Homogeneous Distribution of Demand Type: Is It a Critical Criterion for the Districting Problem?

In this study, we focus on the districting problem of any kind of application where partitioning of individual customers is needed. The main districting criteria which are already studied by earlier researchers are the indivisibility of basic units, compactness, work-load balance, and accessibility. Along with these, we introduce another criterion, called homogeneity, which is related to the service demand of each customer. As much as the variations in service demand increase within a district, the service providers need to increase the skillsets consequently. This way overall cost increases. In this study, we consider this criterion as an objective function, and we aim to create districts by minimizing compactness, balancing the work-load, and keeping the variations in service demand as little as possible. We propose a tabu search method consisting of the random local search and compare its results to NSGA-II. Our results establish this new homogeneity criterion as a key objective of the districting problem.