United States Department of Transportation
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Continuous Approximation Models with Temporal Constraints and Objectives
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2023-09-09
[PDF-6.31 MB]
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Edition:Final report (09/01/22-09/30/23)
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Abstract:The purpose of this project is to discover new continuous approximation models for modern logistical problems in which time plays a significant role, with a specific focus on last-mile delivery. Famous examples of such problems include the vehicle routing problem with time windows (VRPTW) and the cumulative travelling salesperson problem (CTSP). The continuous approximation paradigm is a quantitative method for solving logistics problems in which one uses a small set of parameters to model a complex system, which results in simple algebraic equations that are easier to manage than (for example) large-scale optimization models. As a further benefit, one often obtains insights from these simpler formulations that help to determine what affects the outcome most significantly. Although continuous approximation models have been used for over 60 years in logistics systems analysis, there has been very little research conducted on their use to problems with temporal features such as those described above. Based on our experience in this research area, this is likely because the addition of a time dimension complicates the problem in a way that is not readily accessible relative to classical models, which emphasize spatial aspects of modelling. However, our recent advances indicate that one can likely apply modern mathematical machinery to tackle these higher-dimensional problems. This project will combine tools from geospatial optimization, computational geometry, and geometric probability theory to formulate new models that will enable practitioners and policy-makers to solve these temporally-constrained problems, and most importantly, to identify what features are most impactful in their real-world application.
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