ASSIGNMENT QUESTIONS

Q1. Write the math program for the following bids in the lane procurement auction. Clearly define the variables, constraint and objective function

LANES   SUPPLIER I          SUPPLIER II         NUMBER OF TRUCKLOAD

X -> Y     570                         525                         10

Y -> Z     621                         610                         10

X -> Z     475                         500                         10

Include the additional constraints:

1) A minimum of 20% of volume for both the suppliers

2) The following capacity constraints:

LANES           SUPPLIER I          SUPPLIER II        

X -> Y             2                           100                        

Y -> Z             100                         4

X -> Z             100                         2

3) Each supplier should get at least 25% of the business (dollar value)

Solve the three models including the three constraints. Write the math program along with the constraints. Attach the Excel output and the answers (best value for variables and total cost).

Q2. Which of the following lanes can be combined in a combinatorial auction? Why?

X -> Y

Y -> Z

X -> Z

Q3. Who should win the bids for the following lanes in a combinatorial auction? Why? Which will be the winning bids?

LANES 

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X -> Y                       1                                          1             1

Y -> Z                                   1                              1

Y -> X                                                     1                           1

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BID SUPPLIER I         280         276         350         412         508

BID SUPPLIER II        255         301         327         401         525

1. Find the approximate minimum cost flow for the following network using the math program discussed in class.

The distribution cost per ton for the arcs are as follows

1-4 = $ 280           1-5 = $ 325           4-6 = $ 75             4-7 = $ 220

2-4 = $ 175           2-5 = $ 175           5-6 = $ 150           5-7 = $ 100

3-4 = $ 250           3-5 = $ 225

The capacity of the warehouses are 400 units.

The minimum cost flow from suppliers to customers must use the warehouses. Hence ignore all the direct arcs from suppliers to customers. The supplier capacity and customer demands are listed in the figure. Write the math program along with the constraints. Attach the Excel output and the answers (best value for variables and total cost).