A New Model for the Mass Transit Crew Scheduling Problem

Abstract

A new formulation for the “Mass Transit Crew Scheduling” (MTCS) problem is presented. The proposed model is a “task-based” multi-commodity network flow problem in which the variables are defined in conjunction with the tasks and the tasks compatibilities.

Based on the union contracts in the United States the calculations of the task compatibility costs usually cannot be finalized until we establish the workdays and solve the problem. In our approach, we start from an initial model, the relaxed MTCS problem, in which we consider minimum costs for these compatibilities. Then we propose to go through an iterative procedure for establishing the workdays and adjusting the compatibility costs if necessary. This would be accomplished by generating new variables corresponding to the established feasible workdays and a “soft” constraint associated with each new variable.

The relaxed model also lacks the constraints that prevent the construction of the workdays that are illegal based on the union agreements or other rules. For each infeasible workday we could establish a “hard” constraint to be added to the relaxed problem. An exact solution procedure for small instances of this problem could be a constraint and variable generation approach in which the workday variables as well as the soft and the hard constraints would be added to the problem in an iterative procedure.