1. Chapter 5: Inventory Management
Department of Business Administration
FALL
Chapter 5: Inventory Management

2. Outline: What You Will Learn . . .
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.

3. Outline: What You Will Learn . . .
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.

4. Inventory Management
Inventory management is a core operations management activity.
Good inventory management is important for the successful operation of most businesses and their supply chains.
Operations, marketing, and finance have interests in good inventory management.
Bad inventory management hampers operations, diminishes customer satisfaction, and increases operating costs.

5. Objective of Inventory Management
The basic objective of Inventory Management has traditionally been to keep inventory at desired level that will meet product demand and be cost effective.
The major objective of Inventory Management (control system) is to discover and maintain the best possible level of inventory in terms of both unit of product and least possible cost.
In reaching such objectives firms seek out to avoid two common pitfalls.
Management tries to avoid the problem inadequate levels of inventory since too little inventory disrupts production and may results in lost sales.
The existence of too many inventories increases the risk of obsolescence and create unnecessary cost levels.

6. Inventory
Inventory is a stock or store of goods .
Inventory can also be defined as a stock of materials created to satisfy to satisfy eventual demand.
Inventories are idle resources of any kind that possess economic value and held for future use.
Items in inventory ranges from small things such as pencils, paper clips, screws nuts and bolts to large items such as machines, trucks, construction equipment and air planes.

7. Inventory
Inventories are present whenever the inputs and outputs of a company are not used as soon as they become available .
Inventory can be thought as a final product waiting to be sold to a retail customer e.g., a new car, canned foods or drinks, and baked goods.
Inventories contain not only finished goods but also raw materials, supplies, and spare parts.
Some very large firms have tremendous amounts of inventory. For example general motor was reported to have as much as $ 40 mn worth of materials, parts, cars and trucks in its supply chain.
The ratio of inventories to sales in manufacturing, wholesale and retail sectors is one measure that is used to determine health of an economy. Inventories may represent a significant proportion of total asset. It is worth to mention that a reduction of inventories can results in a significant increase in return on investment (ROI is profit after taxes diveded by total asset).

8. Inventory
Inventory decisions in service organization can be especially critical. For example , hospital- being out of stock on some important supplies such as drugs imperil the well-being of a patient.
Many inventory items have a limited shelf life so carring large quantities would mean having to dispose of unused, costly supplies.
On-site repair services for computers, printers and fax machines also have to carefully consider which parts to bring to the site to avaid having to make extra trip to obtain parts.
The major revenue for wholesale and retail business is sale of Inventory. In terms of dollar, the inventory of goods held for sale is the one of largest assets of merchandising business.

9. Inventory
Independent demand – finished goods, items that are ready to be sold
E.g. a computer
Dependent demand – components of finished products
E.g. parts such as chip and system unit that make up the computer

10. Independent demand is uncertain. Dependent demand is certain.
Inventory
Independent Demand A
B(4)
C(2)
D(2)
E(1)
D(3)
F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.

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

12. Functions of Inventory
To meet anticipated demand
A customer can be a person who walks in off the street to buy a new stereo system. These inventories are referred to as anticipation stocks because they are held to satisfy expected demand.
To smooth production requirements
Firms that experience seasonal patterns in demand often build up inventories during preseason period to meet overly high requirements during seasonal period. These inventories are aptly named seasonal inventories. i.e., fresh fruits and vegetables or x-mas cards or greeting cards.

13. Functions of Inventory
To decouple operations
Firms use inventories as buffers between successive operations to maintain continuity of production and breakdown of equipment and accidents that cause the operation to shut down temporarily.The buffers permit other operation to continue temporarily while the problem is solved.
To protect against stock-outs
Delayed deliveries and unexpected increase in demand rise the risk of shortages. Delays can occurs because of whether conditions, suppliers out-stocks, deliveries of wrong materials, quality problems and so on. This risk of shortage can be reduced by holding safety stocks.

14. Functions of Inventory
To take advantage of order cycles
To minimize purchasing and inventory costs, firms often buy in quantities that exceed immediate requirement. This necessites storing some or all of the purchased amount later use. Similarly, it is usually economical to produce in large rather than small quantities. This inventory storage can used later with demand requirements in short-run.
To help hedge against price increases
Firms will suspect that a substantial price increase is about to occur and purchase larger than normal amounts to beat the rise. The ability to store extra amount of goods also allows firms to take advantage of price discounts for larger orders

15. Functions of Inventory
To permit operations
The fact that production operations take a certain amount of time that there will be some work in process including raw materials, semifinished items, unfinished items and finished goods at production site as well as goods stored in warehouse. This leads to pipeline inventories throughout a production-distrubution system.
Little’s Law can be useful in quantifying pipeline inventory.
Little’s Law: the average amount of inventory in a system is equal to the product of average rate at which inventory units leave the system and average time a unit is in the system.
To take advantage of quantity discounts
Suppliers may give price discounts for larger orders.

16. Objective of Inventory Control (IC)
Inaduqate control of inventories can results in both under and over stocking of items.
Understocking results in missed deliveries, lost sales, dissatisfied customers and production bottle necks
Overstocking results in unnecessarily ties up funds that might be more productive elsewhere
Objective: To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service (right time, right quantity)
Costs of ordering and carrying inventory (right place, size)
Inventory turnover is the ratio of average cost of goods sold to average inventory investment (performance of IC).

17. Effective Inventory Management
To be effective, Management has two basic fuctions concerning inventory; 1- establishing system, 2- making decision. The following should be taken into account:
A system to keep track of inventory
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system for inventory items.

18. Inventory Counting Systems
Inventory counting system can be either periodic or perpentual:
Periodic System
Physical count of items in inventory made at periodic intervals such as weekly, monthly etc..many small retailers use this approach. i.e., shelves, stock room etc..
Perpetual Inventory System(continual system) A system that keeps track of removals from inventory continuously, thus monitoring current levels of each item
Two-Bin System – It is very elementary system.Two containers of inventory; reorder when the first is empty. Second bin contains enough stock to satisfy expected demand.
Universal Bar Code (UPC) - Bar code printed on a label that has information about the item to which it is attached. i.e., supermarkets, discount stores etc..

19. 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

20. ABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A more reasonable approach would be to allocate control efforts according to the relatively importance of various items in inventory.
A - very important
B - mod. important
C - least important
Annual
$ value
of items A B C
High
Low
Percentage of Items

21. Cycle Counting A physical count of items in inventory
The purpose of Cycle counting is to find out the real amount between the amount indicated by inventory records and actual quantities of inventory on hand
Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?

22. Example-ABC approach
Using the following annual demand & unit cost and calculate annual dollar value in each raw.
Having computed the annual dollar values, use the concept of ABC classification and array from highest to lowest
Item Number
Annual demand
Unit Cost
Annual Dollar Value
Classification 8
1000
$ 4000 5
3900
700 3
1900
500 6
915 1
2500
330 4
1500
100 12
400
300

23. Example-ABC approach
The first two items have relatively high annual dollar value, so it seems reasonable to classify them as A items. The next three items appear to have moderate annual dollar values and should be classified as B items. The remainder are C items due to their relatively low annual dollar value.
Item Number
Annual demand
Unit Cost
Annual Dollar Value
Classification 8
1000
$ 4000    A 5
3900
700   3
1900
500
 950000 B  6
915
 915000  B 1
2500
330
825000  4
1500
100
150000   C 12
400
300
120000  C 

24. Economic Order Quantity Models (Ford Harris, 1915)
The question of how much to order is frequently determined by using an economic order quantity model (EOQ).
(EOQ) models identify the optimal order quantity by minimizing the sum of certain annual cost that vary with order size. Three order size models are described here:
The Basic Economic Order Quantity (EOQ) model
The Economic Production Quantity Model
Quantity Discount Model

25. Basic Economic Order Quantity Models
The basic economic order quantity model (EOQ) is the simplest of the three model. It is used to identify a fixed order size that minimize the sum of annual cost of holding inventory and ordering inventory. The unit purchase price of items in inventory is not generally included in the total cost because the unit cost is unaffected by the order size unless quantity discounts are a factor. If holding costs are specified as a percentage of unit cost, then unit cost is indirectly included in the total cost as a part of holding costs.

26. Assumptions of the basic EOQ Model
Only one product is involved
Annual demand requirements are known
Demand is spread evenly throughout the year so that the demand rate is reasonably constant
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts

27. Profile of Inventory Level Over Time
The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time
Order size=350 units Useage rate= 50 units per day Lead time= 2 days Reorder point= 100 units

28. Total Cost Annual carrying cost Annual ordering cost Total cost = + Q2 H D S +
TC =
Two basic inventory costs; Ordering Cost: are the basically the costs of getting the items into firm inventory, therefore these costs are the cost of replenishing inventory. Carring or holding cost: are the basically the costs incurred due to maintainance of inventories or are the costs of holding items in storage. As order size varies, one of type of cost will increase whilst the other decreases. The greater level of inventory over time, the higher the carring costs exist

29. The relationship between the type of costs
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q) QO
(optimal order quantity)

30. The relationship between the type of costs
Carring costs are linearly related to order size
Ordering costs are inversely and non linearly related to order size
Total cost curve is U-shape
The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D S =

31. 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.

32. Example- EOQ model
A local distributor for a national tire company expects to sell approximately 9600 steel-belted radial tires of a certain size and tread design next year. Annual carring cost is $ 16 per tire, and ordering cost is $ 75. The distributor operates 288 days a year.
(a) What is the EOQ?
(b) How many times per year does the store reorder?
(c) What is the length of an order cycle?
(d) What is the total annual cost if the EOQ quantity is ordered?

33. Example- EOQ model-Answer
(a) What is the EOQ?
(b) How many times per year does the store reorder?
(c) What is the length of an order cycle?
(d) What is the total annual cost if the EOQ quantity is order?

34. Example- Optimal Quantity
Piddling manufacturing assembles security monitors. It purchases 3600 black and white cathode ray tubes a year at $ 65 each. Ordering costs are $ 31, and annual carring costs are 20 percent of the purchase price.
(a) Compute the optimal quantity
(b) What is the carring cost?
(c) What is the ordering cost?
(d) Calculate the total annual cost ?

35. Example- Optimal Quantity-Answer
(a) Compute the optimal quantity
(b) What is the carring cost?
(c) What is the ordering cost?
(d) Calculate the total annual cost ?

36. Economic Production Quantity (EPQ)
Production done in batches or lots. Even in assembly operations, portions of the work are done in batches.
Capacity to produce a part exceeds the part’s usage or demand rate
As long as production continious, inventory will continue to grow.
This makes sense to periodically produce such items in batches or lots instead of producing continually.
Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

37. Economic Production Quantity 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

38. Setup Cost and Economic Run Size (quantity)
In the case of EPQ, there are no ordering cost, however there are setup costs-the costs required to prepare the equipment for the job, such as cleaning, adjusting changing tools etc.
Setup costs are analogous to ordering costs because they are independent of the lot or run size.
The larger run size, the fewer the number of runs needed as well as the lower the annual setup cost.
D/Q is the number of batches per year.
DS/Q0 is setup cost.

39. Example- Run size
A toy manufacturer uses rubber wheels per year for its popular damp truck series. The firm makes its own wheels which it can produce at the rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carring cost is $ 1 per wheel a year. Setup cost for a production run of wheels is $ 45. The firm operates 240 days per year. Determine
(a) Optimal run size
(b) Minimum total annual cost for carring and setup
(c) Cycle time for the optimal run size
(d) Run time

40. Example- Run size-Answer
(a) Optimal run size
(b) Minimum total annual cost for carring and setup
(c) Cycle time for the optimal run size
(d) Run time

41. The Quantity Discount Model
Quantity discount rate are price reductions for large orders offered to customers to induce them to buy in large quantities.
As prices decrease order of quantities increase.
The buyer’s goal with quantity discount rate is to select the order quantity that minimize total cost in the following equation where p is unit price
Annual
carrying
cost
Purchasing
TC = + Q 2 H D S
ordering PD

42. The Quantity Discount Model
In the basic EOQ model, determination of order size does not involve the purchasing cost. The rationale for not including unit price is that under the assumption of no discount discounts, price per unit is the same for all order sizes.
Inclusion of unit price in the total cost computation in that case would merely increase the total cost by the amount P times D
A graph of total annual purchase cost versus quantity would be a horizontal line. Hence, including purchasing costs would only raise the total cost curve by the same amount (PD) at every point. In the following graph, that would not change the EOQ.

43. Total Costs with PD Cost Adding Purchasing cost doesn’t change EOQ
TC with PD
TC without PD PD
Quantity
Adding Purchasing cost doesn’t change EOQ

44. The Quantity Discount Model
When quantity discounts are offered, there is a separate U-shaped total cost curve for each unit price. Again, including unit prices merely raises each curve by a constant amount.
However, because the prices are all different, each curve is raised by a different amount.
Smaller unit prices will raise a total cost curve less than large unit prices
In the following graph, no one curve applies to the entire range of quantities and each curve applies to only a portion of the range. Hence the applicable or feasible total cost is initially on the curve with highest unit price and then drops down curve by curve at the price breaks which are the minimum quantities needed to obtain the discount.

45. Total Cost with Constant Carrying Costs
Comparison of TC curves for constant carrying costs and carrying costs that are a percentage of unit costs. When carrying costs are constant, all curves have their minimum points at the same quantity. When carrying costs are stated as percentage of unit price, the minimum points do not line up.
TCa
TCb
Decreasing
Price
Total Cost
TCc
CC a,b,c OC
EOQ
Quantity

46. Example- Discount Model
The maintenance department of a large hospital uses about 816 cases of luquid cleanser annually. Ordering costs are $ 12, Carring cost are $ 4 per case a year and the new price schedule indicates that orders of less than 50 cases will cost $ 20 per case, 50 to 79 cases will cost $ 18 per case, 80 to 99 cases will cost $ 17 per cases and larger orders will cost $ 16 per case.
Determine
(a) the common minimum point for EOQ
(b) the total cost if the feasible minimum point is on the lowest price range, that is the optimal order quantity.
(c) the total cost if the feasible minimum point is in any other price range.
Range
Price
1 to 49
$ 20
50 to 79 18
80 to 99 17
100 or more 16

47. Example- Discount Model -Answer
Range
Price
1 to 49
$ 20
50 to 79 18
80 to 99 17
100 or more 16
(a) the common EOQ
(b) total annual cost
(c) total annual cost
TC = Carrying cost + Order cost + Purchase cost
The cases can be bought at $ 18 per case because 70 falls in the range of 50 to 79 cases.

48. Example 2- Discount Model
Surge Electric uses 4000 toggle switches a year. Switch are priced in the following table. It costs approximately $ 30 to prepare an order and receive it, and carring costs are 40 percent of purchase price per unit on an annual basis.
Range
Price
1 to 449
$ 0.90
500 to 999
0.85
1000 or more
0.80
Determine
(a) the common EOQ
(b) the total cost if the feasible minimum point is on the lowest price range, that is the optimal order quantity.
(c) the total cost if the feasible minimum point is in any other price range.

49. Example- Discount Model -Answer
Range
Price
1 to 449
$ 0.90
500 to 999
0.85
1000 or more
0.80
(a) the common minimum point or EOQ
(b) total annual cost
(c) total annual cost
H= 0.40 P
H= 0.40 (0.80)=0.32
H= 0.40 (0.85)=0.34
TC = Carrying cost + Order cost + Purchase cost

50. When to Reorder with EOQ Ordering
Reorder Point (ROP) – This point occurs When the quantity on hand of an item drops to a predetermined amount, the item is reordered.
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.

51. Determinants of the Reorder Point
The rate of demand
The lead time
Demand and/or lead time variability
Stock out risk (safety stock)
If demand and lead time are both constant, the reorder point is simply defined as ROP=(d) x (LT)
Where d = demand rate units per day or week
LT= lead time in days or weeks

52. Example - reorder
Tingly takes two a day vitamins which are delivered to his home by routeman seven days after an order is called in. At what point should Tingly reorder?.
Usage is 2 vitamins per day
Lead time is 7 days
ROP=(2) (7)= 14 vitamins
Thus, Tingly should reorder when 14 vitamin tables are left.

53. Safety Stock Safety stock reduces risk of stockout during lead timeLT
Time
Expected demand
during lead time
Maximum probable demand
ROP
Quantity
Safety stock
ROP= Expected demand in (LT) + safety stock

54. Reorder Point
The ROP based on a normal Distribution of lead time demand
ROP= Expected demand in (LT) + ZαdLT Where z is the number of standard deviationαdLT is the standard deviation lead time demand
ROP
Risk of
a stockout
Service level
Probability of
no stockout
Expected
demand
Safety
stock z
Quantity
z-scale

55. Example – ROP and Z
A manager of a construction supply house determined from historical records that demand for sand during lead time averages 50 tons. In addition, the manager determined that demand during lead time could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons as well as the manager is willingly to accept a stockout risk of no more than 3 percent.
(a) What value of Z is appropriate?
(b) How much safety stock should be held?
(c) What reorder point should be used?

56. Answer– ROP and Z (a) What value of Z is appropriate?
Expected lead time is 50 tons
α dLT=5 tons
risk =3 percent
1-0.03=0.97 from z table (lead time), z= 1.88 (page 569, table 12.3)
(b) How much safety stock should be held?
Safety stock = Z αdLT= (1.88) (5)= 9.40 tons
(c) What reorder point should be used?
ROP= Expected demand in (LT) + ZαdLT = = tons
ROP= Expected demand in (LT) + ZαdLT = = tons

57. Example – shortage and service lead
Suppose standard deviation of lead time demand is known to be 20 units. Lead time demand is approximately normal.
(a) For lead time service level of 90 percent, determine the expected number of units short for any other cycle.
(b) What lead time service level would an expected shortage of 2 units imply?

58. Answer – shortage and service lead
(a) For lead time service level of 90 percent, determine the expected number of units short for any other cycle.
αdLT= 20 units
lead time service level is 0.90 from z table (lead time), (E) z= (page 569, table 12.3)
E(n) =(E)z αdL= (0.048) (20)= 0.96 or about 1 unit.
or E(N) =E (n) (D/Q)
(b) What lead time service level would an expected shortage of 2 units imply?
E(n) = 2
E(n) =(E)z αdL or (E)z = E(n) / αdL =(2)/(20)= from the table, lead time service level is percent or 87%

59. Fixed-Order-Interval Model
Orders are placed at fixed time intervals
Order quantity is 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

60. Fixed-Interval 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

61. Fixed-Interval Disadvantages
Requires a larger safety stock
Increases carrying cost
Costs of periodic reviews

62. Example – Amount to order
Given the following information:
(a) determine the amount to order
Amount to order = expected time during the production interval + safety stock - Amount on hand at reorder time

63. Single Period Model
Single period model: model for ordering of perishables and other items with limited useful lives
Shortage cost: generally the unrealized profits per unit
Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

64. Single Period Model 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

65. 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

66. Example-optimal stocking level
Sweet cider is delivered weekly to Cindy’s bar. Demand varies uniformly between 300 lt and 500 lt per week. Cindy pays 20 cents per liter and charges 80 percent per liter for it. Unsold cider has no salvage value and cannot be carried over into the week due to spoilage.
Find the optimal stocking level and its stockout risk for that quantity
where
Ce = Cost per unit- Salvage value per unit
=$ = $0.20 per unit
Cs = Revenue per unit-Cost per unit
=$0.80-$0.20=$0.60 per unit

67. Answer-optimal stocking level
Ce = $ 0.20 per unit
Cs = $ 0.60 per dozen
Service level = Cs/(Cs+Ce) = 0.60/( )
Service level = .75
S= ( )=450 lt
Service Level = 75%
Quantity Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25

68. Example-Discrete-optimal stocking level
Demand for long-stemmed red roses at a small flower shop can be approximated using a poisson distribution that has a mean of four dozen per. Profit on the roses is $ 3 per dozen. Leftover flowers are marked down and sold the next day at a loss of $2 per dozen. Assume that all marked flowers are sold.
Find the optimal stocking level and its stockout risk for that quantity
where
Ce = Cost per unit- Salvage value per unit
=$ 2 per dozen
Cs = Revenue per unit-Cost per unit
=$ 3 per dozen

69. Answer-Discrete-optimal stocking level
Ce = $ 2 per dozen
Cs = $ 3 per dozen
Service level = Cs/(Cs+Ce) = 3/(3+2)
Service level = .60
It is neccessary to stock 4 dozan.
(D) Dozen per day
Cum.Freq.
0.018 1
0.092 2
0.238 3
0.433 4
0.629 5
0.785
Service Level = 60%
Quantity Ce Cs
Appendix B, Table C
Stockout risk = 1.00 – 0.60 = 0.40

70. Thanks