2. C 11 Inventory Management
Pencils, papers, clips, advertisements-flyer, visiting cards, nuts, bolts, trucks, needles, airplanes
Raw materials, semi-finished goods, finished goods
What is the worth?
Let top management see the money withheld 

3. Inventory- a stock or store of goods
Independent Demand
B(4)
E(1)
D(2)
C(2)
F(2)
D(3) A
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.

4. Inventory Models
Independent demand – finished goods, items that are ready to be sold
E.g. a computer
Dependent demand – components of finished products
E.g. parts that make up the computer

5. Types of Inventories Raw materials & purchased parts
Partially completed goods called work in progress
Finished-goods inventories
manufacturing firms
retail stores (merchandise )
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers

6. Functions of Inventory
To meet anticipated demand
Anticipation stock
To smooth production requirements
Seasonal demand (e.g. Potato case!)
To decouple operations
Buffer for continuous operation
To protect against stock-outs
Delayed delivery, abrupt demand
Safety stocks

7. Functions of Inventory …
To take advantage of order cycles
Purchasing, Producing in Batches (Lots)
Cycle stock for periodic
To help hedge against price increases
Oil price
To permit operations
Intermediate Stocks (WIP)
Pipeline inventory
To take advantage of quantity discounts

8. Objective of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service
Costs of ordering and carrying inventory
Inventory turnover
Ratio of average cost of goods sold to average inventory investment.
Days of inventory on hand

9. Effective Inventory Management
A system to keep track of inventory (and S.O.)
A reliable forecast of demand
Knowledge of lead times (and variability)
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system

10. Inventory Counting Systems
Periodic System
Physical count of items made at periodic intervals
Small Retailers- checks and orders replenishment
Perpetual Inventory System
Keeps track of removals from inventory continuously, thus monitoring current levels of each item
Reorder point Q
Also requires periodic counting
Errors, pilferage, spoliage
Cost?

11. Inventory Counting Systems …
Two-Bin System - Two containers of inventory; reorder when the first is empty
2nd cart has enough inventory for the lead time
Order card
Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached

12. Key Inventory Terms
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply

13. The Inventory Cycle- Figure 12.2 Profile of Inventory Level Over TimeQ
Usage
rate
Quantity
on hand
Reorder
point
Time
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time

14. ABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A - very important
B - mod. important
C - least important
Annual
$ value
of items A B C
High
Low
Percentage of Items
Example 1- P 549

15. Cycle Counting A physical count of items in inventory
Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?

16. Economic Order Quantity Models
Economic order quantity (EOQ) model
The order size that minimizes total annual cost
Economic production model
Quantity discount model

17. Total Cost* Annual carrying cost Annual ordering cost Total cost* = +Q 2 H D S +
TC =

18. Cost Minimization Goal- Figure 12.4C
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q) QO
(optimal order quantity)
Minimum Total Cost

19. Only one product is involved
Annual demand requirements known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
Assumptions of EOQ Model

20. Deriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D S =

21. Economic Production Quantity (EPQ)
Production done in batches or lots
Capacity to produce a part exceeds the part’s usage or demand rate
Similar to EOQ
Orders are received incrementally during production
Assumptions
Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continually
Production rate is constant
Lead time does not vary
No quantity discounts

22. Economic Run Size We do not buy the product. We produce it.
Total demand / year is D
Demand / day or consumption rate is u
Production rate is p / day

23. Instantaneous Replenishment
Incremental Replenishment

24. EPQ: Incremental Replenishment (Production and Consumption)
p-u
Demand / day or consumption rate is u
Production rate is p / day
u × ( number of working days ) = D = Total demand per year

25. EPQ: Ordering Cost and Carrying Cost
State Imax in terms of Q!

26. EPQ : Production & Consumption; rate & time
How much do we produce each time? Q
How long does it take to produce Q? d1
What is our production rate per day? p
How long does it take to consume Q? d1 +d2
What is our consumption rate per day ? u
p-u u
I max d1 d2

27. Example- What is the optimal production size?
A toy manufacturer
Uses parts for one of its products.
Consumption rate is uniform throughout the year.
Working days are 240 / year.
The firm can produce at a rate of 800 parts / day
Carrying cost is $1 / part / year
Setup cost for production run is $45 / setup

28. What is Run Time, What is Cycle Time
Q0 using formula = 2400
u = /240 = 200 units/day
p-u u
I max d1 d2

29. What is the Optimal Total Cost

30. EPQ : Optimal Q

31. Reorder Point- ROP Reorder Point
When the quantity on hand of an item drops to this amount, the item is reordered
If setup time takes 2 days, at which level of inventory we should start setup?
2(200) = 400
200 ?

32. Yet Another Example
A company has a yearly demand of 120,000 boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year.
a) What is the demand rate per day
b) What is the Economic Production Quantity (EPQ)
c) What is the run time
d) What is the maximum inventory
e) What is the total cost of the system

33. Yet Another Example … =16000 What is the demand rate per day
Demand per year is 120,000 there are 240 days per year
Demand per day = /240 = 500
u = D/240 = 500
b) What is the Economic Production Quantity (EPQ)
=16000

34. Yet Another Example … c) What is the run time
We produce units
Our production rate is 2000 per day
It takes 16000/2000 = 8 days
d1 = EPQ/p = 8 days
d) What is the maximum inventory
We produce for 8 days. Each day we produce 2000 units and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That is
Imax = 8(1500) = 12000
Imax = pd1 = 8(1500) = 12000

35. Yet Another Example …
e) What is the total cost of the system

36. Including the Purchasing Cost
Annual
carrying
cost
Purchasing
TC = + Q 2 H D S
ordering PD
Including the Purchasing Cost

37. Total Costs with Vs. Quantity Ordered
EOQ
TC with PD
TC without PD PD
Quantity
Adding Purchasing cost doesn’t change EOQ

38. Total Cost with Constant Carrying CostsOC
EOQ
Quantity
Total Cost
TCa
TCc
TCb
Decreasing
Price
CC a,b,c

39. Total Cost with Variable Carrying Costs
Do the Math
Ex 5, 6
Total Cost with Variable Carrying Costs

40. ROP with EOQ Ordering Safety Stock Service Level
When to Reorder
Safety Stock
Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
Service Level
Probability that demand will not exceed supply during lead time.

41. Determinants of the Reorder Point
The rate of demand
The lead time
Demand and/or lead time variability
Stockout risk (safety stock)

42. Safety Stock- Figure 12.12 Quantity Maximum probable demandLT
Time
Expected demand
during lead time
Maximum probable demand
ROP
Quantity
Safety stock
Safety stock reduces risk of
stockout during lead time

43. Reorder Point- Figure 12.13 The ROP based on a normal
See also: Fig 11.14
The ROP based on a normal
Distribution of lead time demand
Service level
Risk of
a stockout
Probability of
no stockout
ROP
Quantity
Expected
demand
Safety
stock z
z-scale
ROPs = Exp. Demand + z. σdLT

44. Shortage and Service Level
Service level determines ROP
E(n) = E(z) z σdLT
E(n) = Expected number of short/cycle
E(z) = Standardized number of units-short from table 11.3
σdLT = Standard deviation of lead time
Example Page 568

45. Fixed-Order-Interval Model
Orders are placed at fixed time intervals
Order quantity for next interval?
Suppliers might encourage fixed intervals
May require only periodic checks of inventory levels
Risk of stockout
Fill rate – the percentage of demand filled by the stock on hand

46. Calculations
Ex 13

47. Fixed-Interval tradeoffs
Benefits
Tight control of inventory items
Items from same supplier may yield savings in:
Ordering
Packing
Shipping costs
May be practical when inventories cannot be closely monitored
Disadvantages
Requires a larger safety stock
Increases carrying cost
Costs of periodic reviews

48. Single Period Model Model for ordering items with limited useful lives
Perishables
Shortage cost is generally the unrealized profits per unit
Excess cost is the difference between purchase cost and salvage value of items left over at the end of a period
Continuous stocking levels
Identifies optimal stocking levels
Optimal stocking level balances unit shortage and excess cost
Discrete stocking levels
Service levels are discrete rather than continuous
Desired service level is equaled or exceeded

49. Optimal Stocking Level
Service level = Cs
Cs + Ce
Cs = Shortage cost per unit Ce = Excess cost per unit
Service Level So
Quantity Ce Cs
Balance point

50. Example 15 Stockout risk = 1.00 – 0.75 = 0.25 Ce = $0.20 per unit
Cs = $0.60 per unit
Service level = Cs/(Cs+Ce) = .6/(.6+.2)
Service level = .75
Service Level = 75%
Quantity Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25

51. Operations Strategy Too much inventory Wise strategy
Tends to hide problems
Easier to live with problems than to eliminate them
Costly to maintain
Wise strategy
Reduce lot sizes
Reduce safety stock

53. Learning Objectives
Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management.
Discuss the nature and importance of service inventories
Discuss periodic and perpetual review systems.
Discuss the objectives of inventory management.
Describe the A-B-C approach and explain how it is useful.

54. Learning Objectives
Describe the basic EOQ model and its assumptions and solve typical problems.
Describe the economic production quantity model and solve typical problems.
Describe the quantity discount model and solve typical problems.
Describe reorder point models and solve typical problems.
Describe situations in which the single-period model would be appropriate, and solve typical problems.