Multi-Objective Territory Design with Capacity & Geographic Constraints

Territory design can be defined as the problem which is focused on grouping small geographical areas into larger geographic clusters. These clusters may be referenced as territories. On this paper we develop the case where two or more attributes must be considered in order to setup an optimal territory design. We developed a new strategy which is based on a hybrid-mixed integer programming method (HMIP). We introduce the model and present in detail our approach for solving the Territory Design Problem. We start from a large group of basic areas (i.e. blocks) which are characterized individually by two or more attributes. Each attribute has a metric defined by a specific activity measure (i.e. quantity of customers, sales volume, etc). In addition there are some geographic restrictions about contiguity and compactness for the territories that should be constructed from these basic areas. An optimal districting plan is obtained when the constructed territories are well balanced taking in mind each activity measure simultaneously. Our methodology includes a mixed integer model definition. We tested our implementation on a large scale instance that was built from a real world application of more than 4000 basic areas. Some computational results about efficiency and suitability are presented.