Optimization of multilevel investments using dynamic programming based on fuzzy cash flows

Dynamic programming is applicable to any situation where items from several groups must be combined to form an entity, such as a composite investment or a transportation route connecting several districts. The most desirable entity is constructed in stages by forming sub-entities of progressively larger size. At each stage of the development, the sub-entities that are candidates for inclusion in the most desirable entity are retained, and all other sub-entities are discarded. In deterministic dynamic programming, a specification of the current state and current decision is enough to tell us with certainty the new state and costs during the current stage. In many practical problems, these factors may not be known with certainty, even if the current state and decision are known. In this paper, the dynamic programming is applied to the situation where each investment in the set has the following characteristics: the amount to be invested has several possible values, and the rate of return varies with the amount invested. Each sum that may be invested represents a distinct level of investment, and the investment therefore has multiple levels. A fuzzy present worth based dynamic programming approach is used. A numeric example for a multilevel investment with fuzzy geometric cash flows is given. A computer software named FUZDYN is developed for various problems such as alternatives having different lives, different uniform cash flows, and different ranking methods.