Study and Analysis of Mathematical Models for Networking Shipping Planning: An Overview of Transportation Problems in Nonlinear Sciences

Abstract

This paper examines an integrated networking shipping issue with solutions for cargo aggregation. A goods forwarder can combine planned and flexible-time delivery services. One major feature of the issue is time constraints. They are used, for example, to simulate shipping and picking-up times. The several aspects of the issue can be characterized as digraph components, and combining them results in a comprehensive graph description. This allows for a quantitative multi-commodity flow formulation with origin-destination and time structures, side constraints, and non-convex piece-wise quadratic costs. Techniques for creating columns are intended to calculate lower bounds. These algorithms for creating columns are also integrated with heuristics that seek to identify feasible integer answers. When computational outcomes are presented using actual data, the effectiveness of the suggested method is demonstrated. This work is motivated by the work of L. Moccia, et al [35].