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Open AccessArticle

Dimensionality-reduction Procedure for the Capacitated p-Median Transportation Inventory Problem

School of Business and Economics, Universidad Anahuac Mexico, Huixquilucan 52786, Mexico
Mathematics 2020, 8(4), 471; https://doi.org/10.3390/math8040471
Received: 12 February 2020 / Revised: 23 March 2020 / Accepted: 25 March 2020 / Published: 29 March 2020
The capacitated p-median transportation inventory problem with heterogeneous fleet (CLITraP-HTF) aims to determine an optimal solution to a transportation problem subject to location-allocation, inventory management and transportation decisions. The novelty of CLITraP-HTF is to design a supply chain that solves all these decisions at the same time. Optimizing the CLITraP-HTF is a challenge because of the high dimension of the decision variables that lead to a large and complex search space. The contribution of this paper is to develop a dimensionality-reduction procedure (DRP) to reduce the CLITraP-HTF complexity and help to solve it. The proposed DRP is a mathematical proof to demonstrate that the inventory management and transportation decisions can be solved before the optimization procedure, thus reducing the complexity of the CLITraP-HTF by greatly narrowing its number of decision variables such that the remaining problem to solve is the well-known capacitated p-median problem (CPMP). The conclusion is that the proposed DRP helps to solve the CLITraP-HTF because the CPMP can be and has been solved by applying different algorithms and heuristic methods. View Full-Text
Keywords: optimization dimensionality reduction; dimensionality-reduction procedure; p-median problems; NP-hard problem; distribution optimization; freight distribution optimization dimensionality reduction; dimensionality-reduction procedure; p-median problems; NP-hard problem; distribution optimization; freight distribution
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Carmona-Benítez, R.B. Dimensionality-reduction Procedure for the Capacitated p-Median Transportation Inventory Problem. Mathematics 2020, 8, 471.

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