How to Combine Supply Chain Optimization and Simulation

 

In our previous blog on Supply Chain Optimization Versus Simulation, we talked about the difference between optimization and simulation and their applications in modern supply chain design and analysis. The decision to use optimization or simulation has to be guided by the pressing needs and questions of your business. Optimization is better suited for situations when the goal is to determine “what’s best” while simulation should be reserved for when the goal is to understand “what is” so that “what if” questions can be addressed.

This distinction, however, does not preclude the combined use of optimization and simulation in addressing supply chain business questions. In fact, in many of our inventory optimization engagements, simulation has proven time and again to be an essential technique for testing the robustness of solutions from optimization models. This is especially useful because, while you can plan optimally, you will most definitely execute sub-optimally in practice. 

 

Use Simulation to Test the Robustness of Solutions from Optimization

A typical benefit from an inventory optimization project should be to reduce inventory by 10-30%. In many cases, the optimization model is built and ran using an off-the-shelf multi-echelon optimization software tool. These tools are designed to provide a target safety stock level and a committed service time for each product at each location in the supply chain such that the overall supply chain inventory holding cost is minimized while meeting pre-set service levels.

One of the first questions clients ask is “why should I trust the recommended safety stock from this software?” Most reasonably skeptical clients will not accept reasons such as “this software vendor is a reputable company, or "this software has been used by more than 1,000 customers, so you should trust the recommendation.” Clients often require an objective validation of the safety stock target provided by the optimization tool as a way to engender confidence in the recommendation before they are comfortable implementing it.

Here is where simulation comes to the rescue and optimization passes the baton; it’s a tag-team effort after all. In the case of the inventory optimization example, it is often a straight forward exercise to build a simulation model to check that the optimization model’s suggested safety stock level can achieve the desired fill rate. 

 

A Simple Simulation for Validating Inventory Optimization Solution

As an example, we present a simulation model that can be used to validate the recommended safety stock levels from an inventory optimization model. The simulation model takes the following as input: demand profile, order fulfillment process, inventory replenishment process, and essential data collection process. Data gathering and preparation should be easy as there is an almost perfect overlap between the data required for simulation and optimization.

Because of the stochastic nature of an inventory simulation model, a sufficient warm-up period should be allowed during run-time to allow the model to reach steady state. The simulation output should provide data that can be used to calculate metrics such as number of stock outs per year, average inventory level, and fill rate. The derived fill rate from simulation, which is based on the recommended safety stock levels, will confirm whether the solution is robust or not. Similarly the average inventory level from simulation can be used to confirm that the size of the inventory opportunity suggested by the optimization model is realizable.

 

Conclusion

Optimization and simulation are not mutually exclusive. While optimization provides the best solutions, simulation can be used to confirm optimization output and build confidence in recommendations before implementation. In fact, in many of our engagements, simulation is the tool of choice to insert confidence in recommendations from the optimization model.

What Drives Inventory in Your Supply Chain?

One of the largest, if not the largest, investment of many businesses is inventory. This includes raw material, components, finished goods and spare parts. Inventory protects the business from fluctuations related to the order cycle, called cycle stock and changes in expected demand and lead times called safety stock. Maintaining the right inventory levels and understanding the tradeoffs requires knowledge of what drives inventory. In the following, we will go into the details of how cycle stock and safety stock are calculated and therefore what drives the levels of inventory required.

Cycle Stock
The portion of an inventory which companies cycle through to satisfy market demand for a specific replenishment period is called cycle stock. Cycle stock level depends on a product’s order frequency and demand profile. The equation for calculating average cycle stock is as follows:

Where

• RP = Replenishment Period
• D = Average Demand
• RP(D) = Average Demand during Reorder Period

 

It is not difficult to see that cycle stock is driven by demand and replenishment period. Cycle stock will rise when the demand and reorder period increase.

For example, if a product has an average demand of 10 units per business day and is replenished every 5 business days, then the average cycle stock level is 25 units, half of the average demand during the reorder period.

If product is replenished every business day, then the average cycle stock level is reduced to 5 units. The key to cycle stock reduction is to reduce the replenishment period.

Safety Stock
Safety stock, as the name suggests, is the buffer inventory kept to prevent stock outs arising due to misalignment of actual and forecasted demand, utilization and delivery time shortfalls. In order to understand the proper levels of safety stock, it is important to understand the drivers. The general equation for safety stock, assuming both lead time and demand are normally distributed, is as follows:

Where

• D = Average Demand
• StdD = Standard Deviation of the Demand
• LT=Average Lead time
• StdLT = Standard Deviation of the Lead Time

 

1. Demand Variability - occurs when actual demand deviates from forecast demand. Naturally, the way to combat fluctuations is to hold more inventory. The first factor affecting that amount of inventory is demand variability. The amount of inventory needed due to demand variability is the product of square root of the average lead-time and the standard deviation of demand. This portion of the equation covers the demand fluctuations between the order date and receipt date considering the lead time and the demand that might occur.
2. Lead time Variability - drives the safety stock similar to the demand variability where in the amount of inventory needed to mitigate the effect of variation of time between order date and ship date is calculated by the product of Average demand during that period and lead time standard variation.
3. Service Level - defined as the probability of not having stock-outs. It is used in the safety stock equation in terms of its Z score. In statistical terms, the Z score refers to the number of standard deviations above mean that a parameter can fluctuate. Here, with respect to safety stock, Z(service level) is the number of standard deviations above mean demand needed to protect you from having stock-outs.

Safety stock is not needed when the fluctuations are happening below the mean demand. That is because the fluctuations will be taken care of by cycle stock when the demand moves between zero and mean demand. After the mean demand, safety stock is needed to combat fluctuations

To understand this, we need to look at how service level based on the Z-Score drives inventory. Service levels and Z-scores have a non-linear relationship. Hence, higher service levels incur highly disproportionate safety stock. Imagine that no safety stock is carried.

 

In this situation, the Z score is zero. Even then based on the Safety Stock equation, there will be enough inventory to meet demand in 50 percent of the time. If the Z-score equals 1, the safety stock will protect against one standard deviation; there will be enough inventory 84 percent of the time. But if you want to have a service level of 98%,Then you have to hold two times the safety stock as in the case of 84% Service Level.

It is always a managerial decision to balance between prevention of stock outs and customer service. Based on the organization’s culture, optimum safety stock is calculated using the above mentioned equation by choosing a proper service level so as to balance inventory costs and customer service. However, it is also possible using advanced optimization techniques to move the tradeoff curve and improve both inventory levels and service levels.

As you can see, calculating inventory for one product on one level is already quite complex. But to fully realize inventory savings you also need to analyze the interplay between the location where the inventory is maintained as you may be losing on risk pooling and other potential savings by looking at inventory in one location.

In fact, I recently worked with Schneider Electric on calculating the difference, With traditional single location methods they could save 11% but with multi-echelon inventory optimization they could save 30%. These savings are achieved while still maintaining the same service levels.