Multiple commodity supply chain with maximal covering approach in a three layer structure

Many scholars have already investigated the location problem of supply chain facilities and centres under different conditions. In a three-echelon multiple commodity supply chain, the aim is to fulfil customer demand at a minimum cost by optimising the flow of products from factories to distribution centres (DC) and from DCs to customers. In a situation where there are limited numbers of DCs and each of them covers bounded area, locating DCs for the purpose of, maximising coverage of customers' demand and optimising allocation of the customers to those centres, are quite important. In this research, a three-echelon multiple commodity supply chain model with maximal covering approach that meets the following two objectives through appropriate selection of DC sites is presented: 1) maximise coverage of customer demand; 2) minimise the associated transportation cost required for fulfilment of the customer demand. To address such models in small scales, one can easily apply LP-metric method to make a combined dimensionless objective and solve it with lingo software. Considering the fact that the presented model is an NP-hard problem and cannot be solved in this manner, we apply customised version of a heuristic algorithm named Greedy and clearly indicate its robustness