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This paper discusses the integrated vehicle- and crew-scheduling problem in public transit with multiple depots. It is well known that the integration of both planning steps discloses additional flexibility that can lead to gains in efficiency, compared to sequential planning. We present a new modeling approach that is based on a time-space network representation of the underlying vehicle-scheduling problem. The integrated problem is solved with column generation in combination with Lagrangian relaxation. The column generation subproblem is modeled as a resource-constrained shortest-path problem based on a novel time-space network formulation. Feasible solutions are generated by a heuristic branch-and-price method that involves fixing service trips to depots. Numerical results show that our approach outperforms other methods from the literature for well-known test problems.

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The Robotic Mobile Fulfillment Systems (RMFS) is a new type of robotized, parts-to-picker material handling system, designed especially for e-commerce warehouses. Robots bring movable shelves, called pods, to workstations where inventory is put on or removed from the pods. This paper simulates both the pick and replenishment process and studies the order assignment, pod selection and pod storage assignment problems by evaluating multiple decision rules per problem. The discrete event simulation uses realistic robot movements and keeps track of every unit of inventory on every pod. We analyze seven performance measures, e.g. throughput capacity and order due time, and find that the unit throughput is strongly correlated with the other performance measures. We vary the number of robots, the number of pick stations, the number of SKUs (stock keeping units), the order size and whether returns need processing or not. The decision rules for pick order assignment have a strong impact on the unit throughput rate. This is not the case for replenishment order assignment, pod selection and pod storage. Furthermore, for warehouses with a large number of SKUs, more robots are needed for a high unit throughput rate, even if the number of pods and the dimensions of the storage area remain the same. Lastly, processing return orders only affects the unit throughput rate for warehouse with a large number of SKUs and large pick orders.

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