Inventory Managementfor Independent Demand

Chapter 12

MGMT 326

Foundations

of Operatio

nsIntroductio

n

Strategy

ManagingProjects

QualityAssuran

ce

Facilities

& WorkDesign

Products &

Processes

ProductDesign

ProcessDesign

ManagingQuality

Statistical

ProcessControl

Just-in-Time & Lean Systems

FacilityLayout

Capacity

and Locatio

n

LinearProgram-ming

ManagingInventory

Planning& Control

Chapter Outline

Basic concepts Objectives of inventory management Dependent and independent demand

ABC inventory analysis Inventory costs

Item costs Holding costs Order or setup costs Shortage costs

Chapter Outline (2)

Inventory policy Fixed order quantity method Economic order quantity – the

optimal fixed order quantity Reorder point

Reorder point when demand is constant Reorder point when demand is variable

Economic production quantity – the optimal production quantity

Objectives of Inventory Management

Maintain good customer service Minimize inventory investment,

consistent with the required level of customer service

Types of DemandDependent Demand

Demand for raw materials, component parts, and subassemblies used to make a finished product

Both the amount of demand and the date required depend on the production schedule

Types of Demand (2) Independent Demand

Any demand that is not used to meet a production schedule is called independent demand

Examples of independent demand: finished goods; retail and distributor inventories; service inventories; maintenance, repair, and operating (MRO) inventories MRO includes fuels, repair parts, office

supplies, cleaning supplies

Dependent and Independent Demand:

Types of Inventory

Dependent demand:used to meet a

production schedulein manufacturing

Independent demand:

not used to meet a production schedule

Work-in-process(WIP)

Raw materials

Component parts

Manufacturer Service Company

Finished goods

MRO

Retail ordistributorinventories

Service inventories

MRO

ABC Inventory Analysis For an inventory item, the annual usage in dollars is

(annual demand)x(cost per unit). Annual demand is also called annual usage in units. ABC inventory analysis divides inventory items into 3

categories: A items usually account for at least 60% of annual

usage and should be controlled most closely B items require a moderate level of control. A and B

items should account for at least 80% of annual usage. C items require less control than other items. These

items are those with the least usage that were not classified asA and B items

© Wiley 2007

The AAU Corp. is considering doing an ABC analysis on its entire inventory but has decided to test the technique on a small sample of 15 of

its SKU’s. The annual usage and unit cost of each item is shown below

Steps in ABC Analysis

1. Compute Annual Usage in Dollars for each item.

2. Compute Total Annual Usage.3. Compute the percentage of Annual

Usage for each item.4. Sort the list of items by the percentage

of Annual Usage in Dollars, from largest to smallest.

Steps in ABC Analysis (2)

5. Calculate the Cumulative Percentage of Annual Usage in Dollars for the first item, first 2 items, first 3 items, etc. For the last item, the cumulative % should be 100%.

6. Using Cumulative % as a guide, assign the items to A, B, and C categories.

© Wiley 2007

© Wiley 2007

Relevant Inventory Costs

Measurable Cost of Inventory =

ItemCosts

HoldingCosts

Order Costs for purchased

itemsOR

Setup Costs foritems made byyour company

Shortage costs:Administrative& transportationcosts related toback orders

+ + +

Shortages and back orders result in lost sales and lost goodwill. These costs are relevant but hard to measure.

Item Costs

Item costs For purchased items, the item cost is

the purchase price, plus shipping For work in process, the item cost is

the cost of materials and labor used in the item

For finished goods, the item cost is the cost of goods sold.

Inventory Holding Costs Inventory holding costs include capital

costs, storage costs, and risk costs Capital costs:

If inventory is financed with borrowed money, the capital cost is the interest rate paid

If inventory is financed from retained earnings, the capital cost is the opportunity cost of not putting the money into other investments

Storage costs: the costs of space, people, and equipment used in inventory storage

Inventory Holding Costs (2)

Risk costs: cost of taxes and insurance on inventory, damage, obsolescence, and theft

Inventory holding costs are usually computed as a percentage of item costs

Ordering and Setup Costs

For purchased items, ordering costs are the fixed costs associated with placing an order with a supplier

For items made internally, setup costs are used instead of order costs. The setup cost is the cost of work that must be done before production actually begins.

Shortage Costs

Administrative and transportation costs related to back orders

Lost good will and lost sales due to product shortages – hard to measure

Inventory Management Policies

An inventory management policy should determine How much to order When to order

Fixed Order Quantity Method

An inventory policy for independent demand. Based on the following rules:

1. Order the same amount, Q, each time Q is called the order quantity

2. Place an order when the amount in inventory gets down to the reorder point, R

Compute Q and R for each item.

Fixed Order Quantity Method (2)Relevant Costs

Assume Quantity discounts are not available Orders are placed early enough that

shortages do not occur Relevant costs

Order costs Inventory holding costs

Fixed Order Quantity Method (3)

Annual Inventory Cost

Figure 12.2, page 430Given:D = annual demand =

10,400Weekly demand = 200L = lead time = 1 weekQ = order quantity = 600Average inventory= (Q/2) = 600/2 = 300

Fixed Order Quantity Method (4)Notation

Q = order quantity D = annual demand for the item S = cost of placing one order H = inventory holding cost per unit per year

(commonly called holding cost) L = lead time (time between order placement

and order receipt) R = reorder point TC = annual cost of placing orders

+ annual cost of holding inventory

Fixed Order Quantity Method (5)Costs

Annual cost of placing orders =

Annual cost of holding inventory =

Total annual cost =

Economic Order Quantity

The economic order quantity (EOQ) is the fixed order quantity (Q) that minimizes the total annual costs of placing orders and holding inventory (TC).

Economic Order QuantityAssumptions

Demand (D) is known and constant H is known and constant Order costs (S) are constant The order quantity arrives in a

single shipment No quantity discounts are available All demand will be met (no

shortages)

We want to minimize TC D, S, and H are constant. TC is a function of Q.

1

2 2

D Q HTC S H DS Q

Q Q

Economic Order Quantity (3)

* 2DSQ

H

*

* 2

D QTC S H

Q

Let Q* be the economic order quantity. Then

For Q*, annual order cost = annual inventory cost

*

* 2

D QS H

Q

Simple Reorder Point

Use this method when daily demand is constant.

R = reorder point d = daily demand (may have to

compute this) L = lead time (Caution: if lead time is

given in weeks, convert this to days. A week may be 5, 6, or 7 days).

R = dL

Reorder Point with Safety Stock Safety stock (SS) is extra inventory that is

kept to meet unexpected demand.

Reorder point withoutsafety stock

Reorder pointwith safety stock

Reorder Point with Safety Stock (2)

How much safety stock (SS) ?

Reorder point with safety stock: Service level is the probability of having

enough inventory to meet demand during lead time

The probability of a stockout is (1 - service level)

Demand during lead time is normally distributed with mean and standard deviation dL

SSLdR demanddaily average d

Ld

Reorder Point with Safety Stock (2)

How much safety stock (SS) ?

z is the number of standard deviations required to meet the desired service level

SS = zdL

Reorder point with safety stock: R = +

zdL

Ld

Reorder Point with Safety StockExample

Given D = annual demand = 10,000 N = number of business days per year = 250 The company operates 5 days per week = average daily demand dL = standard deviation of demand during lead

time = 20 L = lead time = 1 week Service level = 96%Find: reorder point with safety stock: R = + zdL

Ld

d

Computing Reorder Point with Safety Stock

1. If average daily demand ( ) is not given, compute it.Note: = D/N and D = = 10,000/250 = 40

2. If the lead time is given in weeks or months, compute lead time in days.L = 1 week = 1(5) = 5 daysNote: 1 week is the number of days per

week that the company operates. This may be 5, 6, or 7.

d

d

d dN

Computing Reorder Point with Safety Stock (2)

3. Find the z value for the service level (96%)

Probability of a stockout =1 – servicelevel = 4%

z

50% 46%

Ld

Appendix B givesthis area.

Computing Reorder Point with Safety Stock (3)

3. Find the z value for the service level (96%) (cont.)(a) Write the service level as a decimal

96% = 0.9600(b) Subtract 0.5000 from the service level

0.9600 – 0.5000 = 0.4600(c) Use the table in Appendix B, page 652, to

find the area that is closest to 0.4600The closest area in the table is 0.4599, which occurs when z = 1.75Use z = 1.75

Computing Reorder Point with Safety Stock (4)

4. Compute R

R = L+ zdL

= 40(5) + 1.75(20) = 200 + 35 = 235

Note: If the computation gives a fractional value, round up to nearest integer.

Example: Computed R = 210.2 R = 211

d

Economic Production Quantity

Key question: How many units of a part or product should be made at one time?

The economic production quantity (EPQ) is the production quantity (lot size) that minimizes the total annual cost of setups and holding inventory.

Economic Production Quantity (2)

Notation

Q = Amount to make (lot size) D = annual demand for the item d = daily demand for the item p = daily production rate S = cost of one setup H = inventory holding cost per unit per year

(commonly called holding cost) TC = annual cost of setups

+ annual cost of holding inventory The EPQ is the quantity that minimizes TC

Economic Production Quantity (3)Assumption: Daily demand < daily production. When the item is being made, some is sold or used to make a product. The remainder goes into inventory. When production stops, the inventory is used until there is no inventory left. Then production resumes.

Ending inventory= beginning inventory+ production- sales or usage

Economic Production Quantity (4)

Length of production run = Q/p During production, d units are sold or used each day. (p

– d) units go into inventory.

p

dQdp 1)(

p

QIMAX

Maximum inventory:

Total cost:

H

2

IS

Q

DTC MAX

EPQ

Economic productionquantity (EPQ):

p

d1H

2DSEPQ

EOQ vs. EPQ When to use economic order quantity

(EOQ): Demand is independent Compute how much to order (order quantity)

When to use economic production quantity (EPQ): Parts or products will be produced: demand

is dependent Compute how much to make at one time

(production lot size)