OPERATIONS
MANAGEMENT
PUAF U6217
Inventory Management
Importance of Inventory
Average Firm Carries 10,000 – 50,000 Items of inventory
Typical Value of Inventory: 10% – 60% of Production Cost
National Inventory Value: 20% – 30% of US GNP
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Inventory Examples
Boeing Aircraft – $10.5 billion Inventory with $25.5 billions in Sales
Saks Fifth Avenue – $543.1 millions Inventory with $2.2 billions in Sales
Barnes & Noble – $852 millions Inventory with $2.8 billions in Sales
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Definition
Stock, Materials, Paperwork or Other Resources Used in an Organization to Produce a Final, Useable Product
The Final Product Before Use or Sale
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Types of inventory
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Types of Inventory
Raw Materials
Finished Products
Component Parts
Supplies
Work In Progress
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Why Would We Want Inventory?
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Why Would We WantInventory?
To Maintain Independence of Operations
To Meet Variation In Product Demand
To Allow Flexibility in Production Scheduling
To Provide a Safeguard for Variation in Raw Material Delivery Time
To Take Advantage of Economic Purchase Order Size
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Inventory Measures
Number of Units
Dollar Value
Weeks of Supply
Inventory Turnover
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Inventory Systems
2 BIN
ABC
EOQ
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Costs of InventoryBroad Categories
Holding or Carrying Costs
Acquisition Costs
Ordering Costs
Shortage Costs
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Holding Costs
Storage (Rent & Maintenance), Energy (Heat, Light, Refrigeration), and Handling
Cost of Capital
Insurance
Spoilage, Pilferage & Damage
Obsolescence
Property Taxes
Information processing
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Set Up Costs
Machine & Tool Adjustment
Cleaning
Material Handling
Scrap
Start Up
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Ordering Costs
Administrative and Clerical
Transportation
Insurance
Handling and Inspection
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Shortage Costs
Lost Sales (Present)
Lost Sales (Future)
Backordering
Extra Shipping
Loss of Goodwill
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Types of Inventory Systems
Designed to Account for Variable, Independent Demand
Designed to Recognize Planned, Dependent Demand
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Dependent Demand
Material Requirement Planning (MRP)
Demand is Known or Predicted
Aggregate Plan/Customer Orders/Forecasts
Master Schedule
Eliminate Variability/ Establish Priorities
Getting the Right Materials to the Right Place at the Right Time
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MRP
How Many Items Do We Want to Make and When? – Master Schedule
Final Demand “Exploded” Into Parts Needed – Bill of Materials
Plan Backwards From When You Need Final Parts Given the Assembly Procedure
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Independent Demand
Fixed Order Quantity- Order Same Amount Each Time, Order When Inventory Position Drops Below the Reorder Point (Inventory Position Equals Inventory On Hand Plus On Order Minus Backorders or Shortages)
Fixed Order Period -Review Inventory Position At Same Intervals and Order Amount To Return Your Position To The Calculated Base Stock Level
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Continuous review Models
Inventory is continuously monitored.
Order placed whenever inventory goes below a re-stocking level.
The amount ordered is a constant
Useful when a computerized system is used to manage inventory.
Examples: ordering stationary in an office; Just-In-Time production system in automobile manufacturing.
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EOQ Model Assumptions
Single product or item
Demand rate known and constant
Item produced in lots, or purchased in orders
Each lot or order received in single delivery
Lead time known and constant
Ordering, or setup costs are constant
No backorders are allowed
No quantity discounts are allowed
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General Inventory Representation
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Reorder Point (ROP)
Time
Inventory Level
AverageInventory (Q*/2)
Lead Time
Optimal Order Quantity(Q*)
Economic Order Quantity (EOQ)
Find Optimal Order Size to Minimize Holding Costs Plus Ordering Costs
Larger Order Size Higher Holding Costs Lower Ordering Costs (Fewer Orders)
Smaller Order Less Holding Cost Higher Ordering Costs (More Frequent Orders)
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Definitions
D = Average Annual Demand
S = Ordering Cost ($ per Order)
H = Unit Holding Cost Per Year ($/Unit/Yr)
Alternate: H = I x C, where
I = Inventory Carrying Charge per $ Value of Inventory Per Year
C = $ Value Per Unit
Q = Order Quantity
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Annual Inventory Cost
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Total Cost:
Total Annual = Cost
Annual Ordering + Cost
Annual Cost Of Items +
Ordered
Annual Holding Cost
EOQ Model Equations
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Re-ordering point:
Optimal Order Quantity:
Expected Number of Orders:
Expected Time Between Orders:
Days:
Total Cost:
EOQ Model Application
An EOQ model is applicable when
Demand does not change significantly from one ordering period to another
Example: long lifecycle stable products such as groceries, automobile components, chemicals, heavy industrial equipment, etc.
Demand can be forecasted accurately. In other words, it has less randomness
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Practice Problem
For the following set of numbers, calculate and plot on one graph the ordering cost, the holding cost, and the total cost. Also calculate the reorder point. Calculate EOQ.
Annual Demand = 1,000 units (365 days)
Cost to Place an Order = $10, Holding Cost per unit per year = $2.50, Unit Cost = $15
Lead Time = 7 days
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EOQ With Variablity
Probabilistic Model
Variability in Demand and Supply Lead Times
Lead Time Demand: Demand during leadtime
Leadtime demand follows normal distribution (forecasting)
Other EOQ assumptions apply
Result: You Need Safety Stock
Trade Off of Lost Use or Sales vs. Overstocking
How much & when to order
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Safety Stock Computation
Leadtime demand is a normal distribution
Decide on the target performance (service level) α (i.e 99%)
Find the corresponding level of inventory ROP
Likelihood that leadtime demand is smaller than ROP is α
ROP = μld + Safety Stock = μld + sld * z*
z* is such that F(z) = α
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red area = a
zs
m
ld = N(m,s)
F(z) = area = a
z
0
N(0,1)
Safety Stock
Consider service level & safety stock
Service level = 1 – Probability of stockout
Higher service level means more safety stock
More safety stock means higher ROP
ROP = mean of leadtime demand + safety stock
Safety stock = standard deviation of leadtime demand × z,*
z* is determined by the desired service level
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Probabilistic Models: When to Order?
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Safety Stock (SS)
Time
Inventory Level
X
SS
ROP
Service Level
P(Stockout)
Frequency
ROP
Lead Time
Place order
Receive order
Mean demand during leadtime
ROP = re-order point
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Standard Normal Distribution
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F(z)
z
0
F(z) = Prob( N(0,1) < z)
= 98.7% implies z* = 2.23
Transform back, knowing z*
ROP = m + z*s
Probabilistic Models Examples
1. Demand during leadtime for one brand of TV is normally distributed with a mean of 36 TVs and a standard deviation of 15 TVs. What safety stock should be carried for a 90% service level? What is the appropriate reorder point?
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Probabilistic Models Examples
2. Based on available information, the daily demand for iPhones averages 10 units (normally distributed), with a standard deviation of 1 drive. The leadtime is exactly 5 days. Management wants a 97% service level. What safety stock should be carried? What is the appropriate reorder point?
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Other Inventory Control Systems
Continuous review systems: each time a withdrawal is made from inventory, the remaining quantity is reviewed to determine whether an order should be placed.
Periodic review systems: the inventory of an item is reviewed at fixed time intervals, and an order is placed for the appropriate amount.
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Fixed Period Models (fixed review)
Orders placed at fixed intervals, e.g., once a week or once a month
Inventory is brought up to target amount
The amount ordered is not constant but varies because of randomness of demand
No continuous inventory count
Since inventory is counted once a period, there is a possibility of stockout between intervals
Useful when vendors visit routinely
Example: P&G representative calls every 2 weeks
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Fixed Period Models (fixed review)
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Time
Inventory Level
Target maximum
1 Period
1 Period
1 Period
Demand
How much to Order ?
Continuous review Models
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Time
Inventory Level
Reorder point
Demand
Order quantity
Time between orders is not fixed
When to Order?
Continuous vs. periodic review
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Continuous Review
System Advantages
Lower Safety Stock
Fixed lot size may make it easier to obtain quantity discounts
Individual review of items is used and this may be very desirable for expensive items
Periodic Review
System Advantages
Less time consuming and expensive to maintain
Allows combining orders to the same supplier
Inventory record keeping costs can be reduced
