What'sBest!
Truck Loading

Problem: Packing a container with objects of varying sizes to maximise efficiency, a "knapsack" problem.

This is an example of the "Knapsack" class of problems, in which a number of things - boxes, books, or Bradley Fighting Vehicles - must be efficiently or profitably packed in a container (trucks, crates, or C130 aircraft). The objective can be to minimise wasted space in the container, to maximise or minimise total load weight, or, as in this case, to maximise the value of the load.

You have to decide which items to load on a truck. Each item must be shipped in its entirety or not at all (i.e., 25% of an item cannot be shipped). The Truck Loading problem illustrates a situation in which non-integer (fractional) answers are not acceptable. To demonstrate potential problems involved in rounding fractional answers, we'll solve the problem using two different methods.

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In the first case, we'll use What'sBest! to optimise by the conventional method. The solution may suggest fractional answers, but we'll just round the fractions to the nearest whole number that does not violate any constraints. In the second case, we'll find an integer solution using the binary Integer command.

Items are to be loaded onto a truck with a 10,000 pound capacity. However, the items currently scheduled for shipment will exceed the capacity of the truck, so you have to make a "Yes /No" decision as to whether each item gets shipped.

Each item has an associated dollar value and weight. 

The objective of optimisation is to maximise the total value of the items loaded onto the truck without exceeding the truck's weight capacity.

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