Travel time models for tier-to-tier SBS/RS with different storage assignment policies and shuttle dispatching rules

This paper explores both random and class-based storage policies and three shuttle dispatching rules, random, distance-based, and demand-rate based, for a tier-to-tier shuttle-based storage and retrieval system (SBS/RS). Modeling the system as a discrete-time Markov Chain, this study derived the shuttle distribution under each policy combination, and further developed the expected travel time models for both single-command (SC) and dual-command (DC) operations. The developed models can help a warehouse designer or manager to comprehensively make four decisions for SBS/RS, whether SC or DC operations should be adopted, the most appropriate storage policy, the best shuttle dispatching rule, and the number of shuttles. The travel time models can evaluate each possible policy combination quickly through multiple criteria, such as the capacity, customer responsiveness, and costs of shuttles. Numerical experiments showed significant impacts of the policy combination on the expected travel time. Class-based storage, if implementable, is always better than random storage under each combination of shuttle dispatching rule and operational mode (i.e., SC or DC). Under random storage and SC operations, the distance-based shuttle dispatching rule is always better than the random rule, and their difference is concave in the number of shuttles. When classed-based storage is adopted and the number of shuttles is small, the demand-rate-based rule is the best under SC operations. Its benefit becomes more obvious when demand rates become more heterogeneous until some point but decreases as the system has more shuttles. Under DC Operations, depending on equipment speeds, the distance-based shuttle dispatching rule can be worse than the random rule under random storage. Under class-based storage and DC operations, the demand-rate-based rule is still the best when demand rates are heterogeneous. The differences between SC and DC operations are more significant when demand rates are more homogenous. When a system wants to be more responsive to customers, it should be run under SC operations. If the overall capacity is of interest, DC operations are much better.