Congestion and Penalization in Optimal Transport

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Tác giả: Jorge Chávez, Marcelo Gallardo, Manuel Loaiza

Ngôn ngữ: eng

Ký hiệu phân loại: 616.242 Diseases

Thông tin xuất bản: 2024

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Bộ sưu tập: Metadata

ID: 204456

Comment: v.4: Removed quadratic model, explored applications of the penalized model. Compared the algorithm with folkloreWe introduce a novel model based on the discrete optimal transport problem that incorporates congestion costs and replaces traditional constraints with weighted penalization terms. This approach better captures real-world scenarios characterized by demand-supply imbalances and heterogeneous congestion costs. We develop an analytical method for computing interior solutions, which proves particularly useful under specific conditions. Additionally, we propose an $O((N+L)N^2 L^2)$ algorithm to compute the optimal interior solution. For certain cases, we derive a closed-form solution and conduct a comparative statics analysis. Finally, we present examples demonstrating how our model yields solutions distinct from classical approaches, leading to more accurate outcomes in specific contexts, such as Peru's health and education sectors.
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