Stock Levels by Profitability and Inventory Holding Cost

Executive Summary

  • Service levels and inventory holding costs must be socialized within companies so that the right service levels can be selected. One of the best ways of showing this relationship is with the service level inventory curve. The service level inventory curve shows the costs of attaining various service levels.

Introduction

There is a public relationship between service level and stock levels. A significant part of supply chain management is keeping service levels high while keeping inventories low. Although this probably oversimplifies the scenario a bit. It also involves keeping production efficiency high, and transportation costs low.

There are in fact many trade-offs that can be analyzed in supply chain management. But for this article, we will investigate the trade-off between service level and inventory holding cost.

The Service Level Versus Inventory and Inventory Holding Cost and Holding Costs Curve

One of the more frequently shown diagrams in inventory management is the service level versus stock curve. I have one such curve in the chart below.

This service level is the case service level — rather than the order line service level — which will be lower. The case service level takes merely all cases fulfilled and divides by all cases demanded. However, I use the case service level because it is the service level which is the basis for dynamic safety stock calculation. 

The service level versus inventory curve is essential in communicating that the amount of stock increases disproportionately with increases in service level.

This is why it can be infeasible to maintain the desired service levels often proposed by companies as their goals.

Socializing the Inventory/Service Level Curve

I believe this curve — with the company’s data should be shown to executive decision makers. I say this because few know how quickly the costs increase as service levels are increased. That is raised to the levels that they routinely propose as not only desirable but necessary.

A Model for Calculating the Costs of Service Level

We will start off by using the service level versus the cost curve. However, before we do this, we need to use some assumptions. Each set of assumptions will, of course, lead to a different outcome regarding the costs of service level. So we will test several scenarios. The best way to keep these scenarios straight is by using a table. The table below catalogs our scenarios.

Two costs are traded off. One is the cost of a lost sale, which is typically calculated as the multiple of the margin of the product. The cost of lost sales is then given by the following formula.

Total Demand * (1-Service Level) * Gross Margin * Margin Multiple

The table below calculates this cost for the different scenarios. To save space the columns that are labeled “CLS at XYZ%” means — the “Costs of Lost Sales at XYZ Service Level.” The column titled “ICC” stands for “Inventory Carrying Cost.”

Costs of Service Level Scenarios - Cost of Lost Sales

Scenario NameCostMarginICCCLS at 85%CLS at 85%CLS at 90%CLS at 95%CLS at 99%
Low Profit Items - High Carry Cost$50$1520%$6000$4500$3000$1500$300
Low Profit Items - Low Carry Cost$50$2025%$8000$6000$4000$2000$400
High Profit Items - High Carry Cost$50$5012.5%$20,000$15,000$10,000$5000$1000
High Profit Items - Low Carry Cost$50$7015%$28,000$21,000$14,000$7000$1400

On the other side is the cost of maintaining the inventory. This is given by the following formula.

Total Inventory Units * The Cost of the Inventory * Inventory Holding Cost

The table below calculates this cost for the different scenarios. To save space the columns that are labeled “COI at XYZ%” means — the “Costs of Inventory at XYZ Service Level.”

Costs of Service Level Scenarios - Inventory Costs

Scenario NameCostMarginICCCOI at 85%COI at 85%COI at 90%COI at 95%COI at 99%
Low Profit Items - High Carry Cost$50$1520%$1510$1870$2310$2960$4190
Low Profit Items - Low Carry Cost$50$2025%$1888$2338$2888$3700$5238
High Profit Items - High Carry Cost$50$5012.5%$944$1169$1444$1850$2619
High Profit Items - Low Carry Cost$50$7015%$1133$1403$1733$2220$3143

Now all that we have to do is subtract the two costs from each other for each combination. If the value is positive, this means that more money is lost due to lost sales versus the costs of maintaining inventory. If the values are negative, this means that the cost of maintaining inventory is higher than the costs of lost sales.

Costs of Service Level Scenarios - Net Costs

Scenario NameCostMarginICCCOI at 85%COI at 85%COI at 90%COI at 95%COI at 99%
Low Profit Items - High Carry Cost$50$1520%$4490$2630$690-$1460-$3890
Low Profit Items - Low Carry Cost$50$2025%$6113$3663$1113-$1700-$4838
High Profit Items - High Carry Cost$50$5012.5%$19,056$13,831$8556$3150-$1619
High Profit Items - Low Carry Cost$50$7015%$26,868$19,598$12,268$4780-$1734

Notice that the costs are positive — meaning service level increases continue to make sense until the service level begins to range from 95% to 99%.

At this service level, the inventory carries cost exceeds the cost of lost sales for the low margin item and then becomes negative for both at the 99% level.

Conclusion

There is a way to determine the trade-off between costs and of inventory holding cost and holding costs and higher service levels. Optimally a logical and mathematical analysis of this type would be how the company would develop its service level and inventory strategy.

This calculation can be performed in aggregate. That is either taking averages of all items, or aggregates of product groups. Or it can be applied to an individual product either for all locations or a single location. Both inventory holding cost and holding costs, as well as the quantification of the benefits of incremental service level improvements, are challenging to calculate.

Applications, like inventory optimizers, often assume that service levels are known by companies. In fact, their service levels targets are most often guestimates driven by sales of the service level they would like to have. Few companies have a mechanism for determining service levels based on trade-offs.

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References

Plossl, George. Orlicky’s Material Requirement’s Planning. Second Edition. McGraw-Hill. 1984. (first edition 1975)

Plossl, George. Wight, Oliver. Production and Inventory Control: Principles and Techniques. Prentice Hall. 1967.

I cover this topic in detail in the following book.

Safety Stock and Service Level Book

Safety Stock

Safety Stock and Service Levels: A New Approach

Important Features About Safety Stock

Safety stock is one of the most commonly discussed topics in supply chain management. Every MRP application and every advanced planning application on the market has either a field for safety stock or can calculate safety stock. However, companies continue to struggle with the right level to set it. Service levels are strongly related to safety stock. However, companies also struggle with how to set service levels.

How Systems Set Safety Stock

The vast majority of systems allow the setting of safety stock by multiple means (static, dynamic, adjustable with the forecast in days’ supply, etc..). However, most systems do not allow the safety stock to be set in a way that is considerate of the inventory that is available to be applied.By reading this book you will:

  • Understand the concepts and formula used for safety stock and service level setting.
  • Common ways of setting safety stock.
  • Service levels and inventory optimization applications.
  • The best real ways of setting both service levels and safety stock.

Chapters

Chapter 1: Introduction
Chapter 2: Safety Stock and Service Levels from a Conceptual Perspective
Chapter 3: The Common Ways of Setting Safety Stock
Chapter 4: The Common Issues with Safety Stock
Chapter 5: Common Issues with Service Level Setting
Chapter 6: Service Level Agreement
Chapter 7: Safety Stock and Service Levels in Inventory Optimization and Multi-Echelon Software
Chapter 8: A Simpler Approach to Comprehensively Setting Safety Stock and Service Levels

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