SearcharxivSearch

arXiv · 2603.24574

Coordinating Spot and Contract Supply in Freight Marketplaces

Abstract

The freight industry is undergoing a digital revolution, with an ever-growing volume of transactions being facilitated by digital marketplaces. A core capability of these marketplaces is the fulfillment of demand for truckload movements (loads) by procuring the services of carriers who execute them. Notably, these services are procured both through long-term contracts, where carriers commit capacity to execute loads (e.g., contracted fleet of drivers or lane-level commitments), and through short-term spot marketplaces, where carriers can agree to move individual loads for the offered price. This naturally couples two canonical problems of the transportation industry: contract assignment and spot pricing. In this work, we model and analyze the problem of coordinating long-term contract supply and short-term spot supply to minimize total procurement costs. We develop a Dual Frank Wolfe algorithm to compute shadow prices which allow the spot pricing policy to account for the committed contract capacity. We show that our algorithm achieves small relative regret against the optimal -- but intractable -- dynamic programming benchmark when the size of the market is large. Importantly, our Dual Frank Wolfe algorithm is computationally efficient, modular, and only requires oracle access to spot-pricing protocols, making it ideal for large-scale markets. Finally, we evaluate our algorithm on semi-synthetic data from a major Digital Freight Marketplace, and find that it yields significant savings ($\approx 10\%$) compared to a popular status-quo method.

Explore related subjects

Keep this discovery

BibTeXRIS

Philip Kaminsky, Rachitesh Kumar, Roger Lederman. 2026-03-25. Coordinating Spot and Contract Supply in Freight Marketplaces. https://arxiv.org/abs/2603.24574

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS