White Paper: Impact of Inventory on Network Design

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1 White Paper: Impact of Inventory on Network Design Written as Research Project at Georgia Tech with support from people at IBM, Northwestern, and Opex Analytics Released: January 2014 Georgia Tech Team Members Chandreshekar Sundaresan MS SCE Graduate Student Seth Webster MS SCE Graduate Student Sponsor Writers Michael Watson, Ph.D Adjunct Professor, Northwestern Partner, Opex Analytics (312) Sara Lewis Opex Analytics Faculty Advisor Dr. Alan Erera Associate Professor (404)

2 Introduction Supply chain network design is about determining the right number, location, and size of facilities in your network. It is a critical factor in determining the overall effectiveness and efficiency of any firm s supply chain. Its significance continues to grow in today s market as customers and competition evolve. However, supply chain network design and modeling is a complex process involving many variables including transportation, warehousing, and numerous other more specific supply chain costs. When inventory is added to the mix, decisions become even more complicated and therefore more difficult to quantify and understand as well. Most supply chain managers are accurately aware that transportation typically drives the majority of costs in a supply chain. And, it is well known that there is a direct relationship between the location of facilities and the transportation costs. In theory, the closer you are to your customers, the lower your costs will be. Figure 1 shows that for most distribution networks, transportation costs are the biggest contributor to a firm s total supply chain costs at over 50%. Thus, many Supply Chain Managers focus their network design efforts on generating reductions in transportation costs. Although less than transportation, it is also important to note that inventory costs are also significant cost drivers in a supply chain at about 22%. Ignoring costs that account for almost a quarter of the total could prove to be an expensive mistake. Many supply chain managers are unsure about how the number and location of facilities will impact inventory. It is also unclear how to incorporate inventory considerations into their analysis. The purpose of this paper is to provide a deeper understanding of how supply chain network design decisions drive inventory variables and vice versa. We will identify when inventory matters to network design and when it does not. We think that you might be surprised by the complex relationships. You may conclude that you need to worry less than you thought about the impact of changing warehouses on inventory. Figure 1: Supply Chain Cost Drivers 2

3 Square Root of N Law Past attempts to provide an easy to understand explanation of the relationship between the number of warehouses and inventory have resulted in various basic guidelines or rules of thumb for evaluating network design decisions. The most popular is the Square root of N law which attempts to explain the relationship between number of warehouses and system wide safety stock. This rule states that: The system-wide total safety stock is directly related to the square root of the number of warehouses. The benefit of this rule is that it is very simple and gives us some nice insight. It also provides a sound reason why we assume safety stock changes as the number of warehouses changes. The problem is that it is based on simplistic assumptions. The Square Root of N law assumes there is no variability in replenishment lead time, territories assigned to different warehouses have more or less equal demand, and that customer demand is independent of each other. However, the further away a system gets from these assumptions, the less effective the law. Real supply chain networks generally do not operate under many of these assumptions. In addition, this rule only focuses on safety stock. It is imperative to understand cycle stock implications as well. The general difficulty in understanding this topic may be due to the fact that the inherent link between network design choices and inventory levels is not necessarily intuitive. This further increases the complexity of any supply chain network design project as well. Most supply chains currently face high service level requirements, lead time with variability, and varying replenishment frequencies, making it difficult to effectively use simple rules to make accurate predictions about inventory. This paper will present a more in-depth look at the factors that drive inventory in a network design study. It will help supply chain managers think through the implications of adding or not adding inventory considerations to their modeling. And, it will provide supply chain managers with ideas on how to add inventory to their analysis. Problem We will highlight some of the most significant inventory variables with a case study taken from the text Supply Chain Network Design. In this case, Al s Athletics is a major sporting equipment and apparel retailer in the United States. For simplicity, we will assume that Al s product profile consists of 100 SKUs. 3

4 Review of Al s Athletics 1 In the late 1960s, Al Alford, a young football coach in a small Texas town many miles away from a major city, decided that the kids in his town shouldn t be held back because they didn t have access to the right sporting equipment to practice with. Opening a store close to them to supply the right equipment could be the first step for these kids to grow up to be the next Nolan Ryan, Mean Joe Green, or Olympic gymnast Kim Zmeskal. Before Al knew it, his business was booming. Al and his family quickly realized that they could repeat their success within similar cities across the south, and 50 years later Al s Athletics has grown to be one of the largest retail sporting-goods chains in the U.S. Al s Athletics now has major retail-store outlets in 41 U.S. states. Figure 2 Al's Athletics Store Locations and Potential DC Locations Al s grandson (Al the third) is now the CEO and lives and works near the original store in Brownfield, Texas. He realizes that competition in the sporting-goods industry is high, and he has always believed in the philosophy of his grandfather that proximity to the customer means everything in this business. As a result, Al wants to look at adding and optimizing warehouse locations across the country to lower costs and provide the best service of any sporting goods chain in the US. At the moment, Al s Athletics has 200 Stores located across the nation. This case originally discusses a number of distribution strategies that involve redesigning their supply chain network with up to 10 warehouses from a choice of 26 potential locations. We will now extend the case by adding multiple SKUs to the analysis. This will allow us to further explore the inventory implications. To keep it simple, we will use a sample of 100 SKUs that fall into 4 different categories, namely: high value light weight, high value heavy weight, low value light weight, and low value heavy weight. 1 Case Study Referenced from Supply Chain Network Design ( 4

5 CASE STUDY SCENARIOS Now that we know the background for our case, let s take a look at the following scenarios which will provide us further insight into the complex link between network design and inventory levels. Each scenario will highlight a different variable or assumption that impacts inventory levels, and examine its effects based on both high and low demand variability. Scenario 1 Square Root of N Law Tested For the first scenario, let s set up the problem with simplistic assumptions in an attempt to replicate the Square Root of N law. We will use a Table 1: Baseline Assumptions straight forward model of Al s Athletics network that has no variability in lead time, a fixed review period, and equal order amounts no matter the number of warehouses. This initial model has small demand variability, but we will examine a higher variability example later in the analysis. The parameters and assumptions are shown in Table 1. The results of Al s safety stock within this MIP model, shown in Figure 3 on the left, validate the Square Root of N law, with system wide safety stock almost exactly as the law estimated, and directly proportional to the square root of the number of warehouses. Figure 3: Simplistic Model: Safety Stock 5

6 But what about Cycle Stock? Any company s inventory cost is comprised of two components however, safety stock and cycle stock. While the square root of N law accurately estimates the safety stock levels under the said assumptions for Al s Network, it does not provide insight into cycle stock, and thus total inventory costs. Cycle stock is driven by demand and replenishment frequency. For the purpose of this case study, let s assume that Al s network is replenished on a weekly basis. Later on we will explore what happens to cycle stock when their replenishment frequency changes. Figure 4: Low Demand Variability - Inventory Cost Breakdown When Al s supply chain managers saw the results from the square root of N law, they were naturally concerned about the increase in the number of warehouses in their network causing them to hold excess safety stock. However, in many companies, cycle stock can be orders of magnitude higher than safety stock, thereby making increases to safety stock, and their anxieties, insignificant. Figure 4 shows both safety stock costs and cycle stock costs for the purposes of comparison. Here we can see that the total inventory cost is more or less constant, following the path of cycle stock. In other words, while we see a 123% increase in safety stock as we go from 2 to 10 warehouses in the network, the increase in total inventory is only 6%. Al s team finds it apparent from this first analysis that their inventory costs remain relatively flat regardless of network design decisions. They might, however, want to look at other analysis besides the Square Root of N law to conclude the effects of inventory in general. 6

7 Is the Square Root of N rule to be avoided? Maybe not. As mentioned previously, Al s Athletics initial model considered a demand profile with low variability. With low standard deviation of demand, the initial safety stock required is very low, and thus the square root of N law is not very effective in determining how overall inventory levels will be affected by changing the network. However, if Al s experiences high standard deviation of demand (or, in other words, a lot of demand variability), their initial safety stock cost can be much higher relative to the cycle stock costs. Figure 5: High Demand Variability - Inventory Cost Breakdown In this high demand variation situation, Al s safety stock cost most definitely increases as they add warehouses to the network, and the Square Root of N law is actually pretty effective at estimating how total costs will change. Total inventory costs now track with changes in safety stock costs in this situation. Figure 5 shows how safety stock costs can again be accurately predicted by the square root of n law in the graph on the left, and the one on the right shows how total inventory costs are now driven by safety stock costs. Let s not forget that this analysis relied on a number of additional assumptions that often do not accurately represent real-world situations however. In the following scenarios of Al s Athletics Network, we will see how inventory is affected when these assumptions are removed, and the implications these affects will have on total costs and network design decisions considering both high and low variability in demand. 7

8 Scenario 2 When does inventory really matter? As mentioned previously, it is often seen that inventory costs are significantly lower compared to transportation costs. In this version of Al s network, even as the number of warehouses rises, the penalty associated with increased inventory costs is irrelevant. Since transportation costs are always higher in Al s network, the transportation savings realized with more warehouses trumps the additional inventory costs that are accrued, seen in the graph on the left in Figure 6. This makes transportation, and therefore site location, the primary driver of Al s distribution strategy. On the other hand, if inventory holding costs are high, inventory may actually play an important role in determining the optimal number of warehouses to have in the system. With that said, let s take a look at the two scenarios to demonstrate this tradeoff: 1. A typical scenario where Al s Athletics inventory costs are less than transportation costs 2. A scenario where Al s Athletics inventory is expensive to hold and drives the decision. 8 Figure 6: Inventory vs. Transportation Costs We find that typically, a company s inventory costs never approach the transportation costs, regardless of the number of warehouses. In fact, in the scenario portrayed by the graph on the left in Figure 6, we validate the ratio between inventory costs and transportation costs shown previously in Figure 1. Thus, in terms of network design, despite a slight increase in inventory costs by increasing the number of warehouses, the lower transportation costs drive the decision for the network strategy. The graph on the right exhibits a version of Al s Athletics with higher inventory costs (about 5 times the industry standard). In this case, we highlight that there are scenarios where inventory costs outweigh the transportation costs, and thus the total cost line shows a more complicated decision process, with the 5 warehouse scenario being optimal. While the graph on the right shows that expensive inventory costs can have an impact on the network design decisions, the graph on the left demonstrates that typically companies only need consider transportation costs, confirming why most supply chain managers may leave

9 inventory out of their decision process altogether. Let s be sure to understand what drives the impact of safety stock however. Demand variability greatly affects safety stock and therefore total inventory. In most networks with relatively low demand variability, safety stock levels and thus total inventory costs are low. As a result, a larger gap between warehouse holding costs and transportation costs occurs. In this way, transportation will always be the overbearing costs and any savings afforded on the warehouse holding cost front won t be enough to tip the scale in terms of network design decisions. The exception to this occurs with companies carrying high value product (pharmaceuticals, electronics, etc.) or large bulky product which may be expensive to store. For these companies, inventory holding costs are typically high even though demand variability may be low. In this instance the overall cost trends would be along the lines of the graph on the right in Figure 6. Our next scenario takes a closer look at the underlying drivers of inventory in a system. Scenario 3 Lead Time Variability Risk pooling is a term that suggests downstream demand variability is reduced if one aggregates demand across locations to the warehouse. The reasoning here says that if demand is aggregated across different locations, it becomes more likely that high demand from one customer will be offset by low demand from another. This reduction in overall variability allows a decrease in safety stock and therefore reduces average inventory. Knowing this, analysts infer that having fewer warehouses aggregates more demand locations to each warehouse, resulting in the pooling of the risk from variability. When evaluating network design decisions and optimizing for transportation, many companies focus on the downstream demand variability and are encouraged by the benefits from risk pooling. However, if we introduce variability in lead times associated with procurement of product from the vendor (which we feel is a realistic expectation), the benefits of risk pooling are dampened while the total system wide safety stock increases. In Figure 7, the percent increase in safety stock is Figure 7: Safety Stock Costs Under Lead Time Variability 124% (starting at a significantly lower 9

10 cost of course) with no lead time variability, while with constant lead time variability safety stock costs only increase by 2%. The important thing to note is not the large differences in increases but whether significant increases actually take place. When LT Variability in a network is high, you might not need to worry that extra warehouses will drive up inventory you may want to work on reducing LT variability instead. In essence, in cases where lead time variability is high and demand variability is low variability, the benefits of risk pooling exemplified by the Square Root of N Law no longer apply. We often see this in practice, lead time variability has a dramatic impact on inventory while the change in the number of warehouses does not. Figure 8 shows how much more safety stock you need when you have lead time variability (this comparison is from the case of 5 warehouses in Al s model). Figure 8: Inventory Cost Breakdown (Under Lead Time Variability) Increasing Lead Time Variability Before Al s analyst runs to tell the manager that the number of warehouses in their supply chain would not affect safety stock due to lead time variability, it is important to note what happens when lead time variability increases as the number of warehouses increases. This has a profound impact on total costs and the network design decision process as well. Figure 9 shows that Al s may once again realize the benefits of risk pooling if lead time variability increases as the number of warehouses increases. 10

11 Figure 9: Effect of Increasing Lead Time Variability on Safety Stock Lead Time and demand variability Again, it is important to pay attention to all the assumptions involved in the model. We just saw that adding lead time variability will greatly increase safety stock costs and eliminate the benefits of risk pooling, but if the variability is increasing with the number of warehouses, risk pooling is a factor. This effect is compounded due to our low standard deviation of demand assumption as well. Because there was little variability to begin with, and thus a very low initial amount of safety stock, any change in LT variability will lead to a huge increase in safety stock costs. However, as we have done in previous scenarios, let s examine lead time variability when safety stock costs are already large due to a high standard deviation of demand. Figure 10: Effect of Lead Time Variability on Different Types of Demand 11

12 Figure 10 shows that if safety stock is already in place to protect against a high variability of demand (graph on the left), adding lead time variability to the situation will have a much smaller effect on safety stock, and thus total inventory costs. Closing Notes on Lead Time Variability There is nothing mathematical that suggests that lead time variability will increase or decrease as you change the number of warehouses this is in contrast with the theory of risk pooling that states that demand variability will change with the number of warehouse. You will have to investigate this on each project to see how the change in the number of warehouses will impact your lead time variability. Scenario 4 The Effect of Replenishment Frequency For this version of Al s Network, consider similar parameter setting as in the previous scenarios. Now we will investigate the vendor s ability to keep up with Al s order requirements as the number of warehouses in the network increases, and the resulting effect on cycle stock. We will focus specifically on how frequently each warehouse can be replenished. Replenishment frequency drives how much product Al s must request in each order, and thus is a primary factor in system wide cycle stock. In addition, as shown in the first scenario, cycle stock generally represents a larger portion of inventory costs in industries with low demand variability, so this is an area where companies must pay special attention. As the number of warehouses in Al s network increases, it is likely that it is going to take their vendors more time to fill a full truck with product for each facility, resulting in less frequent replenishments. This is not a natural mathematical function, so the supply chain manager at Al s Athletics will need to use judgment in determining how replenishment frequency will change in the new network. In this scenario we assume that for every additional warehouse added to the network, the replenishment frequency decreases by 15%. In effect, if the vendor replenishes two warehouses every seven days, with three warehouses it will be just over 8 days between replenishments. As the replenishment frequency decreases, the system wide cycle stock begins to increase. 12

13 Because this might not be intuitive to many managers, the resulting underestimation of cycle stock could lead them to make a costly decision. Figure 11 shows the effects on system wide cycle stock costs using the first of Al s scenarios described above (with high demand variability). Previously (with low demand variability), transportation was the primary driver of cost and therefore the network design decision, this increase in cycle stock due to decreasing replenishment frequency gives Figure 11: Cycle Stock Costs Under Decreasing Replenishment Frequencies the inventory costs greater weight in the decision process as seen in Figure 12 below. At some point, the inventory holding costs become too high and Al s Athletics must consider balancing this by taking a penalty on the transportation costs utilizing LTL, Multi-Stop Truck Load or other more expensive but more efficient mode of transport. Figure 12: Effect of Decreasing Replenishment Frequencies on Total Costs. Decreasing Replenishment Frequency and demand variability. While changing replenishment frequency won t have a noticeable impact on safety stock when demand variability is low, it is still important to examine how the change in cycle stock will impact total inventory costs when Al s faces a high standard deviation of demand. As we have seen before, cycle stock is not as important in this case. Therefore, the optimal number of warehouses is not impacted as much by decreasing replenishment frequency. 13

14 SUMMARY *In comparing, notice that graph s within the summary may not always follow the same y-axis scale. Baseline Scenarios We started with the most assumptions in order to validate the Square Root of N Model. With Low Demand Variability we see transportation typically dominates in terms of driving the network decisions based on the relatively low inventory costs (although Expensive Inventory increases our holding cost significantly, it s still irrelevant in relation to transportation costs). In this situation, it is easy for managers to ignore inventory considerations when making changes to their Supply Chain network. Low Demand Variability, Inexpensive Inventory Low Demand Variability, Expensive Inventory With High Demand Variability however, Inventory costs take on a much greater role in the network design decision making process. In the case of inexpensive inventory the network design decision remains tight but ten warehouses still remains optimal. Whereas with expensive inventory the holding costs outweigh transportation costs with nine warehouses. Supply chain managers should be aware of this trade-off and explore inventory further within their mode High Demand Variability, Inexpensive Inventory High Demand Variability, Expensive Inventory 14

15 Constant LT Variability Scenarios In situations with low demand variability, considering constant replenishment frequency and lead time variability, the impact on safety stock and thus inventory costs is significant. However, transportation still drives the optimal number of warehouses in the network. In this situation, managers may still be content to ignore inventory considerations when making changes to their Supply Chain network. Low Demand Variability, Inexpensive Inventory Low Demand Variability, Expensive Inventory With High Demand Variability, Inventory costs continue to take on a much greater role, as seen in the baseline. However, safety stock has already been high in order to cover for high demand variability and therefore the addition of a constant LT variability does not have much additional effect on stocking levels. When LT Variability in a network is constant and high, concern for an increase of safety stock as a result of additional warehouses should reduce dramatically. High Demand Variability, Inexpensive Inventory High Demand Variability, Expensive Inventory 15

16 Increasing LT Variability Scenarios When considering a lead time variability that increases with each additional warehouse in the network, we start to see the impact inventory can have on the network design decision process. With Low Demand Variability and Inexpensive Inventory transportation still overwhelms. But with Expensive Inventory we see the trough of the total cost curve now sits at 8 warehouses. Supply Chain managers must now be aware of the inventory costs when selecting their final design decisions. Low Demand Variability, Inexpensive Inventory Low Demand Variability, Expensive Inventory With High Demand Variability however, Inventory costs take on a much greater role in the network design decision making process. In the case of inexpensive inventory the network design decision remains the same. Whereas with expensive inventory the holding costs begin to outweigh transportation costs with just six warehouses. In these situations, Supply chain managers should be sure to accurately measure the Lead Time and the associated variability in order to incorporate into their network design decision process. High Demand Variability, Inexpensive Inventory High Demand Variability, Expensive Inventory 16

17 Decreasing Replenishment Frequency Scenarios Here we assume that with more warehouses your vendor will take longer to fill up a truck for each warehouse, and replenishment frequency will decrease. With Low Demand Variability we again see the transportation dominating in terms of driving the network design. Low Demand Variability, Inexpensive Inventory Low Demand Variability, Expensive Inventory With High Demand Variability however, as replenishment frequency is a key driver of cycle stock, and cycle stock a key driver of inventory costs, the number of warehouses in both of the below scenarios shifts left. As the decrease in frequency is not a natural mathematical function, supply chain managers need to use judgment in determining how replenishment frequency will change in the new network in order to appropriately include the factor in their network design model High Demand Variability, Inexpensive Inventory High Demand Variability, Expensive Inventory 17

18 Closing Comments The interaction between network design and inventory is quite complex and a number of different variables play a key role towards making an informed decision. The white paper details some of the tipping points to look out for while considering network re-design projects and hopefully gives the reader enough insight to know when to consider a detailed inventory analysis as a supplement to the re-design effort. 18 Page

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