The Science of Inventory Calculations and Optimization

Sara Hoormann Principal
Read Time: 6 minutes apprx.



Last Wednesday, January 31st, Opex kicked off its 2018 Analytics Academy season with a series of sessions on ‘All Things Inventory.’ Opex Partner Mike Watson and Opex Sr. Research Associate Larry Snyder teamed up to deliver our first session on The Science of Inventory Calculations and Optimization. The content was aimed at setting the stage for our series with a review of inventory methods and the science behind them.

After introducing inventory and its role in today’s supply chains, Mike and Larry gave an overview of the history of inventory models, from EOQ to Newsvendor to Base Stock Policies, as well as Multi-Echelon Inventory Optimization (MEIO). They emphasized each model’s key assumptions, underlying math, major trade-offs, and contemporary applications.

A final wrap up included a quick review of some additional techniques for managing inventory including fill rate optimization, simulation, and using machine learning to set parameters/inputs.

The models discussed here will be the foundation we build upon throughout our next two sessions on scaling inventory solutions and new applications of machine learning to set inventory levels. If you are interested in downloading the presentation or recording of this session you can find it on our Academy Page.

You can also register for the next two sessions coming up in this series:

Session 2: Feb 21st – Scaling Inventory Solutions with Machine Learning and Good Design

Session 3: March 21st – Machine Learning, Inventory Optimization and The Beer Game


The content generated some great questions from attendees:

Q1: Larry mentioned that customer service level (CSL) and inventory levels don’t always go hand in hand. Is this product dependent?

A1: There are times when overall service levels can be improved simultaneously with overall inventory levels decreasing. For an individual SKU, lower inventory means lower service. But in the aggregate, it’s often the case that an organization has too much inventory of some SKUs and too little inventory of others. By correctly setting base-stock levels (and sticking to them), the net effect can be both an overall reduction in inventory and an overall improvement in service.

Q2: With infinite computing power, why not review inventory position constantly? How does the model change in that case?

A2: Even if we can monitor inventory position constantly (which, in the era of barcodes and RFID, most firms can already do), often we still only want to order every week (or day, or month, or whatever). So as far as the model is concerned, it’s the same as if we only observed the inventory position at those instants. In other words, a periodic-review model is still appropriate if we review the inventory continuously but we only order periodically.

Q3: How pervasive are the various inventory tools in the market?

A3: These tools are fairly well used. There are off-the-shelf software packages that incorporate some of the science we showed, custom-built solutions that have the science embedded, and home-grown solutions using Excel files. What happens a lot is that firms install an ERP system or inventory management system and these do not include any meaningful inventory science. Instead, they have fields for the user to fill in to set safety stock and determine when to order. The problem is that many firms do not use any science to set these targets. As such, people tend not to trust the results.

Q4: Can you recommend some finite multi-period models for electronic goods (limited lifecycle)?

A4: The basic finite-horizon inventory optimization model is covered in many advanced supply chain textbooks (including Section 4.4.3 of my textbook — Snyder and Shen, Fundamentals of Supply Chain Theory, Wiley, 2011). You can also check out this blog post. This model is applicable to a wide range of settings, including electronic goods or other limited-lifecycle products — pretty much anything where the problem inputs (demands, costs, supplies, etc.) change over time.

Q5: Why does optimizing the base stock also mean optimizing the safety stock and not order size? And how is order up to level decided if the stock situation and demand is changing with every review period?

A5: Optimizing base-stock is mathematically the same as optimizing safety stock because the safety stock equals S – [mean demand], where S is the base-stock level. Since the mean demand is a constant (it doesn’t change when we change S), a change in S means a corresponding change in the safety stock level. From a practical point of view, it might work like this: In SAP, you set your safety stock level to, say, 10. SAP uses this to try to get the inventory at the end of the period to equal 10. To do this, it places an order to bring the inventory position to 10 + [mean demand] — in other words, it is using a base-stock level of S = 10 + [mean demand].

To the second question, about how the order-up-to level is chosen if the inventory and demands are changing over time, that’s really where the finite-horizon optimization models come into play. I discussed those briefly near the end of the presentation. That approach makes decisions for the whole time horizon simultaneously, accounting for the changes that will occur during the horizon. Another approach is simply to run separate base-stock models for each review period, but that can lead to some bad inventory decisions. I wrote a blog post on this topic, if you want further discussion: The Newsvendor Doesn’t Tell the Whole Story

Q6: Can you talk about inventory in a manufacturing environment where we need to make production decisions? The challenge is that production lines are shared by many products, line capacity is constrained and there are change over penalties.

A6: This is a much more complicated problem, but there are models to tackle things like this. They are basically extensions of the EOQ model. One example is the “joint replenishment problem” (JRP), where we have an EOQ-like setting (deterministic demands, etc.) but multiple products. The products share manufacturing capacity, and each setup incurs a “major cost” regardless of which item is being set up, and a “minor cost” that is specific to the product being set up. For more on this problem and others like it, I recommend the classic book by Silver, Pyke, and Peterson, Inventory Management and Production Planning and Scheduling.

We look forward to more questions and discussions on the topic of Inventory in the months to come.