Stochastic modeling of multiline orders in integrated storage-order picking system

Due to demanding service levels in e-commerce order fulfillment, modeling and analysis of integrated storage and order picking processes in warehouses deserve special attention. The upstream storage system can have a significant impact on the performance of the downstream order picking process. With a particular focus on multiline e-commerce orders, we develop an analytical modeling framework for integrated analysis of upstream (shuttle-based storage and retrieval system) and downstream (pick system) networks. To capture the consolidation delays in fulfilling multiline orders, the downstream pick system is modeled with a closed queuing network that includes synchronization nodes. The configuration of the synchronization station is adapted to model the variety of order profiles handled at the pick station. For the downstream closed queuing network, we propose a decomposition-based solution methodology that results in good solution accuracy. The resulting semi-open queuing network (SOQN) of the integrated system is analyzed using the matrix-geometric method (MGM). To improve the accuracy of analytical estimates of the measures, we propose a hybrid simulation/analytical framework, where the performance measures of complex subnetworks are obtained from simulation. We also develop a detailed simulation model of the physical system for validating the analytical and hybrid estimates of the performance measures. The results from experiments indicate that the hybrid simulation/analytical approach reduces the error in the throughput time estimates to 3% from 18% obtained from the analytical model. Then, we investigate the effect of the upstream network configuration (such as the number of storage aisles) and the downstream network configuration (such as the mixed vs. dedicated picking, CONWIP control for orders, order batching) on the order throughput times. Our analysis provides a threshold on the maximum numbers of allowable orders (CONWIP control) and number of aisles beyond which the improvement in average throughput time of the integrated system is marginal. Numerical experiments with high-order arrivals also highlight that mixed picking in the downstream network can result in significant throughput time reduction in comparison to dedicated picking.

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