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A Branch-Price-Cut-And-Switch Approach for Optimizing Team Formation and Routing for Airport Baggage Handling Tasks with Stochastic Travel Times

Andreas Hagn, Rainer Kolisch, Giacomo Dall'Olio, Stefan Weltge

TL;DR

This work addresses optimal team formation and routing for airport baggage handling under stochastic apron travel times. It introduces two binary program formulations—one with aggregated workforce and a disaggregated counterpart—implemented via a Branch-Price-Cut-and-Switch framework that dynamically switches master formulations and integrates exact rank-1 CG cuts. The approach leverages ESPPRC pricing networks with time-dynamic costs, a tailored labeling algorithm, and multiple acceleration techniques (graph reduction, decremental state-space, and directional labeling) to solve large instances. Experimental results on real-world-inspired data show substantial improvements over benchmark methods, with stochastic travel times delivering higher service levels and more stable operations than deterministic approximations. The work advances exact solution methods for stochastic TSRPs with multi-skill, multi-mode workforces, offering practical implications for resource-efficient, reliable baggage handling in hubs like Munich Airport.

Abstract

In airport operations, optimally using dedicated personnel for baggage handling tasks plays a crucial role in the design of resource-efficient processes. Teams of workers with different qualifications must be formed, and loading or unloading tasks must be assigned to them. Each task has a time window within which it can be started and should be finished. Violating these temporal restrictions incurs severe financial penalties for the operator. In practice, various components of this process are subject to uncertainties. We consider the aforementioned problem under the assumption of stochastic travel times across the apron. We present two binary program formulations to model the problem at hand and propose a novel solution approach that we call Branch-Price-Cut-and-Switch, in which we dynamically switch between two master problem formulations. Furthermore, we use an exact separation method to identify violated rank-1 Chvátal-Gomory cuts and utilize an efficient branching rule relying on task finish times. We test the algorithm on instances generated based on real-world data from a major European hub airport with a planning horizon of up to two hours, 30 flights per hour, and three available task execution modes to choose from. Our results indicate that our algorithm is able to significantly outperform existing solution approaches. Moreover, an explicit consideration of stochastic travel times allows for solutions that utilize the available workforce more efficiently, while simultaneously guaranteeing a stable service level for the baggage handling operator.

A Branch-Price-Cut-And-Switch Approach for Optimizing Team Formation and Routing for Airport Baggage Handling Tasks with Stochastic Travel Times

TL;DR

This work addresses optimal team formation and routing for airport baggage handling under stochastic apron travel times. It introduces two binary program formulations—one with aggregated workforce and a disaggregated counterpart—implemented via a Branch-Price-Cut-and-Switch framework that dynamically switches master formulations and integrates exact rank-1 CG cuts. The approach leverages ESPPRC pricing networks with time-dynamic costs, a tailored labeling algorithm, and multiple acceleration techniques (graph reduction, decremental state-space, and directional labeling) to solve large instances. Experimental results on real-world-inspired data show substantial improvements over benchmark methods, with stochastic travel times delivering higher service levels and more stable operations than deterministic approximations. The work advances exact solution methods for stochastic TSRPs with multi-skill, multi-mode workforces, offering practical implications for resource-efficient, reliable baggage handling in hubs like Munich Airport.

Abstract

In airport operations, optimally using dedicated personnel for baggage handling tasks plays a crucial role in the design of resource-efficient processes. Teams of workers with different qualifications must be formed, and loading or unloading tasks must be assigned to them. Each task has a time window within which it can be started and should be finished. Violating these temporal restrictions incurs severe financial penalties for the operator. In practice, various components of this process are subject to uncertainties. We consider the aforementioned problem under the assumption of stochastic travel times across the apron. We present two binary program formulations to model the problem at hand and propose a novel solution approach that we call Branch-Price-Cut-and-Switch, in which we dynamically switch between two master problem formulations. Furthermore, we use an exact separation method to identify violated rank-1 Chvátal-Gomory cuts and utilize an efficient branching rule relying on task finish times. We test the algorithm on instances generated based on real-world data from a major European hub airport with a planning horizon of up to two hours, 30 flights per hour, and three available task execution modes to choose from. Our results indicate that our algorithm is able to significantly outperform existing solution approaches. Moreover, an explicit consideration of stochastic travel times allows for solutions that utilize the available workforce more efficiently, while simultaneously guaranteeing a stable service level for the baggage handling operator.
Paper Structure (47 sections, 9 theorems, 79 equations, 5 figures, 11 tables, 1 algorithm)

This paper contains 47 sections, 9 theorems, 79 equations, 5 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Literature on Stochastic Vehicle Routing
  4. Literature on the stochastic TSRP
  5. Problem Description
  6. General Notation
  7. Profiles and Skill Compositions
  8. Travel Times
  9. Routes and Route Feasibility
  10. Route Costs and Objective Function
  11. Two Binary Program Formulations
  12. Master Problem with Aggregated Workforces
  13. Master Problem with Skill-Level Specific Workforces
  14. Solution Approach
  15. Pricing Problem for the ARMP
  16. ...and 32 more sections

Key Result

Theorem 1

For any feasible instance of the AMP, there exists at least one optimal solution $\left(\bar{\lambda}^r_q\right)_{(r,q)\in\mathcal{R}}$ such that $\bar{\lambda^r_q} \in \{0,1\}$ holds for all $(r,q)\in\mathcal{R}$:

Figures (5)

  • Figure 1: Tour Schedule satisfying (\ref{['model:tasksdone_aggregated_mp']})--(\ref{['model:workerconstr_aggregated_mp']}) (from dallolio_temp)
  • Figure 2: Labels satisfying dominance rule \ref{['dominance_rule_amp']} and violating rule \ref{['dominance_rule_dmp']}
  • Figure 3: Box plot of optimality gap percentage for all solver configurations
  • Figure 4: Distribution of service levels
  • Figure 5: Frequency of durations of time window violations

Theorems & Definitions (17)

  • Example 1
  • Example 2
  • Definition 1: Dominance Rule
  • Definition 2: Dominance rule for the DRMP
  • Example 3
  • Definition 3: Dominance Rule
  • Theorem 1
  • Corollary 1
  • Theorem 2
  • Lemma 1
  • ...and 7 more