#6 - Reevaluating Safety Stock Amidst Supply Chain Challenges

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Introduction

Welcome back, supply chain innovators! ?? With the recent disruptions in the Red Sea linked to the ongoing Israel-Palestine conflict, the importance of robust safety stock strategies has never been clearer. With Castorama, we were compelled to reassess our safety stock levels to navigate these challenges effectively. Together with Thomas Coffin and Thibault Triscos , we delved into how our current Replenishment Solution calculates store safety stock. But what we discovered was disappointing—a black box with minimal documentation from our solution provider. This lack of transparency sparked an idea: what if I reworked everything from scratch to truly understand and optimize our safety stock strategy? ??

In this edition, I’m excited to take you through a comprehensive exploration of safety stock, stripping away the complexity and unveiling the essential principles. I promise to guide you step by step, ensuring I don’t lose 99% of my readers before chapter 2 ??! Whether you’re new to safety stock or looking to refine your approach, this deep dive will offer valuable insights to help you better manage uncertainty in today’s volatile supply chain landscape.

Chapter 1: What is Safety Stock?

Safety stock is the extra inventory a company holds to protect against the inherent variability in demand and supply ??. This stock buffer is crucial in preventing stockouts—situations where items are unavailable for sale—by compensating for unexpected fluctuations in demand or in supply. The fundamental goal of safety stock is to ensure that businesses can continue to meet customer demand even when disruptions occur, maintaining smooth operations and customer satisfaction.

In the retail industry, safety stock plays an especially vital role due to the unique challenges faced by this industry, like demand fluctuations ?? and supply uncertainties due to long lead times, complex routes, hundreds of thousands of articles, thousands of vendors, and stores ??.

Chapter 2: Key Factors Influencing Safety Stock Levels

Several key factors determine the appropriate level of safety stock in a retail supply chain. Understanding these factors helps ensure that your safety stock is neither excessive nor insufficient, striking the right balance between availability and cost ??.

1. Demand Variability: The more unpredictable the demand, the higher the safety stock needed ??. Variability can arise from seasonality, promotions, or shifts in customer preferences. Safety stock acts as a cushion against these fluctuations, ensuring stock availability when demand spikes unexpectedly.
2. Lead Time Variability: The time it takes to replenish stock isn’t always consistent ??. Longer and more variable lead times increase the risk of stockouts, especially if supply chains involve international shipping or multiple hand-offs. Higher safety stock compensates for this variability, bridging the gap between order placement and delivery.
3. Vendor OTIF (On-Time In-Full): A supplier’s reliability in delivering the right quantity on time directly impacts safety stock levels ??. Low OTIF performance from a vendor means a higher likelihood of stockouts, requiring additional safety stock to mitigate this risk.
4. Target Service Level: The service level is the probability of not running out of stock during the lead time ??. Higher service levels require more safety stock to reduce the risk of stockouts. For instance, a 95% service level means there’s a 5% risk of stockout, which necessitates holding more inventory as a buffer than a 90% service level.
5. Class of Items: Not all products require the same level of safety stock ??. Top sellers usually warrant higher safety stocks due to their importance, while slow-moving or low-value items require less. Tailoring safety stock to the class of items helps optimize inventory levels.

Chapter 3: Optimizing Safety Stock with AI and Operational Research

Traditional methods for calculating safety stock rely on simple statistical models and historical data ??. While effective to a degree, these methods often fall short in dynamically adapting to the complexities and uncertainties of modern supply chains.

Today, AI and operational research techniques offer advanced approaches to optimize safety stock, reducing excess inventory while ensuring high service levels.

1. ??Machine Learning for Enhanced Forecasting: Machine Learning (ML) plays a crucial role in optimizing safety stock, primarily through more accurate demand forecasting. By reducing uncertainty in demand predictions, ML indirectly helps lower the required safety stock. Additionally, ML can forecast key parameters influencing safety stock which were considered permanent before: supply lead time and vendor OTIF (On-Time In-Full). Traditional methods often use fixed lead times and overlook OTIF, leading to either excessive or insufficient safety stock. With ML, these factors can be predicted dynamically, enabling more responsive and precise inventory management.
2. ??Operational Research Techniques: Operational Research (OR) methods, such as linear programming and simulation models, go beyond statistical calculations by incorporating multiple constraints and objectives. These techniques are used to optimize safety stock levels, finding the ideal balance between minimizing inventory costs and maintaining desired service levels. For instance, linear programming can help determine the most cost-effective safety stock levels across different products, while simulation models can assess how various scenarios (e.g., changes in demand patterns, supplier reliability) impact safety stock needs. These advanced methods enable businesses to manage inventory more strategically, aligning stock levels with both operational goals and market conditions.
3. ?? Beyond Normal Distribution Assumptions: Most replenishment systems traditionally assume that demand follows a normal distribution, which is often only valid for stable, fast-moving products. However, demand for many items can be irregular, seasonal, or exhibit trends that deviate from normality. AI and Machine Learning can help assess the true demand distribution more accurately, detecting non-normal patterns such as skewness or multimodality. By modeling these distributions accurately, AI can refine safety stock calculations, ensuring that inventory levels are neither excessive nor insufficient. ML can also adapt to changes in demand patterns over time, continually optimizing safety stock to match the real-world dynamics of demand.

Chapter 4: Safety Stock Mathematical Framework

In this chapter, we dive into the mathematical foundation of safety stock calculation, building on the concepts weve discussed. Our goal is to ensure that safety stock is optimized to balance service levels with inventory costs.

4.1 - Safety Stock calculation based on Service Level Target

Lets define the following variables :

Service Level (????): The desired probability of not running out of stock during the lead time.

Z-Score (Z): The Z-score corresponds to the desired service level (????) and is determined by the demand distribution. For a normal distribution, the Z-score maps the service level to a specific point on the standard normal distribution curve.

Average Lead Time Demand (μL): The mean expected demand during the lead time. Best is using ML sales forecasting and ML lead time forecasting to get it.

Standard Deviation of Lead Time Demand (σL): The variability in demand during the lead time.

On-Time Adjustment Factor (OTAF): Accounts for lead time variability due to the supplier’s On-Time performance. It is calculated as: OTAF=(1?OTnbsp;Percentage)/OT Percentage

Standard Deviation of In-Full Deliveries (??????): Represents the variability due to partial vendor deliveries in quantities. To calculate it, you would typically analyze historical data on orders placed versus quantities received. And use ML OTIF predictions.

Z'-Score (Z'): The Z'-score corresponds to the desired service level (????) and is determined by the In Full distribution.

Safety Stock Formula

The optimized safety stock (SS) model I suggest is calculated as follows:

SS=Z × σL ×(1+OTAF) + Z' x σIF

This formula accounts for demand variability, lead time variability, and the reliability of suppliers in terms of both timing and quantity. SS will cover the risk of running out of stock with the targeted service level. If I make my self-criticism, OTAF impact could be assessed through a distribution calculation, but anyway this model looks optimized enough.

4.2 - Safety Stock calculation based on Operational Research solving the min total cost equation!

To balance inventory holding costs and stockout costs, the safety stock total cost TC(SS) is modeled as:

TC(SS)=H×SS+P×G(SS)

Where:

H is the holding cost per unit typically including logistics cost, capital cost and stock depreciation.

P is the penalty cost per unit of stockout typically including the lost margins

G(SS) is the expected shortage based on the safety stock level and on the lead time demand

Understanding Expected Shortage

The expected shortage G(SS) represents the number of demand units that cannot be fulfilled (sales lost) when demand during the replenishment lead time exceeds the sum of the average demand during lead time μL and the safety stock SS. In other words, G(SS) is the average quantity of lost sales when demand x surpasses the threshold μL+SS

Probability of Demand Exceeding the threshold μL+SS

To express the probability that demand exceeds the safety level, we denote P(x>μL+SS). This implies that sales may potentially be lost if demand exceeds this threshold, as available stock would be insufficient.

Using the Standard Normalized Variable

To determine this probability and the expected shortage amount, we introduce the standardized normal variable z=(x?μL)/σL, where σL is the standard deviation of demand during the lead time. This normalized variable translates the safety stock level into a probability measure!

The Loss Function L(z)

The loss function L(z) is used to estimate the expected shortage based on demand distribution. It expresses this shortage as a fraction of the standard deviation σL and is defined as follows:

L(z)=z->∞∫(x?z)??(x)?dx

where ?(x) is the probability density function of the demand distribution. This calculation essentially determines the average gap between actual demand and the threshold μL+SS when demand exceeds this threshold.

For a normal distribution, L(z) can also be expressed as:

L(z)=?(z)?z×(1?Φ(z))

where Φ(z) is the cumulative distribution function of the normal distribution.

Final Formula for Expected Shortage

Using the loss function and we can calculate the expected shortage G(SS) as:

G(SS)=σL×L(z)

This formula allows us to estimate the number of units in stockout by multiplying the probability of exceeding the threshold by the demand’s standard deviation

Resolution of the Optimal Safety Stock (OSS) when the demand is considered a normal distribution!

The Optimal Safety Stock can be resolve using a computer, but in the case of a normal demand, it's analytical doable!

Analytically, solving the min total cost is finding the case where the derived dTC(SS)/d(SS) = 0 So using the integral form of L(z) and Leibniz's rule for derivation, dL(z) / dSS = ??(z)/σL.

Therefore dTC(SS)/d(SS) = H?P×?(z)

Setting this equal to zero to find the minimum: H=P×?(z*)

To recap, we introduced the standardized variable z=(x?μL) / σL and now we know z?, the value that achieves the optimal balance of costs. We also introduced the x = μL+SS as the threshold above which sales may be lost. Thus, the optimal safety stock OSS can be expressed as:

OSS = x??μL

OSS = z?×σL where ?(z?)=H/P with ?(z) as the probability density function of the standard normal distribution.

Limitations of the Normal Distribution Model

The ratio H/P can theoretically exceed the maximum value of 1/racine(2π) ≈0.3989, the peak of the normal distribution’s density function ?(z). In this case, the safety stock equation has no solution, meaning no level of safety stock would satisfy both the holding cost H and the stockout cost P simultaneously.

This scenario can indicate:

1. Excessive Service Level: A high H/P ratio may suggest that too much emphasis is placed on reducing inventory costs relative to stockout costs, making it impossible to balance the two.
2. Re-evaluation of Costs: It may be necessary to reassess H and P to ensure a realistic ratio.
3. Model Assumption Adjustments: In some cases, it may be necessary to adjust the safety stock model, especially if the assumption of normally distributed demand is not appropriate.

Conclusion: Wrapping Up the Safety Stock Journey

Congratulations! ?? You did it—you’ve navigated through the intricacies of safety stock, from foundational concepts to complex mathematical modelization. If you’re reading this, it means you’ve survived the complexity of this publication and made it to the finish line ??.

To celebrate, why not drop a “I did it!” in the comments below? And while you’re at it, I’d love to hear about your own safety stock strategies. Whether you rely on traditional methods, cutting-edge AI, or a mix of both, I’m always eager to learn from the experiences of fellow supply chain enthusiasts. So, share your thoughts, strategies, or just a thumbs-up—let’s keep the conversation going!

Looking forward to your insights, and until the next edition, keep innovating!