Capacity Analysis of Sequential Zone Picking Systems

Abstract

This paper develops a capacity model for sequential zone picking systems. These systems are popular internal transport and order-picking systems because of their scalability, flexibility, high-throughput ability, and fit for use for a wide range of products and order profiles. The major disadvantage of such systems is congestion and blocking under heavy use, leading to long order throughput times. To reduce blocking and congestion, most systems use the block-and-recirculate protocol to dynamically manage workload. In this paper, the various elements of the system, such as conveyor lanes and pick zones, are modeled as a multiclass block-and-recirculate queueing network with capacity constraints on subnetworks. Because of this blocking protocol, the stationary distribution of the queueing network is highly intractable. We propose an approximation method based on jumpover blocking. Multiclass jump-over queueing networks admit a product-form stationary distribution and can be efficiently evaluated by mean value analysis and Norton's theorem. This method can be applied during the design phase of sequential zone picking systems to determine the number of segments, number and length of zones, buffer capacities, and storage allocation of products to zones to meet performance targets. For a wide range of parameters, the results show that the relative error in the system throughput is typically less than 1% compared with simulation.

Integrated storage-order picking systems: Technology, performance models, and design insights

“…Because an exact analysis of such types of networks is not feasible, we approximate the blocking behavior with the jump-over protocol. As shown in van der Gaast et al (2018), the jump-over blocking protocol admits a product-form stationary queue length distribution for a network with jump-over nodes (like in our case) and allows an accurate estimation of the performance measures. Also see for another application of the jump-over blocking protocol in vertical storage and retrieval system.…”

“…For the MVA application, an initial state was assumed with no jobs in the picking stations and an initial value of the blocking probabilities equal to zero. Like in van der Gaast et al (2018), the algorithm converges very fast and does not depend on the initial value of the blocking probabilities. Appendix B summarizes the iterative algorithm for the blocking probabilities estimation based on MVA.…”

“…From the routing probabilities, the visit ratio of each node in the network can be calculated. It can be shown that the visit ratios follow a geometric distribution (van der Gaast et al, 2018). Considering a downstream system with picking stations, the visit ratio expressed in closed-form formulas are:…”

“…The blocking probabilities and the performance measures can then be estimated iteratively through MVA, taking into account the input buffer size (see Appendix B). MVA is applicable as jump-over networks with non-exponential picking times admit a product-form solution (van der Gaast et al, 2018). For the MVA application, an initial state was assumed with no jobs in the picking stations and an initial value of the blocking probabilities equal to zero.…”

Automated and Robotic Warehouses: Developments and Research Opportunities

“…Research into this has led to models that can quickly and accurately calculate and even optimise different configurations. See Van der Gaast et al (2013). Other researchers have studied the integrated performance of pick stations in conjunction with automated unit-load retrieval systems that supply the pick stations, e.g.…”