Üretim 9.1

8/6/2019 retim 9.1

1/63

Inventory Management

8/6/2019 retim 9.1

2/63

Inventory Management Inventory is one of

the most expensive

assets of manycompanies.

It represents asmuch as 40% oftotal investedcapital.

8/6/2019 retim 9.1

3/63

Inventory Management Inventory is any stored resource that is

used to satisfy a current or future need.

Raw materials, work-in-process, andfinished goods are examples ofinventory.

Two basic questions in inventorymanagement are (1) how much to order(or produce), and (2) when to order (orproduce).

8/6/2019 retim 9.1

4/63

Basic Functions of

Inventory 1. If product demand is high in summer,

a firm might produce during winter.(Decoupling).

2. Inventory can be a hedge againstprice changes and inflation.

3. Another use of inventory is to takeadvantage of quantity discounts (when

buying). (Many suppliers offer discounts for

large orders)

8/6/2019 retim 9.1

5/63

ABC Analysis ABC analysis divides on-hand

inventory into three classifications

on the basis of dollar (TL) volume. It is also known as Pareto analysis.

(which is named after principles

dictated by Pareto).

8/6/2019 retim 9.1

6/63

ABC AnalysisThe idea is to focus resources on

the critical few and not on the

trivial many. (Annual Dollar Volume of an Item)

= (Its Annual Demand) x (Its Cost

per unit)

8/6/2019 retim 9.1

7/63

ABC Analysis Class A items are those on which

the annual dollar volume is high.

They represent 70-80% of totalinventory costs, but they accountfor only 15% of total inventory

items.

8/6/2019 retim 9.1

8/63

ABC Analysis Class B items are those on which

annual dollar volume is medium.

They represent 15-25% of totaldollar value, and they account for30% of total inventory items on the

average.

8/6/2019 retim 9.1

9/63

ABC Analysis Class C items are low dollar

volume items.

They represent only the 5% of totaldollar volume, but they include asmany as 50-60% of total inventory

items.

8/6/2019 retim 9.1

10/63

ABC Analysis

8/6/2019 retim 9.1

11/63

ABC Analysis Some of the Inventory Management

Policies that may be based on ABC

analysis include: a) Class A items should have tighter

inventory control.

b) Class A items may be stored in a more

secure area. c) Forecasting Class A items may warrant

more care.

8/6/2019 retim 9.1

12/63

Cycle Counting of

Inventory Inventory records must be verified

through a continuing audit.

Such audits are known as(periodical) cycle counting.. (e.g.,counting items at supermarket).

8/6/2019 retim 9.1

13/63

Cycle Counting of

Inventory Cycle counting uses inventory

classifications developed by ABC analysis.

That is: Class A items are counted frequently,perhaps once a month.

Class B items are counted less frequently,

perhaps once a quarter. Class C items are counted perhaps once

every six months.

8/6/2019 retim 9.1

14/63

Just-in-Time Inventory

Just in Time

Inventory is theminimuminventory that

is necessary tokeep a systemperfectlyrunning.

8/6/2019 retim 9.1

15/63

Just-in-Time Inventory With just in time (JIT) inventory,

The exact amount of items arriveat the moment they areneeded, Not a minute before OR

not a minute after.

8/6/2019 retim 9.1

16/63

Just-in-Time InventoryTo achieve JIT inventory, Managers

should Reduce the Variability

Caused by some Internal and ExternalFactors. (Goldratts boys scout example Apply the pace of the slowest boy).

Existence of Inventory hides thevariability. What causes variability?

8/6/2019 retim 9.1

17/63


Most variability is caused bytolerating waste (inventory).

(1) For example, employees ormachines produce units that do not

conform to standards. These arewaste. And they cause variability.

8/6/2019 retim 9.1

18/63


(2) Or, engineering drawings areinaccurate, Again resulting in loss of

production And consecutivelyresulting in Variability.These are the internal (controllable)

factors that cause Variability. However, Some of the variability is

caused by some external factors.

8/6/2019 retim 9.1

19/63


For example, customer demandsmay change due to some external

factors (such as competitorsactions or promotions)

In summary, To achieve JIT

inventory, Managers must beginwith Reducing Inventory.

8/6/2019 retim 9.1

20/63


Reducing Inventory uncovers theRocks located along the way on a

river, And the water streambecomes more clear.

8/6/2019 retim 9.1

21/63


8/6/2019 retim 9.1

22/63


In the figure, the section calledOthers are the Rocks on the

river.Those rocks include Quality

Variability, In-transit Delays,

Machine Breakdowns, Large Lot-sizes, Inaccurate drawings,Employee attendance variability.

8/6/2019 retim 9.1

23/63

Just-In-Time Production

JIT production means (1) Elimination ofWaste, (2) Synchronized Manufacturing, and(3) Little Inventory.

Reducing the order batch size can be a majorhelp in reducing inventory.

Average Inventory = (Maximum Inventory +

Minimum Inventory) / 2

8/6/2019 retim 9.1

24/63


Average Inventory drops as theinventory re-order quantity drops

because the maximum inventorylevel drops. (show by drawing) Moreover, the smaller the lot size,

the fewer the problems are hidden. One way to achieve small lot sizes

is to Move Inventory through theshop Only as needed.

8/6/2019 retim 9.1

25/63


This is called a pull system. In thissystem, Ideal Lot size is 1.

Japanese call this system asKanban system.

Kanban is a Japanese word for Card.

A card is used to signal the need formaterial in a work center.

8/6/2019 retim 9.1

26/63


Sending a card authorizes theprevious work center to send its

finished batch to the subsequentwork center.

Batches are typically very small.

Such a system requires tightschedules and frequent set-ups formachines.

8/6/2019 retim 9.1

27/63


On the other hand,Small batches allow a

very limited amountof faulty material,less damages, lessspace occupation,

less materialhandling, lessaccidents, etc.

8/6/2019 retim 9.1

28/63

Holding, Ordering andSet-up Costs

Holding Costs are the costsassociated with holding or

carrying inventory over time. It includes costs related to

Storage; such as insurance, extra

staffing, interest, and so on.

8/6/2019 retim 9.1

29/63


Some example holding costs arebuilding rent or depreciation, building

operating cost, taxes on building,insurance on building, materialhandling equipment leasing ordepreciation, equipment operating

cost, handling manpower cost, taxeson inventory, insurance, etc.

8/6/2019 retim 9.1

30/63


Ordering Costs include, cost ofsupplies, order processing, clerical

cost, etc.The ordering cost is valid if the

products are purchased NOT

produced internally.

8/6/2019 retim 9.1

31/63


Set-up costis the cost to prepare amachine for manufacturing an

order. Set-up cost is highly correlated

with set-up time.

8/6/2019 retim 9.1

32/63


Machines that traditionally havetaken long hours to set up Are Now

being set up in less than a minuteby employing FMSs or CIMsystems.

Reducing set up times is anexcellent way to Reduce Inventory.

8/6/2019 retim 9.1

33/63

Inventory Models

Demand for an item is either dependenton the demand for other items or it is

independent. For example, demand for refrigerator is

independent of the demand for cars.

But, demand for auto tires is certainly

dependent on the demand of cars.

8/6/2019 retim 9.1

34/63

Inventory Models

In this section, we will deal with theIndependent Demand Situation.

In the independent demand situation, weshould be interested in answering:

a) When to place an order for an item,and

b) how much of an item to order.

8/6/2019 retim 9.1

35/63

Inventory Models

There are Four Basic IndependentDemand Inventory Models:

1) Economic Order Quantity (EOP)Model (the most known model).

2) Production Order Quantity Model.

3) Back order inventory model.

4) Quantity discount model.

8/6/2019 retim 9.1

36/63

Economic OrderQuantity (EOQ) Model

EOQ model makes a number ofassumptions:

1-) Demand is known and constant.

2-) Lead time (the time betweenplacement of order and receipt of

the order) is constant and known.

8/6/2019 retim 9.1

37/63


3-) Orders arrive in one batch at a time,and they arrive in one point in time.

4-) Quantity discounts are not possible.5-) The costs include only setup cost (or

ordering cost when buying) and holdingcost.

6-) Orders are always placed at the righttimes. Therefore, stock outs (orshortages) can be completely avoided.

8/6/2019 retim 9.1

38/63


With these assumptions, thegraphic of inventory usage over

time is as follows:

8/6/2019 retim 9.1

39/63


8/6/2019 retim 9.1

40/63


Q = order quantity (That is alsoequal to the Maximum Inventory)

Minimum Inventory = 0 When inventory level reaches 0, a

new order is placed and received.

8/6/2019 retim 9.1

41/63


The objective of inventory modelsis to minimize total cost.

If we minimize the setup andholding costs, we will be able tominimize total cost:

8/6/2019 retim 9.1

42/63


8/6/2019 retim 9.1

43/63


As the quantity ordered (Q)increases, holding cost increases,

And setup cost decreases. In this graph, Optimal order

quantity (Q*) occurs at a point

where setup cost is equal to thetotal (annual) holding cost.

8/6/2019 retim 9.1

44/63


By using this fact, we can write anequation for Q* as follows:

D: Annual Demand in units for the inventoryitem.

S: Setup cost (or the ordering cost) for eachorder.

Notice: (Setup cost for production, ordercost for buying).

H: Annual Holding cost of inventory per unit.

8/6/2019 retim 9.1

45/63


There will be (D/Q) times of ordering ina whole year.

Therefore,Annual Setup cost = (D/Q) . S

Average Annual Holding Cost = (AverageInventory) . H = (Q/2) . H

Annual Setup Cost = Annual HoldingCost

(D/Q) . S = (Q/2) . H

8/6/2019 retim 9.1

46/63


Therefore,

Q2 = 2DS / H

Q* = [2DS / H]1/2

Q* value is also called as EOQ.

8/6/2019 retim 9.1

47/63

Example

An Inventory model has the followingcharacteristics:

Annual Demand (D) = 1000 units

Ordering (Setup) cost (S)= $10 per order;

Holding cost per unit per year (H) = $.50

Assume that there are 270 working days in a

year (excluding holidays and weekends).

8/6/2019 retim 9.1

48/63

Example

Questions:

a) Find the Economic Order Quantity (Q*)

for this inventory model.b) How many orders should be placedduring one year?

c) What is the expected time between two

consecutive orders?d) What is the total annual cost of this

inventory model?

8/6/2019 retim 9.1

49/63

Example

Answers:

a) Q* = [2(1000)10 / .50]1/2 = 200

units

b) Expected number of ordersplaced during the year (N) = D / Q*

= 1000 / 200 = 5 times.

8/6/2019 retim 9.1

50/63

Example

c) Expected time between orders (T) =(Working days in a year) / N = 270 / 5

= 54 days.d) Total Annual Cost = Annual Setup

Cost + Annual Holding Cost

= DS / Q* + (Q*)H / 2

= 1000 (10) / 200+ (200) (.50) / 2= $100

8/6/2019 retim 9.1

51/63

Proof of Optimality byUsing Derivation

If we take the derivative of TotalCost (TC) function, based on the

order quantity (Q), we get thefollowing:

TC = DS / Q + (Q)H / 2dTC/dQ = (- DS / Q2) + (H / 2)

f f i li b

8/6/2019 retim 9.1

52/63


As a mathematic rule, if we set thisderived equation equal to zero, we

get the optimal (minimum) point ofthe total cost function:

Therefore,

f f O i li b

8/6/2019 retim 9.1

53/63


P f f O i li b

8/6/2019 retim 9.1

54/63


One more check is needed for theoptimality of Q.

That is we take the second derivative ofthe total cost function based on Q.

If the second derivative is positive, theQ* value is a real optimum. (Rule)

In fact, second derivative is equal to2DS / Q3 which is a positive value (It isa real optimum).

C id i h

8/6/2019 retim 9.1

55/63

Considering theReorder Point

So far, we only decided how muchto order (That is Q*).

Now, we should find what time toorder.

We assumed that firm will wait

until its inventory reaches to zerobefore placing an order.

C id i th

8/6/2019 retim 9.1

56/63


And, we also assumed that theOrders will receive immediately.

However, there is a time betweenplacement and receipt of an order.

This is called LEAD TIME or delivery

time.

C id i th

8/6/2019 retim 9.1

57/63


Here, we will use the term ReorderPoint (ROP) for when to order.

ROP (in units) = (Demand Per Day). (Lead time for a new order in

days)

ROP = d . L

C id i th

8/6/2019 retim 9.1

58/63


C id i th

8/6/2019 retim 9.1

59/63


When the inventory level reachesthe ROP, a new order is required.

It will take a time that is equal tothe Lead Time (L) to receive the

new order.

C id i th

8/6/2019 retim 9.1

60/63


Here, Demand per day (d) is found bythe following equation:

d = D / Number of working days in ayearThis ROP equation assumes that

demand is uniform and constant. If this is not the case, an extra

(safety) stock is added (because ofuncertainty).

8/6/2019 retim 9.1

61/63

Example

Annual demand for an item is D =8000/year.

This year there will be 200 workingdays in a year.

Delivery of an order for this item

takes 3 working days (L = 3 days).

8/6/2019 retim 9.1

62/63

Example

Questions:

a) Find the demand per day for thisitem.

b) What is the ROP for this item?

8/6/2019 retim 9.1

63/63

Example

Answers:

a) Demand per day for this item (d)

= 8000 / 200 = 40 units / day.b) ROP = d . L = 40 . 3 = 120 units.

When inventory level becomes 120units, an Order should be placed.

Üretim 9.1

Documents