HMIP Model for a Territory Design Problem with Capacity and Contiguity Constraints

Abstract

Small geographic basic units (BU) are grouped into larger geographic territories on a Territory Design Problem (TDP). Proposed approach to solve a TDP is presented through a study case developed on a large soft drinks company which operates in the city of Monterrey, México. Each BU of our TDP is defined by three activity measures: (1) number of customers, (2) sales volume and (3) workload. Some geographic issues about contiguity and compactness for the territories to be constructed are considered. An optimal solution is obtained when the constructed territories are well balanced taking into consideration each activity measure simultaneously. In particular, contiguity is hard to be represented mathematically. All previous research work indicates that this NP-Hard problem is not suitable for solving on large-scale instances. A new strategy which is based on a hybrid-mixed integer programming (HMIP) approach is developed. Specifically, our implementation is based on a Cut-Generation Strategy. We take advantage from territory centers obtained through a relaxation of a P-median based model. This model has a very high degree of connectivity. Thus, small number of iterations to find connected solutions is required. The authors detail out their methodology and then they proceed to its computational implementation. Experimental results show the effectiveness of our method in finding near-optimal solutions for very large instances up to 10,000 BU’s in short computational times (less than 10 minutes). Nowadays, this model is being used by the firm with important economical benefits.