1. Static decision models

Suppose a decision-maker has a choice between several baskets of goods or commodities. If there are n possible goods, each good is indexed by i = 1,...,n and the basket of goods is represented by a vector x = (x ₁ ,...,x _n ) where x _i represents the quantity of good i in the basket. Obviously the term basket is a metaphor. As for goods, we'll assume that each good is defined by all its own characteristics (if it's a manufactured object this may include brand, model, possible obsolescence,...) but also by its complementary characteristics such as location (for example, place of delivery), etc. For example, the same item may correspond to two different goods depending on whether it is in Paris or Moscow. On the other hand, a good does not necessarily correspond...