1. Inventory
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Overview of inventory Inventory functionality and definitions
Inventory carrying cost
Planning inventory
Managing uncertainty
Inventory management policies
Inventory management practices

3. Why do we have inventories?
Because the customer usually isn’t sitting at the plant exit!
Queen Elizabeth research station in Antarctica

4. Risks associated with holding inventory
Time duration
Depth of commitment
Width of commitment
Typical measures of exposure to investments in inventory
Manufacturer’s exposure is typically narrow, but deep and of long duration
Wholesaler’s exposure is wider than manufacturers and somewhat deep
Duration is medium
Retailer’s exposure is wide, but not very deep
Duration is usually short except for specialty retailers
Supply chain exposure based on location

5. Functions of Inventory
Geographical specialization allows us to specialize production across different locations
Decoupling allows us to run processes for maximum economic lot sizes within a single facility
Supply/Demand balancing accommodates the elapsed time between inventory availability and consumption
Buffering uncertainty accommodates uncertainty related to:
Demand in excess of forecast or
Unexpected delays in delivery (aka safety stock)

6. Inventory policy Inventory policy is a firm’s guidelines concerning
What to purchase or manufacture
When to take action
In what quantity should action be taken
Where products should be located geographically
Firm’s policy also includes decisions about which inventory management practices to adopt

7. Service level
Service level is a performance target specified by management and defines inventory performance objectives
Common measures of service level include
Performance cycle is the elapsed time between release of a purchase order by the buyer to the receipt of shipment
Case fill rate is the percent of cases ordered that are shipped as requested
Line fill rate is the percent of order lines (items) that were filled completely
Order fill is the percent of customer orders filled completely

8. Inventory definitions
Inventory includes materials, components, work-in-process, and finished goods that are stocked in the company’s logistical system
The cycle inventory (base stock) is the portion of average inventory that results from replenishment
Order quantity is the amount ordered for replenishment
Transit inventory represents the amount typically in transit between facilities or on order but not received
Obsolete inventory is stock that is out-of-date or is not in recent demand
Speculative inventory is bought to hedge a currency exchange or to take advantage of a discount
Safety stock is the remainder of inventory in the logistics system

9. Average inventory is the typical amount stocked over time
Average inventory equals the maximum inventory plus the minimum inventory divided by two
Typically equal to ½ order quantity + safety stock + in-transit stock
Figure 7.1 Inventory Cycle for Typical Product

10. Figure 7.3 Alternative Order Quantity and Average Inventory
Smaller replenishment order quantities results in lower average inventory
Policy must decide how much inventory to order at a specified time
Reorder point defines when a replenishment order is initiated
However, other factors are important like performance cycle uncertainty, purchasing discounts, and transportation economies
Figure 7.3 Alternative Order Quantity and Average Inventory

11. Inventory expense is: Cost components:
Inventory carrying cost is the expense associated with maintaining inventory
Annual inventory carrying cost percent times average inventory value
Inventory expense is:
Cost of capital is specified by senior management
Taxes on inventory held in warehouses
Insurance is based on estimated risk or loss over time and facility characteristics
Obsolescence results from deterioration of product during storage
E.g. food and pharmaceutical sell-by dates
Storage is facility expense related to product holding rather than product handling
Cost components:

12. Final carrying cost percent used by a firm is a managerial policy
Table 7.2 Inventory Carrying Cost Components

13. Inventory ordering cost components
Order preparation costs
Order transportation costs
Order receipt and processing costs
Material handling costs
Total cost is driven by inventory planning decisions which establish when and how much to order

14. When to order × = T R D + SS × = T R D
Basic reorder formula if demand and performance are certain
R = Reorder point in units
D = Average daily demand in units
T = Average performance cycle length in days
If safety stock is needed to accommodate uncertainty the formula is
SS = Safety stock in units × = T R D + SS × = T R D

15. Figure 7.4 Economic Order Quantity
How much to order
Economic order quantity is the amount that balances the cost of ordering with the cost of maintaining average inventory
Assumes demand and costs are relatively stable for the year
Does not consider impact of joint ordering of multiple products
Figure 7.4 Economic Order Quantity

16. Standard mathematical solution for EOQ

17. Example EOQ solution using Table 7.3
Total ordering cost is $152 = (2400/300 x $19.00)
Inventory carrying cost is $150 = [300/2 x (5 x 0.20)]

18. Simple EOQ model assumptions
All demand is satisfied
Rate of demand is continuous, constant and known
Replenishment performance cycle time is constant and known
Constant price of product that is independent of order quantity or time
An infinite planning horizon exists
No interaction between multiple items of inventory
No inventory is in transit
No limit is placed on capital availability

19. Relationships useful for guiding inventory planning
EOQ is found at the point where annualized order placement cost and inventory carrying cost are equal
Average base inventory equal one-half order quantity
Value of the inventory unit, all other things being equal, will have a direct relationship with replenishment order frequency
Higher value products will be ordered more frequently

20. Typical adjustments to EOQ
Compare total cost with each transportation rate option
Volume transportation rates offer a freight-rate discount for larger shipments
If discount is sufficient to offset added inventory carrying cost less the reduced cost of ordering then it is viable choice
Quantity discounts offer a lower per unit cost when larger quantities are purchased
Production lot size
Multiple-item purchase
Limited capital
Dedicated trucking
Unitization
Other EOQ adjustments

21. Uncertainty in inventory management
Demand uncertainty — when and how much product will our customers order?
Performance cycle uncertainty — how long will it take to replenish inventory with our customers?
Inventory policy must deal with uncertainty
Variations must be considered in both areas to make effective inventory planning decisions

22. Demand uncertainty can be managed using safety stock
To protect against stockout when uncertain demand exceeds forecast we add safety stock to base inventory
Determine the likelihood of stockout using a probability distribution
Estimate demand during a stockout period
Decide on a policy concerning the desired level of stockout protection
Planning safety stock requires three steps

23. Probability theory enables calculation of safety stock for a target service level
E.g. a service level of 99% results in a stockout probability of 1%
Service level is equal to 100% minus probability % of stockout
From analysis of historical demand data the safety stock required to ensure a stock out only 1% of the time is possible
A one-tailed normal distribution is used because only demand that is greater than the forecast can create a stockout
The most common probability distribution for demand is the normal distribution

24. Example of historical demand analysis using a normal distribution
Figure 7.6 Historical Analysis of Demand History
Figure 7.7 Normal Distribution

25. Performance cycle uncertainty means operations cannot assume consistent delivery
Table 7.10 Calculation of Standard Deviation of Replenishment Cycle Duration

26. Safety stock with combined uncertainty
Planning for both demand and performance cycle uncertainty requires combining two independent variables
The joint impact of the probability of both demand and performance cycle variation must be determined
Direct method is to combine standard deviations using a convolution formula

27. Figure 7.8 Combined Demand and Performance Cycle Uncertainty
Typical situation where both demand and performance cycle variation exists
Figure 7.8 Combined Demand and Performance Cycle Uncertainty

28. Summary of alternative solutions to combined uncertainty
Table 7.12 Average Inventory Impact Resulting from Changes in EOQ

29. The fill rate is the magnitude rather than the probability of a stockout
Increasing the replenishment order quantity decreases the relative magnitude of potential stockouts
The formula for this relationship is

30. Figure 7.9 Impact of Order Quantity on Stockout Magnitude
Number of stockouts is reduced from two to one when order quantity is increased
Figure 7.9 Impact of Order Quantity on Stockout Magnitude

31. Increased order size can be used to compensate for decreasing the safety stock
Table 7.15 Impact of Order Quantity on Safety Stock

32. Dependent demand replenishment
Inventory requirements are a function of known events that are not generally random
No specific safety stock is needed to support time-phased procurement programs (e.g. MRP)
Dependent demand does not require forecasting because there is no uncertainty
Procurement replenishment is predictable and constant
Vendors and suppliers maintain adequate inventories to satisfy 100% of purchase requirements
No safety stock assumes:

33. 3 approaches to introduce safety stock into dependent demand situations
E.g. order a component earlier than needed to assure timely arrival
Put safety time into the requirements plan
E.g. assume plan error will not exceed 5 percent
Over-planning top-level demand is a procedure to increase the requisition by a quantity specified by some estimate of expected plan error
Utilize statistical techniques to set safety stocks directly for a component rather than to the item of top-level demand

34. Approaches to implementing inventory management policies
Reactive (or pull) approach responds to customer demand to pull the product through the distribution channel
Planning approach proactively allocates inventory on the basis of forecasted demand and product availability
Hybrid approach uses a combination of push and pull

35. Inventory control using reactive approaches
Inventory control defines how often inventory levels are reviewed to determine when and how much to order
Perpetual review continuously monitors inventory levels to determine inventory replenishment needs
Periodic review monitors inventory status of an item at regular intervals such as weekly or monthly

36. Reorder point formulas for reactive methods
Perpetual Review
Periodic Review

37. Assumptions of classical reactive inventory logic
All customers, market areas, and product contribute equally to profits
Infinite capacity exists at the production facility
Infinite inventory availability at the supply location
Performance cycle time can be predicted and that cycle lengths are independent
Customer demand patterns are relatively stable and consistent
Each distribution warehouse’s timing and quantity of replenishment orders are determined independently of all other sites, including the supply source
Performance cycle length cannot be correlated with demand

38. Two planning approaches
Planning approaches coordinate requirements across multiple locations in the supply chain
Fair share allocation provides each distribution facility with an equitable distribution of available inventory
Limited ability to manage multistage inventories
Requirements planning integrates across the supply chain taking into consideration unique requirements
Materials requirements planning (MRP) is driven by a production schedule
Distribution requirements planning (DRP) is driven by supply chain demand
Two planning approaches

39. Example of fair share allocation method
Figure 7.11 Fair Share Allocation Example
Allocation of 500 available units from plant
Warehouse 1 = 47
Warehouse 2 = 383
Warehouse 3 = 70

40. Figure 7.12 Conceptual Design of Integrated MRP/DRP System
Integrated planning approach for raw materials, work-in-process, and finished goods
MRP system
DRP system
Figure 7.12 Conceptual Design of Integrated MRP/DRP System

41. Limitations to planning approaches
Requires accurate and coordinated forecasts for each warehouse
Requires consistent and reliable product movement between warehouse facilities
Subject to frequent rescheduling (system nervousness) because of production breakdowns or delivery delays

42. Collaborative inventory replenishment programs
Intent is to reduce reliance on forecasting and position inventory using actual demand on a just-in-time basis
Replenishment programs are designed to streamline the flow of goods within the supply chain
Quick response (QR) is a technology-driven cooperative effort between retailers and suppliers to improve inventory velocity while matching supply to consumer buying patterns
Vendor-managed inventory (VMI) is a modified QR that eliminates the need for replenishment orders
Profile replenishment (PR) extends QR and VMI by giving suppliers the right to anticipate future requirements according to their knowledge of a product category

43. Managerial considerations when developing an inventory policy
Table 7.18 Suggested Inventory Management Logic

44. Inventory management practices
E.g. classify by sales, profit contribution, inventory value, usage rate or item category
Product/market classification groups products, markets, or customers with similar characteristics to facilitate inventory management
E.g. service objectives, forecasting method, management technique, and review cycle
Segment strategy definition specifies all aspects of inventory management process for each segment of inventory
E.g. data requirements, software applications, performance objectives, and decision guidelines
Policies and parameters must be defined at a detailed level

45. Example of product classification by sales
Table 7.19 Product Market Classification (Sales)

46. Sample illustrating segment strategy definitions
Table 7.20 Integrated Strategy