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

• Main Author: Rafael Bernardo Carmona-Benítez
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Mathematics
• Subjects: optimization dimensionality reduction; dimensionality-reduction procedure; p-median problems; NP-hard problem; distribution optimization; freight distribution
• Online Access: https://www.mdpi.com/2227-7390/8/4/471
• ISSN: 2227-7390

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.