6 0

Table 4

Unit Transportation Cost from Warehouse To Factory

From To

Warehouse FactoryF1 F2

W1 6 30W2 50 6W3 90 110

SOLUTION

STEP-I

From table 1,table 2, table 3 and table 4 we obtain the transportation formulation of the transhhipment problem after adding, a buffer stock of 450 which is the total capacity and total requirement in the original transportation problem. The resulting transportationproblem to each row and column of the transshipment problem.The resulting transportation problem has m+n=5 origins and m+n=5 destinations

TRANSHIPMENT TABLEF1 F2 W1 W2 W3

F1 2 6 2 6 30 600F2 6 10 6 10 50 750W1 6 30 0 46 2 450W2 50 6 2 0 6 450W3 90 110 130 6 0 450

450 450 600 600 600 2700

STEP IISOLVING THE ABOVE BY TRANSPORTATION PROBLEM

Now the above problem can be solved by the transportation problem.

We have solved it by least cost method.

Ans. (600*2)+(450*6)+(300*10)+(450*2)+(150*110)+(150*6) = 25200

Transhipment nodes

Dummy demand point(ie. Not balanced)

Problem 2

Widgetco manufactures widgets at two factories, one in Memphis and one in Denver. The Memphis factory can produce as 150 widgets, and the Denver factory can produce as many as 200 widgets per day. Widgets are shipped by air to customers in LA and Boston. The customers in each city require 130 widgets per day. Because of the deregulation of airfares, Widgetco believes that it may be cheaper first fly some widgets to NY or Chicago and then fly them to their final destinations. The cost of flying a widget are shown next. Widgetco wants to minimize the total cost of shipping the required widgets to customers.

PROBLEM

Step1. If necessary, add a dummy demand point (with a supply of 0 and a demand equal to the problem’s excess supply) to balance the problem. Shipments to the dummy and from a point to itself will be zero. Let s= total available supply.

Step2. Construct a transportation table as follows: A row in the table will be needed for each supply point and transshipment point, and a column will be needed for each demand point and transshipment point.

STEPS

Supply point=Original supply Demand point=Original demand Transshipment point: supply=points original supply + s demand= points original demand + s

# This is to make sure that, when Transshipment point acts as;Supplier=it has maximum supplyDemander= it has maximum demand

Solution; Cost of transportation

NY Chicago LA Boston Memphis $8 $13 $25 $28 Denver $15 $12 $26 $25 NY $0 $6 $16 $17 Chicago $6 $0 $14 $16

NY Chicago LA Boston Supply Memphis $8 $13 $25 $28 150 Denver $15 $12 $26 $25 200 NY $0 $6 $16 $17 350 Chicago $6 $0 $14 $16 350

Demand 350 350 130 130

Not balanced; add dummy demand.

Demand and supply

NY Chicago LA Boston Dummy Supply Memphis $8 $13 $25 $28 $0 150 Denver $15 $12 $26 $25 $0 200 NY $0 $6 $16 $17 $0 350 Chicago $6 $0 $14 $16 $0 350

Demand 350 350 130 130 90

Balanced!! Proceed the problem with, any of the methods for

transportation method and find initial feasible solution.

Add dummy demand…

SOLVING THE ABOVE BY TRANSPORTATION PROBLEM

We have solved it by least cost method.

Ans. (60*8)+(200*12)+(60*6)+(450*2)+(130*14)+(130*16) = $7140