Mathematical Methods of Organizing and Planning Production

By L. Kantorovich. 1960

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Han-Jia Ye
2. Da-Wei Zhou
3. De-chuan Zhan
4. Bo Dai
5. Hanjun Dai
6. Manuel Iori
7. Hai-Long Sun
8. Francis R. Bach

Citations in the corpus

• Co-Transport for Class-Incremental Learning (2021, background): “Optimal transport (OT): OT [34, 41] is first formulated to study the optimal transportation and resource allocation problem [18, 31].”
• Selected Topics in Column Generation (2002, background): “For the classical cutting stock problem (4), the above procedure leads to Kantorovich’s formulation (1960) where a commodity is defined for each (identical) available roll.”
• Self-Consuming Generative Models Go MAD (2023, background): “Wasserstein distance (WD), or earth mover’s or optimal transport distance [69], measures the minimum work required to move the probability mass of one distribution to another.”
• A Contextualized Historical Analysis of the Kuhn–Tucker Theorem in Nonlinear Programming: The Impact of World War II (2000, background): “For historical accounts on the development of linear programming in the USSR see, e.g., [Brentjes; Brentjes, 1976b; Charnes and Cooper, 1961; Koopmans, 1961; Isbell and Marlow, 1961; Leifman; 1990; Kantorovich, 1939].”
• Bin packing and cutting stock problems: Mathematical models and exact algorithms (2016, methodology): “The textbook BPP model (1)–(5), which has its roots in the seminal work by Kantorovich [82], was formally defined in 1990 by Martello and Toth [107].”
• On the History of Combinatorial Optimization (Till 1960) (2005, methodology): “Tolsto˘ ı's heuristic also makes use of insight into the geography of the Soviet Union.”
• Expandable Subspace Ensemble for Pre-Trained Model-Based Class-Incremental Learning (2024, background): “9, there are other ways to learn the mapping and complete the prototype matrix, e.g ., Linear Regression (LR) and Optimal Transport (OT) [33, 65].”
• Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, background): “In 1942, together with the linear programming problem (Kantorovich [27]), Kantorovich [26] tackled Monge’s problem originally brought up in the study of optimal transport.”
• Differentiable Top-k with Optimal Transport (2020, methodology): “We first show that the standard top-k operator can be parameterized in terms of the solution of an Optimal Transport (OT) problem (Monge, 1781; Kantorovich, 1960).”