Question

In: Statistics and Probability

Manufacturing and Distribution Your company manufactures commercial security locks at four factories in Macon, Louisville, Detroit,...

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

Solutions

Expert Solution

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


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