Question

In: Operations Management

Consider a transportation problem, shipping a product from two sources to two customers. The following table...

Consider a transportation problem, shipping a product from two sources to two customers. The following table shows the data.

Write a LP model for this problem to minimize the shipping cost (unit in $) while satisfying the demand for each customer and supply for each source. You don’t need to solve your LP model. I just need a LP model only.

Customer1

Customer2

Supply

Source 1

$8/unit

15

15

Source 2

11

7

20

Demand

12

23

Solutions

Expert Solution

Variable Definition:

Xij = Shipment volume from source to customer where i = 1,2 and j = 1, 2

For example, X11 represents shipment volume from source 1 to Customer 1

For example, X12 represents shipment volume from source 1 to Customer 2

Objective Function:

Cost while shipping from source 1 to Customer 1 = $8

Hence, Cost while shipping X11 products motors from source 1 to Customer 1 = 8*X11

Similarly, the cost for all shipment routes can be calculated.

Total Cost= 8*X11 + 15*X12 + 11*X21 + 7*X22

We'd like to minimize the cost.

Therefore,

Minimize Z = 8*X11 + 15*X12 + 11*X21 + 7*X22

Constraints:

Total demand = 12 + 23 = 35

Total Supply = 15 + 20 = 35

As this is a balanced transportation problem (Demand = Supply) complete capacity of every source is expected to be used.

X11 + X12 = 15 ..... Supply constraint on source 1

X21 + X22 = 20 ..... Supply constraint on source 2

As this is a balanced transportation problem (Demand = Supply) complete demand of every customer is expected to be satisfied.

X11 + X21 =12 ..... Demand constraint on customer 1

X12 + X22 =23 ..... Demand constraint on customer 2

Non-negativity Restriction

Xij >=0 .........Non-negativity constraint as volume shipped cannot be negative in value

keosha answered 1 year ago
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