The Optimal Production Transport: Model and Algorithm

TL;DR

This paper introduces a novel optimal production transport model that accounts for adjustable production ranges, along with generalized algorithms that improve accuracy and efficiency, demonstrated through cost-saving numerical simulations.

Contribution

The paper extends classical optimal transport by allowing marginal variation and develops generalized Sinkhorn algorithms with convergence guarantees.

Findings

Achieves 13.17% cost reduction in coal production and transport.

Provides a convergent algorithm for the new model.

Demonstrates improved accuracy and efficiency in numerical tests.

Abstract

In this paper, we propose the optimal production transport model, which is an extension of the classical optimal transport model. We observe in economics, the production of the factories can always be adjusted within a certain range, while the classical optimal transport does not take this situation into account. Therefore, differing from the classical optimal transport, one of the marginals is allowed to vary within a certain range in our proposed model. To address this, we introduce a multiple relaxation optimal production transport model and propose the generalized alternating Sinkhorn algorithms, inspired by the Sinkhorn algorithm and the double regularization method. By incorporating multiple relaxation variables and multiple regularization terms, the inequality and capacity constraints in the optimal production transport model are naturally satisfied. Alternating iteration algorithms are derived based on the duality of the regularized model. We also provide a theoretical analysis to guarantee the convergence of our proposed algorithms. Numerical results indicate significant advantages in terms of accuracy and efficiency. Furthermore, we apply the optimal production transport model to the coal production and transport problem. Numerical simulation demonstrates that our proposed model can save the production and transport cost by 13.17%.