Linear Programming Formulation Worksheet
QUESTION
Restoration Cycles buys used Harley-Davison motorcycles from two different auctions held in Muncie, IN; Ft. Worth, TX; and Des Moines, IA. (It purchased 24 in Muncie, 18 in Ft. Worth, and 18 in Des Moines.) It then must transport the motorcycles to repair shops it contracts with. Once the cycles are restored, Restoration Cycles sells them at three different Restored Vehicle lots in Louisville, Memphis, and El Paso. Twenty (20) motorcycles are sent to each of the restored vehicle lots.
There are various costs associated with the average purchase and transportation prices from each auction to each repair shop. Also, there are transportation costs from the repair shops to the restored vehicle lots. Restoration Cycles is concerned about minimizing it total cost given the costs (in $) in the table below.
| Repair Shops | ||
| Shop 1 | Shop 2 | |
| Auction in Muncie | 550 | 500 |
| Auction in Ft. Worth | 600 | 450 |
| Auction in Des Moines | 650 | 500 |
| Restored Vehicle Lots | |||
| Louisville | Memphis | El Paso | |
| Shop 1 | 250 | 300 | 500 |
| Shop 2 | 350 | 650 | 450 |
1. What type of network problem is this?
Transportation Assignment Transshipment
2. What is your objective (in words)?
The objective is to minimize the total cost for restoration cycles
3. Draw the Network Model for your case problem
4. How many decision variables do you have? _________ How many nodes?
5. Does your Supply equal the Demand? Yes No
6. Write the LP formulation based on your network model
Constraint # In Words Mathematical Expression
