Discussion

IBM ILOG Solver User's Manual > More on Modeling > Combining Constraints: Bin Packing > Describe > Discussion

Discussion

INDEX

What is the known information in this problem?

There are three types of bins: red, blue, green.
There are five types of components: glass, plastic, steel, wood, copper.
There is the following demand for each type of component: 2 glass components, 4 plastic components, 3 steel components, 6 wood components, and 4 copper components.

What are the decision variables in this problem?

What is the type of each bin?
How many components of each type are in each bin?

What are the constraints in this problem?

There are a variety of constraints in this problem. Most of them are summarized in the following table:

Table 8.1 Bin packing constraints

Bin	Bin Capacity	Component
Bin	Bin Capacity	glass	plastic	steel	wood	copper
red	3	yes			at most 1	yes
blue	1	yes		yes		yes
green	4		yes		at most 2	yes

There are a few other constraints relating to the mixing of different types of components in the bins:

wood requires plastic (a bin that contains wood must also contain plastic, but a bin that contains plastic does not necessarily also contain wood)
glass excludes copper (a bin that contains glass cannot also contain copper)
copper excludes plastic (a bin that contains copper cannot also contain plastic)

There are constraints relating to the total number of bins:

the sum over all the bins of the quantities of a given component must be equal to the demand for that component
the total capacity must be equal to or exceed the total demand

What is the objective?

To minimize the number of bins used

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