In: Statistics and Probability
Manufacturing and Distribution
Your company manufactures commercial security locks at four factories in Macon, Louisville, Detroit, and Phoenix. You have seven wholesale distributors in seven cities across the country. The costs of shipping a lock from a factory to a distributor is shown in the following table:
Shipping Costs |
(Dollars per unit) |
||||||
Plants |
Tacoma |
San Diego |
Dallas |
Denver |
St. Louis |
Tampa |
Baltimore |
Macon |
2.5 |
2.75 |
1.75 |
2 |
2.1 |
1.8 |
1.65 |
Louisville |
1.85 |
1.9 |
1.5 |
1.6 |
1 |
1.9 |
1.85 |
Detroit |
2.3 |
2.25 |
1.85 |
1.25 |
1.5 |
2.25 |
2 |
Phoenix |
1.9 |
0.9 |
1.6 |
1.75 |
2 |
2.5 |
2.65 |
The anticipated demand at each distributor for the next year is as follows:
Plants |
Tacoma |
San Diego |
Dallas |
Denver |
St. Louis |
Tampa |
Baltimore |
DEMAND: |
8500 |
14500 |
13500 |
12600 |
18000 |
15000 |
9000 |
The costs (in dollars) of manufacturing a lock at each location, and the annual capacities of each factor, are as follows:
Plants |
Capacity |
Cost/Unit |
Macon |
18000 |
35.5 |
Louisville |
15000 |
37.5 |
Detroit |
25000 |
39 |
Phoenix |
20000 |
36.25 |
You know you will not fill all of your orders, but you would like to fill at least 80% of the demand at each location. How many locks should be manufactured at each location, and where should they be shipped?
If there is any unused capacity at any plant, how should that best be used and distributed?
Please show/explain using excel solver
The Excel setup is:
The formulas are:
The solver parameters are:
The solution is:
Plants | Tacoma | San Diego | Dallas | Denver | St. Louis | Tampa | Baltimore | Capacity | |
Macon | 2.5 | 2.75 | 1.75 | 2 | 2.1 | 1.8 | 1.65 | 18000 | |
Louisville | 1.85 | 1.9 | 1.5 | 1.6 | 1 | 1.9 | 1.85 | 15000 | |
Detroit | 2.3 | 2.25 | 1.85 | 1.25 | 1.5 | 2.25 | 2 | 25000 | |
Phoenix | 1.9 | 0.9 | 1.6 | 1.75 | 2 | 2.5 | 2.65 | 20000 | |
Demand | 8500 | 14500 | 13500 | 12600 | 18000 | 15000 | 9000 | ||
Plants | Tacoma | San Diego | Dallas | Denver | St. Louis | Tampa | Baltimore | Capacity | Cost per unit |
Macon | 0 | 0 | 0 | 0 | 0 | 12000 | 6000 | 18000 | 35.5 |
Louisville | 0 | 0 | 600 | 0 | 14400 | 0 | 5.68E-14 | 15000 | 37.5 |
Detroit | 0 | 0 | 8600 | 10080 | 4.55E-13 | 0 | 1200 | 19880 | 39 |
Phoenix | 6800 | 11600 | 1600 | 0 | 0 | 0 | 0 | 20000 | 36.25 |
Demand | 6800 | 11600 | 10800 | 10080 | 14400 | 12000 | 7200 | ||
>= | >= | >= | >= | >= | >= | >= | |||
Atleast 80% condition | 6800 | 11600 | 10800 | 10080 | 14400 | 12000 | 7200 | ||
Transportation cost | 103630 | ||||||||
Production cost | 2701820 | ||||||||
Total cost | 2805450 |
Total cost = $2805450