A company has three warehouses that supply four stores with a given product. Eac
ID: 371289 • Letter: A
Question
A company has three warehouses that supply four stores with a given product. Each warehouse has 30 units of the product. Stores 1, 2, 3, and 4 require 20, 25, 15, and 25 units of the product, respectively.
The unit shipping costs from each warehouse to each store are:
Part a) Formulate a least-shipping-cost network program for the above problem.
Part b) Will all the units from Warehouse A, B, C be shipped to the stores? Why or why not?
Part c) Suppose the shipments are not allowed for the following two shipping routes due to the recent natural disaster:
Warehouse A to store 2, and
Warehouse B to store 3.
How will you modify your network program to cope with this change?
Warehouse Store 1 Store 2 Store 3 Store 4 A $12 $9.35 $9.50 $12.75 B $10.75 $10.15 $8.55 $10 C $14 $11 $8.85 $11.35Explanation / Answer
TOTAL no. of supply constraints : 3
TOTAL no. of demand constraints : 4
Problem Table is
Here Total Demand = 85 is less than Total Supply = 90. So We add a dummy demand constraint with 0 unit cost and with allocation 5.
Now, The modified table is
Table-1
The maximum penalty, 9.35, occurs in row A.
The minimum cij in this row is c15 = 0.
The maximum allocation in this cell is 5.
It satisfy demand of Ddummy and adjust the supply of A from 30 to 25 (30 - 5 = 25).
Table-2
0(5)
0
0
The maximum penalty, 2.15, occurs in row C.
The minimum cij in this row is c33 = 8.85.
The maximum allocation in this cell is 15.
It satisfy demand of Sre3 and adjust the supply of C from 30 to 15 (30 - 15 = 15).
Table-3
9.5
0(5)
8.55
0
8.85(15)
0
The maximum penalty, 2.65, occurs in row A.
The minimum cij in this row is c12 = 9.35.
The maximum allocation in this cell is 25.
It satisfy supply of A and demand of Sre2.
Table-4
9.35(25)
9.5
0(5)
10.15
8.55
0
11
8.85(15)
0
The maximum penalty, 3.25, occurs in column Sre1.
The minimum cij in this column is c21 = 10.75.
The maximum allocation in this cell is 20.
It satisfy demand of Sre1 and adjust the supply of B from 30 to 10 (30 - 20 = 10).
Table-5
12
9.35(25)
9.5
0(5)
10.75(20)
10.15
8.55
0
14
11
8.85(15)
0
The maximum penalty, 11.35, occurs in row C.
The minimum cij in this row is c34 = 11.35.
The maximum allocation in this cell is 15.
It satisfy supply of C and adjust the demand of Sre4 from 25 to 10 (25 - 15 = 10).
Table-6
12
9.35(25)
9.5
0(5)
10.75(20)
10.15
8.55
0
14
11
8.85(15)
0
The maximum penalty, 10, occurs in row B.
The minimum cij in this row is c24 = 10.
The maximum allocation in this cell is 10.
It satisfy supply of B and demand of Sre4.
Initial feasible solution is
The minimum total transportation cost =9.35×25+0×5+10.75×20+10×10+8.85×15+11.35×15=851.75
Here, the number of allocated cells = 6, which is one less than to m + n - 1 = 3 + 5 - 1 = 7
This solution is degenerate
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