This thesis aims to study the network of a nationwide distributor of a commodity product. As we cannot disclose the actual product for competitive reasons, we will present the research in terms of a similar, representative product, namely salt for ice prevention across United States. The distribution network includes four kinds of nodes, sources, buffer locations at sources, storage points and demand regions. It also includes four types of arcs, from sources to buffer locations and to storage points, from buffer locations to storage points, and from storage points to demand regions. The goal is to maximize the total gross margin subject to a set of supply, demand and inventory constraints. In this thesis, we establish two mathematical models to achieve the goal. The first one is a basic model to identify the optimal flows along the arcs across time by treating product prices and market demand as fixed parameters. The model is built in OPL and solved by CPLEX. We then carry out some numerical analyses and tests to validate the correctness of the model and demonstrate its utility. The second one is an advanced model treating product prices and market demand as additional decision variables. The product price and market demand are related by an exponential function, which makes the model difficult to solve with the available commercial solver codes. We then propose several algorithms to reduce the computational complexity of the model so that we can solve with CPLEX. At last, we compare the algorithms to identify the best one. We provide additional numerical tests to show the benefit from including the pricing decisions along with the optimization of the network flows.
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