Let's assume you have a collection of customer orders to fulfill where the problem is to compute the minimal set of trucks needed to deliver the orders to the customers.

Our imaginary company is able to deliver five types of products. Each order defines the quantity to deliver for each type of product.

A truck is composed of a set of tanks. A truck can be configured with at most five different tanks. There are five types of tanks that correspond to five different capacities.

You assign an order to one and only one truck. Within an order, you must assign the products to the tanks of the truck. You must assign a product in an order to one and only one tank. In a single tank, you can mix the products of different orders, but all these products mixed in one tank must be of the same type.

There is a limit on the overall capacity of each truck: a truck cannot be loaded over 12000 units. A tank cannot be loaded over its capacity.

There is a limit on the types of products that you can assign to a truck: a truck cannot contain more than three different types of products.

Two of the products are incompatible. That is, they cannot be transported in the same truck.