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Posted Price versus Hybrid Mechanisms in Freight Transportation Marketplaces

Ruoran Chen, Sungwoo Kim, He Wang, Xuan Wang

TL;DR

The paper addresses pricing and matching in a two-sided freight marketplace, modeling carrier decisions as a two-stage process (lane choice via MNL followed by booking or bidding). Using a fluid-approximation framework, it derives a convex optimization (FA) that upper-bounds the long-run profit of any stable, IC, IR mechanism and shows that a static posted-price policy SP, derived from FA, is asymptotically optimal under large market size. It then introduces a hybrid mechanism HYB that permits posting plus uniform-price auctions, proves HYB is IC/IR and yields higher profits than SP with tight bounds that shrink as market size grows; numerical experiments with U.S. freight data confirm that HYB reduces carrier costs and improves efficiency, especially in smaller markets. The study provides actionable guidance on when to use hybrid auctions versus posted pricing and establishes a rigorous performance benchmark via the fluid model for networked freight platforms.

Abstract

We consider a freight platform that serves as an intermediary between shippers and carriers in a truckload transportation network. The platform's objective is to design a policy that determines prices for shippers and payments to carriers, as well as how carriers are matched to loads to be transported, to maximize its long-run average profit. We propose a two-stage decision framework to model carriers' load choice behavior, where carriers choose a lane according to the multinomial logit (MNL) model based on the platform's posted price in the first stage and book a load in the second stage. We analyze two types of carrier-side mechanisms commonly used by freight platforms: a posted price mechanism and a hybrid mechanism where carriers can either book loads at posted price or submit their bids in an auction. The proposed mechanisms are constructed using a fluid approximation model to incorporate carrier interactions in the freight network. We show that the hybrid mechanism has higher profits than the posted price mechanism. We prove tight bounds between these mechanisms for varying market sizes. The findings are validated through a numerical simulation using industry data from the U.S. freight market.

Posted Price versus Hybrid Mechanisms in Freight Transportation Marketplaces

TL;DR

The paper addresses pricing and matching in a two-sided freight marketplace, modeling carrier decisions as a two-stage process (lane choice via MNL followed by booking or bidding). Using a fluid-approximation framework, it derives a convex optimization (FA) that upper-bounds the long-run profit of any stable, IC, IR mechanism and shows that a static posted-price policy SP, derived from FA, is asymptotically optimal under large market size. It then introduces a hybrid mechanism HYB that permits posting plus uniform-price auctions, proves HYB is IC/IR and yields higher profits than SP with tight bounds that shrink as market size grows; numerical experiments with U.S. freight data confirm that HYB reduces carrier costs and improves efficiency, especially in smaller markets. The study provides actionable guidance on when to use hybrid auctions versus posted pricing and establishes a rigorous performance benchmark via the fluid model for networked freight platforms.

Abstract

We consider a freight platform that serves as an intermediary between shippers and carriers in a truckload transportation network. The platform's objective is to design a policy that determines prices for shippers and payments to carriers, as well as how carriers are matched to loads to be transported, to maximize its long-run average profit. We propose a two-stage decision framework to model carriers' load choice behavior, where carriers choose a lane according to the multinomial logit (MNL) model based on the platform's posted price in the first stage and book a load in the second stage. We analyze two types of carrier-side mechanisms commonly used by freight platforms: a posted price mechanism and a hybrid mechanism where carriers can either book loads at posted price or submit their bids in an auction. The proposed mechanisms are constructed using a fluid approximation model to incorporate carrier interactions in the freight network. We show that the hybrid mechanism has higher profits than the posted price mechanism. We prove tight bounds between these mechanisms for varying market sizes. The findings are validated through a numerical simulation using industry data from the U.S. freight market.

Paper Structure

This paper contains 21 sections, 17 theorems, 169 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Literature Review
  4. Model
  5. The Platform's Mechanism
  6. Dynamic Program Formulation
  7. Stability, Incentive Compatibility (IC) and Individual Rationality (IR).
  8. Fluid Approximation and Profit Benchmark
  9. The Fluid Model
  10. Convex Reformulation
  11. FA Gives an Upper Bound of the Optimal Profit
  12. Posted Price Mechanisms
  13. Hybrid Mechanisms
  14. Numerical Studies
  15. Cost Gap Ratio and Booking Channel
  16. ...and 6 more sections

Key Result

Lemma 1

The virtual cost function $\psi_{ij}$ defined in (eq:psi-def) is strictly increasing and its inverse function $\psi^{-1}_{ij}$ exists.

Figures (1)

  • Figure 1: An example of freight brokerage apps for carriers (source: Uber freight).

Theorems & Definitions (37)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Theorem 2
  • Lemma 2
  • Theorem 3
  • ...and 27 more