In practice, supply chains have varying degrees of inventory aggregation. For example, Barnes & Noble sells books from retail stores with inventory geographically distributed across the country. Amazon, in contrast, ships all its books from a few facilities. Seven-Eleven Japan has many small convenience stores densely distributed across Japan. In contrast, supermarkets tend to be much larger, with fewer outlets that are not as densely distributed. Redbox rents its movies from tens of thousands of kiosks distributed across the United States. In contrast, Netflix centralizes its DVD inventory at fewer than fifty distribution centers.
Our goal is to understand how aggregation in each of these cases affects forecast accuracy and safety inventories. Consider k regions, with demand in each region normally distributed with the following characteristics:
Di: Mean periodic demand in region i, i = 1, . . . , k
σi: Standard deviation of periodic demand in region i, i = 1, . . . , k
Pij: Correlation of periodic demand for regions i, j, 1 ≤ i ≠ j < k
There are two ways to serve demand in the k regions. One is to have local inventories in each region and the other is to aggregate all inventories into one centralized facility. Our goal is to compare safety inventories in the two cases. With a replenishment lead time of L and a desired cycle service level CSL, the total safety inventory in the decentralized case is (using Equation 12.5):
If all inventories are aggregated in a central location, we need to evaluate the distribution of aggregated demand. The aggregate demand is normally distributed, with a mean of DC, standard deviation of sD, and a variance of var(DC), as follows:
Observe that Equation 12.13 is like Equation 12.1 except that we are aggregating across k regions rather than L periods. If all k regions have demand that is identically distributed, with mean D and standard deviation sD, and have the same correlation p, Equation 12.13 can be simplified as
If all k regions have demand that is independent (pij = 0) and identically distributed, with mean D and standard deviation sD, Equation 12.13 can be simplified as
Using Equations 12.5 and 12.13, the required safety inventory at the centralized location is given as
The holding cost savings on aggregation per unit sold are obtained by dividing the savings in holding cost by the total demand kD. If H is the holding cost per unit, using Equations 12.12 and 12.16, the savings per units are
Holding – cost savings on aggregation per unit sold
From Equation 12.13, it follows that the difference 
is influenced by the correlation coefficients pij. This difference is large when the correlation coefficients are close to -1 (negative correlation) and shrinks as they approach +1 (positive correlation). Inventory savings on aggregation are always positive as long as the correlation coefficients are less than 1. From Equation 12.17, we thus draw the following conclusions regarding the value of aggregation:
- The safety inventory savings on aggregation increase with the desired cycle service level
- The safety inventory savings on aggregation increase with the replenishment lead time L.
- The safety inventory savings on aggregation increase with the holding cost H.
- The safety inventory savings on aggregation increase with the coefficient of variation (sD / D) of demand.
- The safety inventory savings on aggregation decrease as the correlation coefficients increase.
In Example 12-8 (see worksheet Example 12-8), we illustrate the inventory savings on aggregation and the impact of the correlation coefficient on these savings.
EXAMPLE 12-8 Impact of Correlation on Value of Aggregation
A BMW dealership has k = 4 retail outlets serving the entire Chicago area (disaggregate option). Weekly demand at each outlet is normally distributed, with a mean of D = 25 cars and a standard deviation of sD = 5. The lead time for replenishment from the manufacturer is L = 2 weeks. Each outlet covers a separate geographic area, and the correlation of demand across any pair of areas is p. The dealership is considering the possibility of replacing the four outlets with a single large outlet (aggregate option). Assume that the demand in the central outlet is the sum of the demand across all four areas. The dealership is targeting a CSL of 0.90. Compare the level of safety inventory needed in the two options as the correlation coefficient p varies between 0 and 1.
Analysis:
We provide a detailed analysis for the case when demand in each area is independent (i.e., p = 0). For each retail outlet we have
Standard deviation of weekly demand, sD = 5
Replenishment lead time, L = 2 weeks
Using Equation 12.12, the required safety inventory in the decentralized option for CSL = 0.90 is
Now, consider the aggregate option. Using Equation 12.14, the standard deviation of aggregate weekly demand is
For a CSL of 0.90 and p = 0, safety inventory required for the aggregate option (using Equation 12.16) is given as
Using Equations 12.12 to 12.16, the required level of safety inventory for the disaggregate as well as the aggregate option can be obtained for different values of p as shown in Table 12-3 using worksheet Example 12-8. Observe that the safety inventory for the disaggregate option is higher than for the aggregate option except when all demands are perfectly positively correlated. The benefit of aggregation decreases as demand in different areas is more positively correlated.
Example 12-8 and the previous discussion demonstrate that aggregation reduces demand uncertainty—and, thus, the required safety inventory—as long as the demand being aggregated is not perfectly positively correlated. Demand for most products does not show perfect positive correlation across different geographic regions. Products such as heating oil are likely to have demand that is positively correlated across nearby regions. In contrast, products such as milk and sugar are likely to have demand that is much more independent across regions. If demand in different geographic regions is about the same size and independent, aggregation reduces safety inventory by the square root of the number of regions aggregated. In other words, if the number of independent stocking locations decreases by a factor of n, the average safety inventory is expected to decrease by a factor of 1n. This principle is referred to as the square-root law and is illustrated in Figure 12-4.
Most online retailers exploit the benefits of aggregation in terms of reduced inventories. For example, Blue Nile sells diamonds online and serves the entire United States out of one warehouse. As a result, it has lower levels of diamond inventories than jewelry chains such as Tiffany and Zales, which must keep inventory in every retail store.
There are situations, however, in which physical aggregation of inventories in one location may not be optimal. There are two major disadvantages of aggregating all inventories in one location:
- Increase in response time to customer order
- Increase in transportation cost to customer
Both disadvantages result because the average distance between the inventory and the customer increases with aggregation. Either the customer must travel farther to reach the product or the product must be shipped over longer distances to reach the customer. A retail chain such as Gap has the option of building many small retail outlets or a few large ones. Gap tends to have many smaller outlets distributed evenly in a region because this strategy reduces the distance that customers travel to reach a store. If Gap had one large centralized outlet, the average distance that customers need to travel would increase, and thus the response time would increase. A desire to decrease customer response time is thus the impetus for the firm to have multiple outlets. Another example is McMaster-Carr, a distributor of MRO supplies. McMaster-Carr uses UPS for shipping product to customers. Because shipping charges are based on distance, having one centralized warehouse increases the average shipping cost as well as the response time to the customer. Thus, McMaster-Carr has five warehouses that allow it to provide next-day delivery to a large fraction of the United States. Next-day delivery by UPS would not be feasible at a reasonable cost if McMaster-Carr had only one warehouse. Even Amazon, which started with one warehouse in Seattle, has added more warehouses in other parts of the United States in an effort to improve response time and reduce transportation cost to the customer. We illustrate the trade-offs of centralization in Example 12-9 (see worksheet Example 12-9).
EXAMPLE 12-9 Trade-Offs of Physical Centralization
The Shanghai branch office of an Italian coffee machine company is considering setting up either one distribution center for each of its east, south, west, and north regions or simply one center in Ningbo for the whole of China. The weekly demand for the automatic espresso coffee machine is normally distributed with a mean of 1,000 units and a standard deviation of 300 units. Although the demand for each region is independent, the supply lead time is more or less the same—four weeks. Each machine costs $1,000 and the holding cost is 20 percent. With the next-day delivery promise, the branch office needs to bear an inland trucking cost of $10/unit for all four regional centers. However, if a single national distribution center is decided upon, a more expensive transport fleet is needed and that will cost $13/unit for next-day service. Setting up and operating four regional DCs costs $150,000 per year more than building and operating the single Ningbo national distribution center.
Assume that the Italian company would like a CSL of 0.95. What should the Shanghai branch office decide based on the cost considerations?
Analysis:
Observe that using only one distribution center would decrease facility and inventory costs but increase transportation costs. We therefore have to evaluate the change in each cost category on aggregation. We start with inventory costs. For each region we have
Given the desired CSL = 0.95, the required safety inventory across all four regional distribution centers is obtained using Equation 12.9 to be
Now consider the aggregate option. Because demand in all four areas is independent, p = 0. Using Equation 12.14, the standard deviation of aggregate weekly demand is
Standard deviation of weekly demand at national distribution center, 
For a CSL of 0.95, safety inventory required for the aggregate option (using Equation 12.15) is given as
We can now evaluate the changes in inventory, transportation, and facility costs upon aggregation as follows:
Decrease in annual inventory holding cost on aggregation = (3,948 – 1,974) X $1,000 X 0.2 = $394,765
Decrease in annual facility costs on aggregation = $150,000
Increase in annual transportation costs on aggregation = 52 X 1,000 X (13 – 10) X 4 = $624,000
Observe that in this case, the annual costs for the Shanghai branch office will be increased by $624,000 – $394,765 – $150,000 = $79,235 upon centralization. It is clearly better to run the four centers in the east, south, west, and north regions instead of the Ningbo center.
Example 12-9 and the previous discussion highlight instances in which physical aggregation of inventory at one location may not be optimal. However, aggregating safety inventory has clear benefits. We now discuss various methods by which a supply chain can extract the benefits of aggregation without having to physically centralize all inventories in one location.
1. Information Centralization
Redbox uses information centralization to virtually aggregate its inventories of DVDs despite having tens of thousands of vending machines. The company has set up an online system that allows customers to locate nearby vending machines with the DVD they are searching for in stock. This allows Redbox to provide a much higher level of product availability than would be possible if a customer found out about availability only by visiting a vending machine. The benefit of information centralization derives from the fact that most customers get their DVD from the vending machine closest to their house. In case of a stockout at the closest vending machine, the customer is served from another vending machine, thus improving product availability without adding to inventories.
Retailers such as Gap also use information centralization effectively. If a store does not have the size or color that a customer wants, store employees can use their information system to inform the customer of the closest store with the product in inventory. Customers can then either go to this store or have the product delivered to their house. Gap thus uses information centralization to virtually aggregate inventory across all retail stores even though the inventory is physically separated. This allows Gap to reduce the amount of safety inventory it carries while providing a high level of product availability.
Walmart has an information system in place that allows store managers to search other stores for an excess of items that may be hot sellers at their stores. Walmart provides transportation that allows store managers to exchange products so they arrive at stores where they are in high demand. In this case, Walmart uses information centralization with a responsive transportation system to reduce the amount of safety inventory carried while providing a high level of product availability.
2. Specialization
Most supply chains provide a variety of products to customers. When inventory is carried at multiple locations, a key decision for a supply chain manager is whether all products should be
stocked at every location. Clearly, a product that does not sell in a geographic region should not be carried in inventory by the warehouse or retail store located there. For example, it does not make sense for a Sears retail store in southern Florida to carry a wide variety of snow boots in inventory.
Another important factor that must be considered when making stocking decisions is the reduction in safety inventory that results from aggregation. If aggregation reduces the required safety inventory for a product by a large amount, it is better to carry the product in one central location. If aggregation reduces the required safety inventory for a product by a small amount, it may be best to carry the product in multiple decentralized locations to reduce response time and transportation cost.
The reduction in safety inventory due to aggregation is strongly influenced by the demand’s coefficient of variation. For a product with a low coefficient of variation, disaggregate demand can be forecast with accuracy. As a result, the inventory benefit from aggregation is minimal. For a product with a high coefficient of variation of demand, disaggregate demand is difficult to forecast. In this case, aggregation improves forecast accuracy significantly, providing great benefits. We illustrate this idea in Example 12-10 (see worksheet Example 12-10).
EXAMPLE 12-10 Impact of Coefficient of Variation on Value of Aggregation
Assume that W.W. Grainger, a supplier of MRO products, has 1,600 stores distributed throughout the United States. Consider two products—large electric motors and industrial cleaner. Large electric motors are high-value items with low demand, whereas the industrial cleaner is a low-value item with high demand. Each motor costs $500 and each can of cleaner costs $30. Weekly demand for motors at each store is normally distributed, with a mean of 20 and a standard deviation of 40. Weekly demand for cleaner at each store is normally distributed, with a mean of 1,000 and a standard deviation of 100. Demand experienced by each store is independent, and supply lead time for both motors and cleaner is four weeks. W.W. Grainger has a holding cost of 25 percent. For each of the two products, evaluate the reduction in safety inventories that will result if they are removed from retail stores and carried only in a centralized DC. Assume a desired CSL of 0.95.
Analysis:
The evaluation of safety inventories and the value of aggregation for each of the two products is shown in Table 12-4. All calculations use the approach discussed earlier and illustrated in Example 12-8. As Table 12-4 shows, the inventory reduction benefit from centralizing motors is much larger than the benefit from centralizing cleaner. From this analysis, W.W. Grainger should stock cleaner at the stores and motors in the DC. Given that cleaner is a high-demand item, customers will be able to pick it up on the same day at the stores. Given that motors are a low-demand item, customers may be willing to wait the extra day that shipping from the DC will entail.
Items with low demand are referred to as slow-moving items and typically have a high coefficient of variation, whereas items with high demand are referred to as fast-moving items and typically have a low coefficient of variation. For many supply chains, specializing the distribution network with fast-moving items stocked at decentralized locations close to the customer and slow-moving items stocked at a centralized location can significantly reduce the safety inventory carried without hurting customer response time or adding to transportation costs. The centralized location then specializes in handling slow-moving items.
Of course, other factors also need to be considered when deciding on the allocation of products to stocking locations. For example, an item that is considered an emergency item because the customer needs it urgently may be stocked at stores even if it has a high coefficient of variation. In this case the customer will be willing to pay a premium for having the item available at a store. One also needs to consider the cost of the item. High-value items provide a greater benefit from centralization than do low-value items.
The insights from Example 12-10 and the above discussion are summarized in Figure 12-5. In general, decentralized networks like Costco provide a low-cost supply chain for fast-moving, predictable, low-value products like detergent. Centralized networks like Blue Nile provide a low-cost supply chain for slow-moving, unpredictable, high-value products like diamonds. A decentralized supply chain like Tiffany may carry slow-moving items like diamonds as long as customers are willing to pay a premium for this choice. Similarly, a centralized supply chain like Amazon may carry a fast-moving item like detergent, but only if customers are willing to pay a premium. It can be argued that Amazon’s inability to extract a significant enough premium from its customers for the fast-moving items it sells has hurt its profitability.
It is important for firms with bricks-and-mortar stores to take the idea of specialization into account when incorporating the online channel into an omni-channel strategy. Consider, for example, a bookstore chain such as Barnes & Noble, which carries about 100,000 titles at each retail store. The titles carried can be divided into two broad categories—best sellers with high demand and other books with much lower demand. Barnes & Noble can design an omni-channel strategy under which the retail stores carry primarily best sellers in inventory. They may also carry one, or at most two, copies of each of the other titles, to allow customers to browse. Customers should be able to access all titles that are not in the store via electronic kiosks in the store, which provide access to barnesandnoble.com inventory. This strategy allows customers to access an increased variety of books from Barnes & Noble stores. Customers could place orders for low-volume titles with barnesandnoble.com while purchasing high-volume titles at the store itself. This strategy of specialization would allow Barnes & Noble to aggregate all slow-moving items to be sold by the online channel. All best sellers would be decentralized and carried close to the customer. The supply chain thus reduces inventory costs for slow-moving items at the expense of somewhat higher transportation costs. For the fast-moving items, the supply chain provides a lower transportation cost and better response time by carrying the items at retail stores close to the customer.
Home Depot follows a similar strategy and integrates its online channel with its retail stores. The retail stores carry fast-moving items, and the customer is able to order slow-moving variants online. Home Depot is thus able to increase the variety of products available to customers while keeping supply chain inventories down. Walmart.com has also employed a strategy of carrying slower-moving items online.
3. Product Substitution
Substitution refers to the use of one product to satisfy demand for a different product. Substitution may occur in two situations:
- Manufacturer-driven substitution: The manufacturer or supplier makes the decision to substitute. Typically, the manufacturer substitutes a higher-value product for a lower-value product that is not in inventory. For example, Dell may install a 1.2-terabyte hard drive into a customer order requiring a 1-terabyte drive if the smaller drive is out of stock.
- Customer-driven substitution: Customers make the decision to substitute. For example, a customer walking into a Walmart store to buy a gallon of detergent may buy the halfgallon size if the gallon size is not available. The customer substitutes the half-gallon size for the gallon size.
In both cases, exploiting substitution allows the supply chain to satisfy demand using aggregate inventories, which permits the supply chain to reduce safety inventories without hurting product availability. In general, given two products or components, substitution may be oneway (i.e., only one of the products [components] substitutes for the other) or two-way (i.e., either product [component] substitutes for the other). We briefly discuss one-way substitution in the context of manufacturer-driven substitution and two-way substitution in the context of customer- driven substitution.
MANUFACTURER-DRIVEN ONE-WAY SUBSTITUTION Consider a server manufacturer selling direct to customers that offers drives that vary in size from 0.8 to 1.2 terabytes. Customers are charged according to the size of drive that they select, with larger sizes being more expensive. If a customer orders a 1-terabyte drive and the manufacturer is out of drives of this size, there are two possible choices: (1) delay or deny the customer order or (2) substitute a larger drive that is in stock (say, a 1.2-terabyte drive) and fill the customer order on time. The first case is potentially a lost sale or loss of future sales because the customer experiences a delayed delivery. In the second case, the manufacturer installs a higher-cost component, reducing the company’s profit margin. These factors, along with the fact that only larger drives can substitute for smaller drives, must be considered when the manufacturer makes inventory decisions for individual drive sizes.
Substitution allows the server manufacturer to aggregate demand across the components, reducing safety inventories required. The value of substitution increases as demand uncertainty increases. Thus, the manufacturer should consider substitution for components displaying high demand uncertainty.
The desired degree of substitution is influenced by the cost differential between the higher- value and lower-value component. If the cost differential is very small, the manufacturer should aggregate most of the demand and carry most of its inventory in the form of the higher-value component. As the cost differential increases, though, the benefit of substitution decreases. In this case, the manufacturer will find it more profitable to carry inventory of each of the two components and decrease the amount of substitution.
The desired level of substitution is also influenced by the correlation of demand between the products. If demand between two components is strongly positively correlated, there is little value in substitution. As demand for the two components becomes less positively correlated (or even negatively correlated), the benefit of substitution increases.
CUSTOMER-DRIVEN TWO-WAY SUBSTITUTION Consider W.W. Grainger selling two brands of motors, GE and SE, which have similar performance characteristics. Customers are generally willing to purchase either brand, depending on product availability. If W.W. Grainger managers do not recognize customer substitution, they will not encourage it. For a given level of product availability, they will thus have to carry high levels of safety inventory of each brand. If its managers recognize and encourage customer substitution, they can aggregate the safety inventory across the two brands, thereby improving product availability.
W.W. Grainger does a good job of recognizing customer substitution. When a customer calls or goes online to place an order and the product he or she requests is not available, the customer is immediately told the availability of all equivalent products that may be substituted. Most customers ultimately buy a substitute product in this case. W.W. Grainger exploits this substitution by managing safety inventory of all substitutable products jointly. Recognition and exploitation of customer substitution allows W.W. Grainger to provide a high level of product availability with lower levels of safety inventory.
A good understanding of customer-driven substitution is important in the retail industry. It must be exploited when merchandising to ensure that substitute products are placed near each other, allowing a customer to buy one if the other is out of stock. In the online channel, substitution requires a retailer to present the availability of substitute products if the one the customer requests is out of stock. The supply chain is thus able to reduce the required level of safety inventory while providing a high level of product availability.
The demand uncertainties and the correlation of demand between the substitutable products influence the benefit to a retailer from exploiting substitution. The greater the demand
uncertainty, the greater is the benefit of substitution. The less positive the correlation of demand between substitutable products, the greater is the benefit from exploiting substitution.
4. Component Commonality
In any supply chain, a significant amount of inventory is held in the form of components. A single product such as a server contains hundreds of components. When a supply chain is producing a large variety of products, component inventories can easily become very large. The use of common components in a variety of products is an effective supply chain strategy to exploit aggregation and reduce component inventories.
Dell sells thousands of server configurations to customers. An extreme option for Dell is to design distinct components that are suited to the performance of a particular configuration. Under this option, Dell would use different memory, hard drive, and other components for each distinct finished product. The other option is to design products such that common components are used in different finished products.
Without common components, the uncertainty of demand for any component is the same as the uncertainty of demand for the finished product in which it is used. Given the large number of components in each finished product, demand uncertainty will be high, resulting in high levels of safety inventory. When products with common components are designed, the demand for each component is an aggregation of the demand for all the finished products of which the component is a part. Component demand is thus more predictable than the demand for any one finished product. This fact reduces the component inventories carried in the supply chain. This idea has been a key factor for success in the electronics industry and has also started to play a big role in the auto industry. With increasing product variety, component commonality is a key to reducing supply chain inventories without hurting product availability. We illustrate the basic idea behind component commonality in Example 12-11 (see worksheet Example 12-11).
EXAMPLE 12-11 Value of Component Commonality
Assume that Dell is to manufacture 27 servers with three distinct components: processor, memory, and hard drive. Under the disaggregate option, Dell designs specific components for each server, resulting in 3 X 27 = 81 distinct components. Under the common-component option, Dell designs servers such that three distinct processors, three distinct memory units, and three distinct hard drives can be combined to create 27 servers. Each component is thus used in nine servers. Monthly demand for each of the 27 servers is independent and normally distributed, with a mean of 5,000 and a standard deviation of 3,000. The replenishment lead time for each component is one month. Dell is targeting a CSL of 95 percent for component inventory. Evaluate the safety inventory requirements with and without the use of component commonality. Also evaluate the change in safety inventory requirements as the number of finished products of which a component is a part varies from one to nine.
Analysis:
We first evaluate the disaggregate option, in which components are specific to a server. For each component, we have
Standard deviation of monthly demand = 3,000
Given a lead time of one month and a total of 81 components across 27 servers, we thus use Equation 12.12 to obtain
Total safety inventory required = 81 X NORMSINV(0.95) X √1 X 3,000 = 399,699 units
In the case of component commonality, each component ends up in nine finished products. Therefore, the demand at the component level is the sum of demand across nine products. Using Equations 12.15 and 12.16, the safety inventory required for each component is thus
Safety inventory per common component = NORMSINV( 0.95) X √1 X √9 X 3,000
= 14,803.68 units
With component commonality, there are a total of nine distinct components. The total safety inventory across all nine components is thus
Total safety inventory required = 9 X 14,803.68 = 133,233
Thus, having each component common to nine products results in a reduction in safety inventory for Dell from 399,699 to 133,233 units.
In Table 12-5, we evaluate the marginal benefit in terms of reduction in safety inventory as a result of increasing component commonality. Starting with the required safety inventory when each component is used in only one finished product, we evaluate the safety inventory as the number of products in which a component is used increases to nine. Observe that component commonality decreases the required safety inventory for Dell. The marginal benefit of commonality, however, declines as a component is used in more and more finished products.
As a component is used in more finished products, it must be more flexible. As a result, the cost of producing the component typically increases with increasing commonality. Given that the marginal benefit of component commonality decreases as we increase commonality, we need to trade off the increase in component cost and the decrease in safety inventory when deciding on the appropriate level of component commonality.
5. Postponement
Postponement is the ability of a supply chain to delay product differentiation or customization until closer to the time the product is sold. The goal is to have common components in the supply chain for most of the push phase and move product differentiation as close to the pull phase of the supply chain as possible. For example, the final mixing of paint today is done at the retail store after the customer has selected the color he or she wants. Thus, paint variety is produced only when demand is known with certainty. Postponement coupled with component commonality allows paint retailers to carry significantly lower safety inventories than in the past, when mixing was done at the paint factory. In the past, the factory manager had to forecast paint demand by color when planning production. Today, a factory manager needs to forecast only aggregate paint demand because mixing has been postponed until after customer demand is known. As a result, each retail store primarily carries aggregate inventory in the form of base paint that is configured to the appropriate color based on customer demand.
Another classic example of postponement is the production process at Benetton to make colored knit garments. The original process called for the thread to be dyed and then knitted and assembled into garments. The entire process required up to six months. Because the color of the final garment was fixed the moment the thread was dyed, demand for individual colors had to be forecast far in advance (up to six months). Benetton developed a manufacturing technology that allowed it to dye knitted garments to the appropriate color. Now, greige thread (the term used for thread that has not yet been dyed) can be purchased, knitted, and assembled into garments before dyeing. The dyeing of the garments is done much closer to the selling season. In fact, part of the dyeing is done after the start of the selling season, when demand is known with great accuracy. In this case, Benetton has postponed the color customization of the knit garments. When thread is purchased, only the aggregate demand across all colors needs to be forecast. Given that this decision is made far in advance, when forecasts are least likely to be accurate, there is great advantage to this aggregation. As Benetton moves closer to the selling season, the forecast uncertainty reduces. At the time Benetton dyes the knit garments, demand is known with a high degree of accuracy. Thus, postponement allows Benetton to exploit aggregation and significantly reduce the level of safety inventory carried. Supply chain flows with and without postponement are illustrated in Figure 12-6.
Without component commonality and postponement, product differentiation occurs early on in the supply chain, and most of the supply chain inventories are disaggregate. Postponement allows the supply chain to delay product differentiation. As a result, most of the inventories in the supply chain are aggregate. Postponement thus allows a supply chain to exploit aggregation to reduce safety inventories without hurting product availability. We illustrate the benefits of postponement in Example 12-12 (see worksheet Example 12-12). A more nuanced discussion of the value of postponement is given in Chapter 13.
EXAMPLE 12-12 Value of Postponement
Consider a paint retailer that sells 100 different colors of paint. Assume that weekly demand for each color is independent and is normally distributed with a mean of 30 and a standard deviation of 10. The replenishment lead time from the paint factory is two weeks and the retailer
aims for a CSL = 0.95. How much safety stock will the retailer have to hold if paint is mixed at the factory and held in inventory at the retailer as individual colors? How does the safety stock requirement change if the retailer holds base paint (supplied by the paint factory) and mixes colors on demand?
Analysis:
We first evaluate the disaggregate option without postponement, in which the retailer holds safety inventory for each color sold. For each color, we have
D = 30 / week, σD = 10, L = 2 weeks
Given the desired CSL = 0.95, the required safety inventory across all 100 colors is obtained using Equation 12.12 to be
Now, consider the option whereby mixing is postponed until after the customer orders. Safety inventory is held in the form of base paint, whose demand is an aggregate of demand of the 100 colors. Because demand in all 100 colors is independent, p = 0. Using Equation 12.15, the standard deviation of aggregate weekly demand of base paint is
For a CSL of 0.95, safety inventory required for the aggregate option (using Equation 12.16) is given as
Observe that postponement reduces the required safety inventory at the paint retailer from 2,326 units to 233 units.
Postponement can be a powerful concept when customers are willing to wait a little for their orders to arrive. This delay offers the supply chain an opportunity to reduce inventories by postponing product differentiation until after the customer order arrives. It is important that the manufacturing process be designed in a way that enables assembly to be completed quickly. Given that customers are often willing to wait for delivery, several furniture and window manufacturers have postponed some of the assembly processes for their products.
Source: Chopra Sunil, Meindl Peter (2014), Supply Chain Management: Strategy, Planning, and Operation, Pearson; 6th edition.
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