A study on three different dimensional facility location problems

In supply chain strategy, designing a network is one of the most important part. This model deals with various dimensional facility location models. Initially, this paper begins with two echelon facility location model of dimension two. Then, it is extended to three dimensional model by adding commodity type and then, different types of transportation modes are added to make it four dimensional model. Delivery lead time and outside suppliers are assumed to meet the retailer's demand too. We construct some lemmas to compare the optimal solution for each of the problem. We also study the procedure of reducing the total cost of the supply chain network by applying a small change in constraint set. This is described by another lemma. Some numerical examples are allowed to illustrate the models.