Complexity Analysis of the Parallel Guided Ejection Search for the Pickup and Delivery Problem with Time Windows

TL;DR

This paper analyzes the worst-case time complexity of a parallel algorithm designed to optimize fleet size in pickup and delivery problems with time constraints, providing a step-by-step estimation method.

Contribution

It introduces a systematic approach to estimate the pessimistic time complexity of parallel algorithms for complex transportation problems.

Findings

Provides a step-by-step method for complexity estimation.

Demonstrates applicability to other transportation algorithms.

Offers insights into the algorithm's scalability and efficiency.

Abstract

This paper presents the pessimistic time complexity analysis of the parallel algorithm for minimizing the fleet size in the pickup and delivery problem with time windows. We show how to estimate the pessimistic complexity step by step. This approach can be easily adopted to other parallel algorithms for solving complex transportation problems.