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Recommend-to-Match with Random Supply Rejections: Formulation, Approximation, and Analysis

Haoyue Liu, Sheng Liu, Mingyao Qi

TL;DR

Problem: Address two-stage recommend-to-match under stochastic supplier rejections in crowd-sourcing logistics. Approach: derive an exact MILP for homogeneous independent acceptances, prove general intractability, and develop a mixed-integer exponential-cone programming (MIECP) based approximation with parametric guarantees, including a log-sum-exp bound. Contributions: formal stochastic model $SP$, MILP [R-SP] for the homogeneous case, demonstration of LP-based approximation limitations, and strong MIECP performance guarantees supported by synthetic and real-world freight data. Impact: enables scalable, near-optimal matching in large supply pools and provides a foundation for dynamic, resilient matching policies in freight platforms.

Abstract

Matching demand with supply in crowd-sourcing logistics platforms must contend with uncertain worker participation. Motivated by this challenge, we study a two-stage ``recommend-to-match" problem under stochastic supplier rejections, where each demand is initially recommended to multiple potential suppliers prior to final matching decisions. We formulate a stochastic optimization model that explicitly captures uncertain supplier acceptance behavior. We show that an exact mixed-integer linear formulation is obtainable for the special case with homogeneous and independent acceptance responses, but the general problem does not admit an efficient formulation. Particularly, our analysis reveals that deterministic linear approximation methods can perform arbitrarily poorly in such settings. To overcome this limitation, we propose a new approximation approach based on mixed-integer exponential cone programming (MIECP) and establish its parametric performance guarantees. Extensive experiments on synthetic data and real-world freight data validate the effectiveness of our approach. Our MIECP-based solution achieves near-optimal matching performance while reducing computation time by over 90% compared to benchmark methods.

Recommend-to-Match with Random Supply Rejections: Formulation, Approximation, and Analysis

TL;DR

Problem: Address two-stage recommend-to-match under stochastic supplier rejections in crowd-sourcing logistics. Approach: derive an exact MILP for homogeneous independent acceptances, prove general intractability, and develop a mixed-integer exponential-cone programming (MIECP) based approximation with parametric guarantees, including a log-sum-exp bound. Contributions: formal stochastic model , MILP [R-SP] for the homogeneous case, demonstration of LP-based approximation limitations, and strong MIECP performance guarantees supported by synthetic and real-world freight data. Impact: enables scalable, near-optimal matching in large supply pools and provides a foundation for dynamic, resilient matching policies in freight platforms.

Abstract

Matching demand with supply in crowd-sourcing logistics platforms must contend with uncertain worker participation. Motivated by this challenge, we study a two-stage ``recommend-to-match" problem under stochastic supplier rejections, where each demand is initially recommended to multiple potential suppliers prior to final matching decisions. We formulate a stochastic optimization model that explicitly captures uncertain supplier acceptance behavior. We show that an exact mixed-integer linear formulation is obtainable for the special case with homogeneous and independent acceptance responses, but the general problem does not admit an efficient formulation. Particularly, our analysis reveals that deterministic linear approximation methods can perform arbitrarily poorly in such settings. To overcome this limitation, we propose a new approximation approach based on mixed-integer exponential cone programming (MIECP) and establish its parametric performance guarantees. Extensive experiments on synthetic data and real-world freight data validate the effectiveness of our approach. Our MIECP-based solution achieves near-optimal matching performance while reducing computation time by over 90% compared to benchmark methods.
Paper Structure (19 sections, 9 theorems, 36 equations, 2 figures, 5 tables)

This paper contains 19 sections, 9 theorems, 36 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Literature review
  3. Two-sided Matching Problems
  4. Matching in Transportation and Logistics
  5. Approximation of Stochastic Matching-related Problems
  6. Model and Analysis
  7. Problem Description and Formulation
  8. Direct Assignment Approximation
  9. MIECP Approximation
  10. Approximation Formulation
  11. Approximation Performance Analysis
  12. Numerical Experiments
  13. Synthetic Experiment
  14. Case Study: Full Truck Alliance
  15. Concluding Remarks
  16. ...and 4 more sections

Key Result

Proposition 1

When acceptance random variables $\tilde{\xi}_{ij}$ are i.i.d. across $i$ and $j$, the optimal objective value and the set of optimal solutions of model SP coincide with those of R-SP.

Figures (2)

  • Figure 1: Optimal objective values and running time of R-SP and MIECP on D20-S80 instances
  • Figure EC.2: Optimal objective values and running time of SAA and MIECP with $|\mathcal{A}^{D}|=20$

Theorems & Definitions (12)

  • Remark 1
  • Proposition 1
  • Proposition 2
  • Lemma 1
  • Corollary 1
  • Proposition 3
  • Remark 2
  • Lemma 2
  • Theorem 1
  • Corollary 2
  • ...and 2 more