1. Inventory Control: Part 3 –Independent Demand Inventories

2. Types of Inventories By Function - Lot-Size (Cycle or Replenishment)
- Instantaneous (Purchase)
- Non-Instantaneous (Produce)
- Safety (Fluctuation or Buffer)
- Anticipation (Seasonal)
- Transportation (Pipeline)
- Hedge (Beyond Scope of Class)

3. Safety Stocks Used for Emergencies
Finished Goods: Unexpected Demand (Level Related to Customer Service)
Raw Materials: Orders Not Received
Work-in-Process (WIP): Worker Unavailable or Machine Breakdown - Decoupling Inventory
Also Known as Buffer or Fluctuation Inventory

4. Finished Goods Safety Stocks: Stored with Lot-Size StocksLT
Time
Expected demand
during lead time (DDLT)
Maximum probable demand
during lead time OP
Quantity
Safety stock (SS)

5. Safety Stocks
From Graph: OP = DDLT + SS where OP = Order Point DD = Forecast Demand LT = Lead Time SS = Safety Stock
So: SS = OP – DDLT by Algebra
OP Set from Customer Service Level (SL)

6. Safety Stocks Example 1
The Frigid Corporation manufactures refrigerators. The probability distribution of demand during lead time is:
Demand Probability
Suppose the customer service level is 70%. Determine the reorder point (consider only 10, 20, 30, 40, 50).

7. Safety Stocks Example 1 Let SL = .7 (70%) Demand Probability CDF 
OP = 30 (Meets Demand 70% of Time)

8. Safety Stocks Example1 SS = OP – DDLT DDLT= Expected Value of Demand
If SL is 80%, What is OP and SS?
If SL is 90%, What is OP and SS?

9. Safety Stocks: Normal Demand
Risk of
a Stock Out
Probability of
No Stock Out (Service Level)
Safety
Stock
Mean OP
Quantity

10. Safety Stocks Example 2
The Inandout Production Company requires steel rods at the mean rate of 35 rods per day. This rate follows a normal distribution with a standard deviation of 3 per day. The service level has been set at 90%. If lead time for reordering is one day, what is the optimum safety stock?

11. Safety Stocks: Example 2
Given: SL = .9 (90%), DDLT = 35, DDLT = 3
Z from Normal Table (text page 314) = 1.28
( Z is also known as safety factor)
Z = (OP – DDLT) / DDLT or
OP = DDLT + Z DDLT = 35 + (1.28)(3)  39
SS = OP – DDLT = 39 – 35 = 4

12. Types of Inventories Type Best Size 1. Lot-Size a. Instantaneous Q*/2
b. Non-Instantaneous IMAX*/2
2. Safety OP - DDLT
3. Anticipation Guesstimate
4. Transportation (Usage) (Time)
5. Hedge Guesstimate

13. Implementation of Inventory Control
Q* and N* Cannot Both be Fixed (E.g. Q* = 10, A= 100, N* = A/Q* = 100/10 = 10)
N Varies and Q* Fixed: Order Point System (AKA Fixed Order Quantity). Requires Two-Bin System, Kanban, or Perpetual Inventory. Order say Q* when Actual Inventory ≤ OP.
Q Varies and N* Fixed: Periodic Review System (AKA Fixed Order Cycle System)

14. Periodic Review System
Let T = D (R + LT) + SS Where
T = Target Inventory Level
D = Demand per Unit of Time
LT = Lead Time
R = Review Period (Fixed at 1/N*)
SS = Safety Stock
Order Q = T – I Where
I = Inventory on Hand.
See Example on Page 321 of Text.