Building a mathematical model of the transportation problem under the dynamics of demand restrictions with practical application

Abstract

In this research we built a mathematical model of the transportation problem for data of General Company for Grain Under the environment of variable demand ,and situations of incapableness to determining the supply required quantities as a result of economic and commercial reasons, also restrict flow of grain amounts was specified to a known level by the decision makers to ensure that the stock of reserves for emergency situations that face the company from decrease, or non-arrival of the amount of grain to silos , also it took the capabilities of the tanker into consideration and the grain have been restricted to avoid shortages and lack of processing capability, Function has been adopted in the mathematical model goal is a total of two functions: the first linear to reduce the overall costs of the transportation problem And the second linear fractional represent the proportion of public expenditure for the silos to college profits .a balanced model and equivalent to model the original problem has been formulated . The results proved the efficiency of the model in the distribution of the amount of grain where the total cost was reduced to (24%) with ensuring the existence of reserve stocks and meet the demand of mills.where the reserve stocks sufficed nearly to a month and half , the mathematical model was solved byausing,advancednsoftware(LINGO14.0).