Discrete-time modeling for order picking

My colleague Marc Schleyer and I have written an article entitled, “Throughput Time Distribution Analysis for a One-Block Warehouse.” The article was recently published in Transportation Research E (48).

Non-Technical Summary: Suppose you operate a warehouse that supports “will call” operations, in which customers can place orders and arrange to pick them up at the warehouse.  This exact situation existed at a W.W. Grainger warehouse we visited in the East Bay area of California. The order taker was required to provide customers a time to pick up the order. How soon should he say it will be available?

Because the time to process an order is probabilistic (or stochastic), quoting a time is really a statement of confidence. “I believe there is an `excellent chance’ the order will be ready in 90 minutes, so please pick it up after 10:30AM.” Where did 90 minutes come from, and what defines “excellent chance?” Our research is designed to help answer these questions.

The key observation is that the processing time for an order consists of two main components—order batching time, in which the order stays in a virtual queue before release to a picker, and order processing time. Each of these times varies, as does their sum. We have built probabilistic models of these times to give warehouse managers the ability to quote order completion times with a specified degree of confidence. For example, using our methods, a warehouse can say it completes orders in 90 minutes 95% of the time.

Slightly Technical Summary: We have developed discrete time models for the throughput time distribution of orders arriving to a one-block warehouse. The models accommodate single- or multi-line orders. The main contribution of our research is development of discrete-time models for warehouse systems. We believe such techniques could make stochastic modeling of real warehouse systems much easier.

We also show how to use these models to determine the optimal batch size, given a desired probability of on-time order fulfillment. In the “will call” scenario above, we determine how long we should wait before dispatching the picker. Experiments suggest that the optimal batch size is slightly higher than one would choose if minimizing average throughput time, which is the traditional objective. Here is an example of the output:

Completion time distribution for orders in a warehouse

To understand the funky spikes, please read the paper!

How the model might be used: The nice part of discrete-time modeling is that we can accommodate arbitrary inter-arrival and processing time distributions.  Just collect the data, choose appropriate “bucket sizes” and you have all the input needed for this modeling. In other words, there is no need for estimating the real distribution with analytical distributions—easy to do and easy to explain to potential users!

Companies might be able to use these models to develop promise time policies for arriving orders.  In the will call example above, the company probably wants a “2 hour” policy that is easy to remember and easy to communicate to customers. They would like to establish that policy based on science, rather than intuition.

If you’d like to know more, please download the paper. Your comments are welcome!

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