Due to the critical blood shortages in South Africa and around the world, the assignment of blood can be considered an important real world optimization problem. This paper presents a mathematical model that facilitates good management and assignment of red blood cell units in order to minimize the quantity of imported units from outside the system. The model makes use of the Multiple Knapsack Algorithm, which is implemented using several optimization techniques, in order to determine the most optimal assignments. These include a Genetic Algorithm (GA), Adaptive Genetic Algorithm (AGA), Simulated Annealing Genetic Algorithm (SAGA), Adaptive Simulated Annealing Genetic Algorithm (ASAGA) and finally a Hill Climbing (HC) Algorithm. All techniques were capable of achieving the optimal fitnesses. The AGA, SAGA and ASAGA provide some desirable results over the standard GA, whilst the HC algorithm proves to demonstrate the best results overall.