The Integrated Vehicle and Pollster Routing Problem

TL;DR

The paper defines the Integrated Vehicle and Pollster Routing Problem (IVPRP), which jointly routes vehicles and pollsters (including pedestrian movement) to collect CPI data, and proves $\mathcal{NP}$-hard via a reduction from the TSP. It introduces a multigraph-based IP formulation (IVPRM) with node duplication to capture service and travel times, plus symmetry-breaking and bounds to curb computational complexity. Given the intractability of exact solutions for realistic sizes, the authors propose a three-phase heuristic: partition stores into balanced subsets, solve reduced IVPRM (R-IVPRM) on each subset, and link the partial solutions into a feasible aggregated daily plan. Computational experiments on simulated data and a real Guayaquil case demonstrate substantial cost and time savings over existing empirical planning, with the partition-based approach achieving efficient, near-optimal plans and clear visualization of routes. The work provides a practical framework for city-scale data-collection routing and suggests promising avenues for enhanced heuristics, dynamic routing, and multi-period planning in similar logistics applications.

Abstract

The National Statistics Bureau of Ecuador carries out monthly polls to monitor the evolution of the Consumer Price Index, a metric measuring consumer prices of essential commodities. These surveys are administered across a designated set of stores, with a fleet of vehicles transporting pollsters from the bureau headquarters to the chosen locations. Moreover, pollsters move between stores using pedestrian paths or using a vehicle to shorten the travel time. This paper introduces the Integrated Vehicle and Pollster Routing Problem and presents an integer programming model to effectively schedule pollster visits to selected stores while optimizing the routing of the vehicle fleet. Results on the computational complexity, a three-phase algorithm, and computational experience based on real-world instances are provided.

Figures (5)

• Figure 1: Node duplication: The depot, labeled $0$, and two stores, labeled $i$ and $j$, are associated with their duplicates, labeled $2n+1$, $i+n$, and $j+n$, respectively.
• Figure 2: Multigraph construction for the IVPRP. Focusing only on the depot and two nodes $i, j \in C_{-}$: there are only outgoing arcs from $0$ and only incoming arcs to $2n+1$. One service arc is defined for $i$ and $j$ separately, two walking arcs connect $\{i, j, i+n, j+n\}$, and 18 vehicle arcs connect $\{0, i, j, i+n, j+n, 2n+1\}$.
• Figure 3: Multigraph and optimal solution for an instance of IVPRP.
• Figure 4: Map of Guayaquil showing the locations of stores to be visited.
• Figure 5: Map of Guayaquil displaying the partition subsets, stores, and routes.

Theorems & Definitions (3)

• Theorem 1
• proof
• Remark 1