Intel Igent Optimization Algorithm For Upper Minimal Total Cost Bound Of Transportation Problem With Varying Demands And Supplies

Transportation of a product from multi-source to multi-destination with minimal total transportation cost plays an important role in real life. The minimum total cost transportation problem with fixed demand and supply is the main target of the study of transportation problem. Since the transportation problem is put forward quite a period of time, researchers have paid considerable attention to minimizing total cost with fixed supply and demand quantities. However, these quantities may vary within a certain range in a period due to some reason, changes of the supply and demand can also make the minimum total cost change within a certain range. So, the concerned parties might be more interested in finding the lower and upper bounds of the minimal total cost with varying supplies and demands within their respective ranges for proper decision making.However, even if supply and demand changes in a certain range, the number of choices of supply and demand quantities within their respective ranges increases enormously as the number of suppliers or buyers increases.Although the scholar Liu(2003) has established the mathematical models of the lower and upper minimal total cost bounds for Transportation problem With varying Demands and Supplies(i.e., TPVDS), and given the method to solve the models, it is an NP hard problem to find the upper bound of minimum total cost for TPVDS. Then, Juman and Hoque(2014) have proved that Liu(2003)’s approach cannot find the accurate upper bound of the minimum total cost for TPVDS, and developed a heuristic algorithm to solve the problem. However, when we use the heuristic algorithm to solve some larger scale models of TPVDS, we found that the heuristic algorithm can not find the accurate upper bound yet. Based on the researches of Liu(2003) and Juman and Hoque(2014), we put forward a kind of intelligent optimization algorithm named TPVDS-A, which is proven to be able to find the exact upper minimal total cost bound for a class of TPVDS with the sum of the lower bounds for all the supplies no less than the sum of the upper bounds for all the demands in a polynormial time.