An exact analysis and comparison of manual picker routing heuristics

TL;DR

This paper derives exact formulas for the mean and variance of total picking time for four warehouse routing heuristics, enabling comparison of their efficiency under various conditions.

Contribution

It provides the first exact derivations of moments of picking time for multiple heuristics using general order size distributions and models warehouse operations as an M/G/c queue.

Findings

Exact formulas for first two moments of picking time for four heuristics.

Comparison of heuristics under different order size distributions and layouts.

Warehouse with multiple pickers modeled as an M/G/c queue to estimate lead times.

Abstract

This paper presents exact derivations of the first two moments of the total picking time in a warehouse for four routing heuristics, under the assumption of random storage. The analysis is done for general order size distributions and provides formulas in terms of the probability generating function of the order size distribution. These results are used to investigate differences between routing heuristics, order size distributions and warehouse layouts. In specific, we model a warehouse with $c$ pickers as an M/G/c queue to estimate the average order-lead time.