Analytic properties of two-carousel systems

TL;DR

This paper provides analytic solutions for two-carousel warehouse systems, demonstrating that their performance measures can be accurately approximated through contraction mapping-based integral equations, validated by simulations.

Contribution

It introduces a novel analytic framework for two-carousel systems, enabling fast and precise performance evaluation across various picking strategies.

Findings

Integral equations are contraction mappings, ensuring rapid convergence.

Numerical methods achieve high accuracy within few iterations.

Simulation results confirm the analytic predictions.

Abstract

We present analytic results for warehouse systems involving pairs of carousels. Specifically, for various picking strategies, we show that the sojourn time of the picker satisfies an integral equation that is a contraction mapping. As a result, numerical approximations for performance measures such as the throughput of the system are extremely accurate and converge fast (e.g.\ within 5 iterations) to their real values. We present simulation results validating our results and examining more complicated strategies for pairs of carousels.