Discuss the below:
Q: Jackson Paper Mills, Inc., has plants in Boone, NC and Augusta, Georgia. Warehouses are located in Tampa, FL and Winchester, VA. Distributors are located in Detroit, MI; Knoxville, TN; and New Orleans, LA. Products are shipped from the plants to the warehouses and from the warehouses to the distributors. There is no storage at the warehouses so any product entering the warehouses must be shipped to distributors. The plant capacities and distributor demands are shown in the tables below:
|
Plant
|
Capacity |
|
Dsitributor |
Demand |
| Boone |
400 |
|
Detroit |
200 |
| Augusta |
250 |
|
Knoxville |
300 |
|
|
|
New Orleans |
200 |
The unit transportation costs ($) for the shipments from the two plants to the two warehouses and from the two warehouses to the three distributors are shown below:
|
|
To Warehouse |
To Warehouse |
|
|
Tampa |
Winchester |
| From Plant |
Boone
|
12 |
11 |
| From Plant |
Augusta |
9 |
14 |
|
|
To Distributor |
To Distributor |
To Distributor |
|
|
Detroit |
Knoxville |
New Orleans |
| From Warehouse |
Tampa |
18 |
14 |
13 |
| From Warehouse |
Winchester |
16 |
10 |
12 |
Formulate this problem in Excel and solve to determine the minimum shipping costs required to meet demands. (Hint: you will not be able to satisfy all demands)
a) How many decision variables does this problem have?
b) Not counting the non-negativity constraint - how many constraints does this problem have?
c) What is the total cost to minimize shipping costs from the plants to the distributors?
d) Which routes had zero units shipped?
e) Which distributor was unable to meet its demand?
f) How many units should be shipped from Boone to Winchester?
g) How many units should be from Augusta to Tampa?
h) How many units should be from Tampa to Detroit?
i) How many units should be from Tampa to New Orleans?
j) How many units should be from Winchester to Detroit?
k) How many units should be from Winchester to Knoxville?
l) How many units should be from Winchester to New Orleans?