Question: The Freight Consolidator Company specializes in receiving small packages of various sizes and weights from different shippers and then consolidating them into one truckload to minimize unit freight cost. They charge the customers on per unit weight basis. Their consolidation objective, therefore, is to pack as much as possible into the available volume of the truck to maximize the total packed weight. At one time, they found 6 packages waiting with volume and weight details as follow:
|
Item
|
Volume
|
Weight
|
|
1
|
100
|
40
|
|
2
|
50
|
35
|
|
3
|
45
|
18
|
|
4
|
20
|
4
|
|
5
|
10
|
10
|
|
6
|
5
|
2
|
Their truck has a maximum volume capacity of 100. Each package must be loaded whole or not at all.
1. Use a Greedy Algorithm to find a solution.
2. Formulate the problem as a binary integer programming problem.
3. Solve to find optimum solution using Excel solver.