Optimal Inventory quantity for e-commerce websites

Julien Kervizic
Oct 7, 2019 · 7 min read

Determining the optimal quantity of inventory at a given time, can be an extensive analytical tasks, with input spanning multiple departments. Determining the optimal quantity to hold, means balancing the negative impact of out of stock, with the cost of holding inventory.

Out of stock risk — lost or delayed sales

Beside the poor customer experience, having items out of stock (oos) also leads to lost or delayed sales. Being able to both quantified these lost or delayed sales and effectively manage this out of stock risks are a key to an effective retail and supply chain analytics.


Out of stock can lead to two main negative conversion factors:

  • Empty shelf space impact: having a product that can not be purchased on display, decreases the overall conversion rate
  • Desired item loss : Not having the right products on offer will also decrease the overall conversion rate

Some of the key factor in order to understand the impact of having out of stock items n your website, is the overall size of the catalogue and the substitutability of products within the catalogue. While calculating rigorously the impact of each component can be a daunting tasks, there are a couple first order approximations that can help gauge the impact of out of stock products.

Photo by William Fernandes on Unsplash

The empty shelf impact (PLP) can be approximated, assuming none of its potential conversions would be spilling over to other items, by assuming it’s inStock conversion rate

Empty Shelf Impact ≈ inStock Conversion Rate * Page Traffic * Product Price

One of the way to measure the impact of desired item loss for out of stock items, is by 1) comparing the substitution impact on the Product Listing Page (PLP) 2) Estimate loss sales from traffic to the Product Detail page (PDP)

Comparing the PLP substitution impact

Assuming that there is a mitigation strategy for oos items on the PLP , an approximation of the substitution impact can be calculating by estimating the conversion rate of an item at its expected placement and comparing it with the conversion rate of the substitution item. The impact of the switch of position can be approximated with:

PLP Impact ≈ Δ(Conversion Rate * Page traffic  * Product Price)

Estimated PDP loss

If no mitigation strategies is implemented on the PDP, traffic leading to the PDP will be completely lost and the estimation of the negative impact of out of stock item, can be approximated in a similar manner to the empty shelf (PLP) calculation:

PDP Impact ≈ PDP traffic * inStock Conversion rate * Product Price

Mitigation strategies

Depending on the particular situation, some mitigation strategies can be implemented to limit the impact of out of stock items, such as position down ranking for low inventory items on product listing pages (PLP), setting up back in stock notification, or offering substitution items.

Amazon itself implemented a couple of strategies in order to reduce the impact of an item out of stock on its product detail page (PDP):

At the top of the page, two different save are possible when an item is out of stock. 1 a variant selector, that enables to quickly switch to a very similar SKU and 2 an option to purchase the item from an alternative seller. Other components of the page such as “compare with similar items” or “Customers who viewed this item also viewed” provide a way to mitigate the impact of out of stock when items are substitutable. Back in stock emails are an additional mitigation strategy that however would tend to delay purchase.

Operational Metrics

One of the key operational metrics that can help quantifying and measuring the impact of out of stock items, is capturing the number of oos impressions. This can usually be easily implemented through a good analytics tag/event and doesn’t require complicated analytics to be operational.

Demand forecast

Demand forecasts are the first step to identify what should be the quantity purchased and the amount of inventory needed. E-commerce website generally have a few indicators that can help with establishing these demand forecasts 1) Historical Sales data 2) Page Views such as PDPs views 3) planning data. The demand forecast should take into account seasonality, campaign peaks and overall product demands.

Seasonality is usually tackled using time series forecasting method, libraries such as Python/R’s prophet allows to handle these types of demand forecasts handling at the same time seasonality and uncertainty intervals.

Campaign Peaks: is something that can be hard to estimate, an understanding of price/demand elasticity, media budget and effectiveness is necessary to get a sense of how much extra demand marketing campaigns can generate.

Product introductions: Product introduction represent another challenge to volume forecast. There is limited information as to how popular they could prove. Data points such as page views prior to release, present a measure of anticipation, as do pre-orders. These can be fit into a product lifecycle model, and coupled with product information these could be used to provide demand estimates for these products.

Demand forecast generally require manual adjustments in order to correct the model behavior’s. The typical forecasting models are unconstrained and would not take into account the substitutability of demand for instance.

Replenishment Time

As previously shown, the impact of out of stock items is directly proportional to the page traffic being fed through when the item is out of stock. The impact of being out of stock for a single day is not the same as being out of stock for a full week.

Understanding the replenishment rate of each item, will help us get a better understanding of what is the total potential impact of out of stock. The replenishment time, help us get a better estimate of what would be the maximum out of stock traffic:

Max Out of Stock Traffic = E(Daily OOS Traffic) * Replenishment Days31

Mitigation strategies can be put in place to reduce the replenishment time, such as automated re-ordering triggers when inventory reaches certain thresholds.

Cost of holding Inventory

Warehouse Storage costs

Holding inventory has some direct costs in the form of warehouse storage costs. This is generally a function of the space taken to hold the quantity of inventory.

Product obsolescence & Perishability

Most products held in inventory will have their value decrease the more time they spend in a warehouse. Understanding of the different product value life curves, can help inform how long a product should be held in inventory and what quantity to order.

Different product types tend to have a different product value life curves:

Electronics products tend to have their value decrease at an accelerated pace. A study by wrap found that year 1 trade-in value was only 35% of year 0 trade-in value for Consumer electronics products. Although part of it can be attributed to wear and tear, the accelerated pace of depreciation in the first year compared to the 2nd year (retains 75% on the value), indicates that the initial decrease in value has more to do with the product itself than wear and tear.

Fashion products, tend to have a heavy cliff once they get out of season and steadily lose their value afterwards:

Sales are one way for companies to decrease their holding of inventory of certain goods while still capturing revenue. Many e-commerce fashion websites have introduced outlets page as part of their website in order to smoothen this process.

Perishable goods, tend to have a heavy decrease in value when they are near the best before date or used by date, and have negative value afterwards, due to disposal costs:

Amazon for instance charges as least $0.15 for disposal

Cost of capital Depreciation

There is an implicit cost in holding inventory, in that the capital for it could have been used in other projects, been put into a bond, saving account,… to generate additional revenues. Businesses tend to look at the problem in the opposite way, where they borrow the money to invest in specific projects. The Weighted average cost of capital (WACC), provides the average financing rate that the company is expected to pay.

Because of this cost of finance, even “Stable” Goods, products whose price do not decrease the longer they are held in inventory, also tend to have a decreasing product value life curves as their future revenue needs to be depreciated by the overall expected interest payment.

Overall tradeoffs

Minimizing the risk of Out of Stock and the risk of Holding inventory are conflicting goals that need to be balanced as to their impacts. Getting an understanding of Demand forecast and replenishment helps better assess these impacts and risks.

Additional complexity can arise when dealing with tiered pricing procurement contracts.

Operational Metrics, such as days inventory outstanding offer an easy way to manage some of these aspects.

Hacking Analytics

All around data & analytics topics

Julien Kervizic

Written by

Living at the interstice of business, data and technology | Solution Architect & Head of Data | Heineken, Facebook and Amazon | linkedin: https://bit.ly/2XbDffo

Hacking Analytics

All around data & analytics topics

Julien Kervizic

Written by

Living at the interstice of business, data and technology | Solution Architect & Head of Data | Heineken, Facebook and Amazon | linkedin: https://bit.ly/2XbDffo

Hacking Analytics

All around data & analytics topics

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