Multi-stage stochastic districting: optimization models and solution algorithms

Abstract

This paper investigates a Multi-Stage Stochastic Districting Problem (MSSDP). The goal is to devise a districting plan (i.e., clusters of Territorial Units—TUs) accounting for uncertain parameters changing over a discrete multi-period planning horizon. The problem is cast as a multi-stage stochastic programming problem. It is assumed that uncertainty can be captured by a finite set of scenarios, which induces a scenario tree. Each node in the tree corresponds to the realization of all the stochastic parameters from the root node—the state of nature—up to that node. A mathematical programming model is proposed that embeds redistricting recourse decisions and other recourse actions to ensure that the districts are balanced regarding their activity. The model is tested on instances generated using literature data containing real geographical data. The results demonstrate the relevance of hedging against uncertainty in multi-period districting. Since the model is challenging to tackle using a general-purpose solver, a heuristic algorithm is proposed based on a restricted model. The computational results obtained give evidence that the approximate algorithm can produce high-quality feasible solutions within acceptable computation times.