Homework 12

315

However, given demand fluctuations and forecast errors, actual demand over the three weeks may be higher or lower than the 300 purses that were forecast. If the actual demand at Bloomingdale’s is higher than 300, some customers will be unable to purchase purses, resulting in a potential loss of margin for Bloomingdale’s. The store manager thus decides to place an order with Gucci when the store still has 400 purses. This policy improves product availability for the customer because the store now runs out of purses only if the demand over the three weeks exceeds 400. Given an average weekly demand of 100 purses, the store will have an aver- age of 100 purses remaining when the replenishment lot arrives. Safety inventory is the average inventory remaining when the replenishment lot arrives. Thus, Bloomingdale’s carries a safety inventory of 100 purses.

Given a lot size of Q = 600 purses, the cycle inventory, the focus of the previous chapter, is Q>2 = 300 purses. The inventory profile at Bloomingdale’s in the presence of safety inven- tory is shown in Figure 12-1, which illustrates that the average inventory at Bloomingdale’s is the sum of the cycle and safety inventories.

This example illustrates a trade-off that a supply chain manager must consider when plan- ning safety inventory. On one hand, raising the level of safety inventory increases product avail- ability, and thus the margin captured from customer purchases. On the other hand, raising the level of safety inventory increases inventory holding costs. This issue is particularly significant in industries in which product life cycles are short and demand is volatile. Carrying excessive inven- tory can help counter demand volatility but can really hurt if new products come onto the market and demand for the product in inventory dries up. The inventory on hand then becomes worthless.

In today’s business environment, it has become easier for customers to search across stores for product availability. If Amazon is out of a book, for example, a customer can easily check to see whether barnesandnoble.com has the title available. The increased ease of searching puts pressure on firms to improve product availability. Simultaneously, product variety has grown with increased customization. As a result, markets have become increasingly heterogeneous and demand for individual products is unstable and difficult to forecast. Both the increased variety and the greater pressure for availability push firms to raise the level of safety inventory they hold. Given the product variety and high demand uncertainty in most high-tech supply chains, a sig- nificant fraction of the inventory carried is safety inventory.

As product variety has grown, however, product life cycles have shrunk. Thus, it is more likely that a product that is “hot” today will be obsolete tomorrow, which increases the cost to firms of carrying too much inventory. Thus, a key to the success of any supply chain is to figure out ways to decrease the level of safety inventory carried without hurting the level of product availability.

The importance of reduced safety inventories is emphasized by the experience of Nord-

Average Inventory

Cycle Inventory

Safety Inventory

Inventory

Time

Q

FIGURE 12-1 Inventory Profile with Safety Inventory

M12_CHOP0203_06_SE_C12.indd Page 315 26/09/14 11:48 AM f-w-147 /203/AW00176/9780133800203_CHOPRA/CHOPRA_SUPPLY_CHAN_MANAGEMENT06_SE_978013380020 ...

σ L = 707

332 Chapter 12 • Managing Uncertainty in a Supply Chain: Safety Inventory

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, however, situations where physical aggregation of inventories in one location may not be optimal. There are two major disadvantages of aggregating all inventories in one location:

1. Increase in response time to customer order 2. 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 has to travel farther to reach the product or the product has to 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.com, 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.

Trade-offs of Physical Centralization

An online retailer is debating whether to serve the United States through four regional distribu- tion centers or one national distribution center. Weekly demand in each region is normally distributed, with a mean of 1,000 and a standard deviation of 300. Demand experienced in each region is independent, and supply lead time is four weeks. The online retailer has a holding cost of 20 percent and the cost of each product is $1,000. The retailer promises its customers next-day delivery. With four regional distribution centers, the retailer can provide next-day delivery using ground transportation at a cost of $10/unit. With a single national distribution center, the retailer

EXAMPLE 12-9

Number of Independent Stocking Locations

Total Safety Inventory

FIGURE 12-4 Square-Root Law

M12_CHOP3952_05_SE_C12.QXD 11/15/11 6:52 PM Page 332

s

====

1,000week,300,L4weeks,0.95

D

DCSL

1

4()

sD

ssFCSLL

s

-

=´´´

(

)

=´´´=

40.9543003,948

NORMSINV

4300600

C

D

s

=´=

(

)

s

-

=´´

C

sD

ssFL

1

0.95

(

)

=´´=

NORMSINV

0.9546001,974

()

3,9481,974$1,1000.2

=-´´

$394,765

=

$150,000

=

=´´-

521,000(1310)

$624,000

=

=´´´

=

81(0.95)13,000

399,699units

NORMSINV

(

)

=´´´

=

NORMSINV

0.95193,000

14,803.68units

=9´14,803.68=133,233

(

)

1

100

sD

ssFCSLL

s

-

=´´´

(

)

1000.952102,326

NORMSINV

=´´´=

10010100

C

D

s

=´=

(

)

1

(0.95)2100233

D

C

s

ssFCSLLNORMSINV

s

-

=´´=´´=

LD

L

ss

=

–1

()()

SLDL

ssFCSLNORMSINVCSLL,ROPDss

ss

=´=´=+

+£=

LTOULCSL

(demandduring)

+

=+

TL

DTLD

()

ss

+

=+

TLD

TL

TL

OULDss

+

=+

1

1

()()

Averagelotsize,

sDTL

T

ssFCSLNORMSINVCSL

QDDT

ss

-

++

=´=´

==´

()

(24)2,50015,000

TL

DTLD

+

=+

=+=

(42)5001,225

TLD

TL

ss

+

=+

=+=

(

)

(

)

(

)

1

0.901,2251,570boxes

15,0001,57016,570

SDLTL

TL

ssFCSLNORMSINVCSL

NORMSINV

OULDss

ss

-

++

+

=´=´

=´=

=+=+=

LT

+