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 Stocks

LT Time

Expected demandduring lead time (DDLT)

Maximum probable demandduring lead time

OP

Qu

anti

ty

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

10 .20

20 .20

30 .30

40 .20

50 .10

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

10 .2 .220 .2 .430 .3 .7 40 .2 .950 .1 1.0

OP = 30 (Meets Demand 70% of Time)

8

Safety Stocks Example1

SS = OP – DDLT

DDLT= Expected Value of DemandDDLT= .2(10)+.2(20)+.3(30)+.2(40)+.1(50)DDLT= 28

SS = 30 – 28 = 2

If SL is 80%, What is OP and SS? If SL is 90%, What is OP and SS?

9

Safety Stocks:Normal Demand

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 ofInventory 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 LevelD = Demand per Unit of TimeLT = Lead TimeR = Review Period (Fixed at 1/N*)SS = Safety Stock

Order Q = T – I WhereI = Inventory on Hand.

See Example on Page 321 of Text.

15