Dynamic optimization with hybrid numbers: two case studies

Abstract

Dynamic programming is an optimization system method or its mathematical representation, operating in phases, in other words, decisions are made sequentially. In many situations the available information is not homogeneous, this is objective data and uncertain one. In these cases, the use of hybrid numbers which combine randomness with fuzziness is useful to avoid losing information. In the present paper dynamic programming is applied in two cases: the design of a highway which construction should have the lowest possible cost and the distribution of investments in advertising which should provide the maximum benefit. In both situations, the values obtained with the available information are expressed by means of hybrid numbers, using a different representation in each case.

Keywords

• Dynamic optimization
• hybrid numbers
• fuzziness
• randomness