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14. Your company buys and sells fresh catfish, utilizing containerized chill boxes. Each box is carried by airfreight to either of two airfreight hubs, where it is further routed to restaurant wholesalers in various cities. Once loaded with fish, containers may be held at origin for further shipment for up to three days until orders are received. Minimizing cost of transportation is one of the keys to maintaining an operating profit margin.
The possible transshipment hubs are Birmingham, AL or Atlanta, GA.
Today you have available 3 containers in Slidell, La., 6 containers in Greenville, Mississippi, and 5 containers in Dothan, Alabama. You have sales for today of 2 containers in Macon, Georgia, 4 containers in Greenville, South Carolina, and 3 each in Jacksonville, Florida and Savannah, Georgia.

Airfreight shipping charges, per pound, in cents, for the class and size of your containers is as shown in the table below.

from/to Birmingham Atlanta

Slidell 8 6
Greenwood 3 8
Dothan 9 3
Macon 44 57
Greenville 35 34
Jacksonville 34 28
Savannah 24 32

a. Determine the optimum routing that will minimize shipping costs and satisfy demand.
b. Where, if at all, will containers have to be held and how many at each site?

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Slixtrix Conversions, located in Waldo, Florida specializes in conversions of pick-up trucks and vans. In particular, they do a very good business in their signature line of each.

The business has three production shops which, using good project scheduling skills, work on the vehicles simultaneously. The shops are preparation, upholstery, and electric/electronics.

The company nets $5000 for each truck and $6000 for each van produced and sold. The work requirements for each, in hours, and personnel available are given in the table below. Personnel work 8 hours per day, five days per week on the conversions.

shop trucks vans personnel
preparation 8 12 10
upholstery 10 8 8
electrical 12 16 12

shop trucks vans personnel personnel hours
preparation 8 12 10 400
upholstery 10 8 8 320
electrical 12 16 12 480

trucks vans
Profit 5000 6000
Standing Order 12 10

Decision Variables
trucks vans
Units Made 20 15


1) Hours used in each dept < hours available
Used <= Available
preparation 0 <= 400
upholstery 0 <= 320
electrical 0 <= 480

2) Total made >= standing orders
trucks vans
Units made 20 15
>= >= >=
Standing Order 12 10

3) total vans made should be less than or equal to 20
Vans made 15
<= <=
Max parts qty 20

Objective Fn
Maximize total profit

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