A GP SOLUTION TO COOPERATIVE GAME-DYNAMIC PROGRAMMING OPTIMIZATION

Abstract

In this paper, we developed a robust method for optimizing a Cooperative Game-Dynamic Programming (CG-DP) problem. The method first establishes a relationship between cooperative games and dynamic programming, and optimizes the cooperative game solution via dynamic programming. We established a relationship between dynamic programming and geometric programming. By extension, cooperative game solutions can be optimized via Geometric Programming (GP), which is what we did, and we found that GP produced a better result. Optimization via DP to the CG solution yields an additional 7.20 million naira by allocating the coalitions in the order (3, 1, 1). In contrast, optimization via GP to the CG solution yields an additional 17.12 million naira by allocating the coalitions in the order (1.2, 1, 1). We compared the two methods and found that the GP method of solution to the CG problem is better because it produced an optimal gain of 50.6 million naira against the 40.68 million-naira gain from the DP method to the CG solution.