A synchronous crew scheduling problem with time fairness based on a two-phrase assignment strategy in an urban rail transit network

Abstract

Crew scheduling problem (CSP), which involves finding the optimal match between crew members and scheduling tasks, is of utmost importance for completing all train runs within a workday in an urban rail transit (URT) system. Given the variations in train runs, crew compositions, and pooled-station sets across different operational lines, companies that only consider the CSP within a single line may inadvertently cause a significant disparity in working-time fairness among crews, even if they are part of the same organization. To address these concerns, this paper initially proposes an Integer Linear Programming (ILP) model that simultaneously optimizes the two phases of task assignment and task generation, aiming to solve a synchronous crew scheduling problem (SCSP) for the URT network, with a focus on the time fairness of each crew member. Generally, ILP is a set-partitioning-based model with decision variables set to assign tasks. To solve this model, a modified Column Generation (CG) algorithm has been redesigned to generate an optimal solution. Finally, a real-life instance from Beijing is introduced to evaluate the effectiveness of the proposed method. The results demonstrate that the cross-line scheduling plan (CLSP) based on the URT network can conserve crew resources by 4.73 % (reducing 13 crews) and shorten the average working time by up to 3.48 min. compared to the single-line scheduling plan (SLSP). Moreover, the CLSP manages to keep the working time fluctuations for each crew within an acceptable range of [0 min, 8 min]. This indicates that CLSP in the URT network is effective in meeting the fairness requirements for crews.