inventory management

Inventory Management

Chapter 13

Learning Objectives

• Define the term inventory• List the different types of inventory• Describe the main functions of inventory• Discuss the main requirements for effective inventory

management• Describe the A-B-C approach and explain how it is useful• 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.

• From the video, what are the elements relevant to inventory management?

Inventory Management at Cox Hardware

Inventory

• Definition– A stock or store of goods– Dependent demand items

• Items that are subassemblies or component parts to be used in the production of finished goods.

– Independent demand items• Items that are ready to be sold or used

• Inventories are a vital part of business: – necessary for operations– contribute to customer satisfaction

Types of Inventory

• Raw materials and purchased parts• Work-in-process (WIP)• Finished goods inventories or merchandise• Tools and supplies• Maintenance and repairs (MRO) inventory• Goods-in-transit to warehouses or customers

(pipeline inventory)

Discussion

• Which of them are dependent demand items and independent demand items? – Raw materials and purchased parts– Work-in-process (WIP)– Finished goods inventories or merchandise– Tools and supplies– Maintenance and repairs (MRO) inventory– Goods-in-transit to warehouses or customers

(pipeline inventory)

Inventory Functions

• Inventories serve a number of functions such as:1. To meet anticipated customer demand2. To smooth production requirements

• Firms that experience seasonal patterns in demand often build up inventories during preseason periods to meet overly high requirements during seasonal periods.

3. To decouple operations• Buffers between operations

4. To protect against stockouts• Delayed deliveries and unexpected increases in demand

increase the risk of shortages.

Inventory Functions

• Inventories serve a number of functions such as:5. To take advantage of order cycles

• It is usually economical to produce in large rather than small quantities. The excess output must be stored for later use.

6. To hedge against price increases• Occasionally a firm will suspect that a substantial price increase is about

to occur and purchase larger-than-normal amounts to beat the increase

7. To permit operations• The fact that production operations take a certain amount of time (i.e.,

they are not instantaneous) means that there will generally be some work-in-process inventory.

8. To take advantage of quantity discounts• Suppliers may give discounts on large orders.

Objectives of Inventory Control

• Inventory management has two main concerns:1. Satisfactory Level of customer service

• Having the right goods available in the right quantity in the right place at the right time

2. Costs of ordering and carrying inventories• The overall objective of inventory management is to

achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds

MIS 373: Basic Operations Management 10

Inventory Management

• Management has two basic functions concerning inventory:1. Establish a system for tracking items in inventory

2. Make decisions about• When to order• How much to order


Effective Inventory Management

• Requires:1. A system keep track of inventory2. A reliable forecast of demand3. Knowledge of lead time and lead time variability4. Reasonable estimates of

• holding costs• ordering costs• shortage costs

5. A classification system for inventory items


• Measures of performance:– Customer satisfaction

• Number and quantity of backorders• Customer complaints

– Inventory turnover = a ratio of

during a period

(average) cost of goods sold

(average) inventory investment

Measures of performance


• Periodic System• Physical count of items in inventory made at periodic intervals

• Perpetual Inventory System• System that keeps track of removals from inventory

continuously, thus monitoring current levels of each item

– Point-of-sale (POS) systems• A system that electronically records actual sales

– Radio Frequency Identification (RFID)

Inventory Counting Systems


Inventory Costs• Purchase cost

– The amount paid to buy the inventory• Holding (carrying) costs

– Cost to carry an item in inventory for a length of time, usually a year• Interest, insurance, taxes (in some states), depreciation, obsolescence,

deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security).

• Ordering costs– Costs of ordering and receiving inventory

• determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage.

• Shortage costs– Costs resulting when demand exceeds the supply of inventory; often

unrealized profit per unit


• A-B-C approach– Classifying inventory according to some measure of

importance, and allocating control efforts accordingly– A items (very important)

• 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value

– B items (moderately important)– C items (least important)

• 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value

ABC Classification System


• How to classify?1. For each item, multiply

annual volume by unit price to get the annual dollar value.

2. Arrange annual values in descending order.

3. A items: the few with the highest annual dollar value

C items: the most with the lowest dollar value.

B items: those inbetween

# Annual demand

Unit price

Annual value Class % of items

% of value

8 1,000 4,000 4,000,000 A 5.3 52.7

3 2,400 500 1,200,000 B

31.4 40.86 1,000 1,000 1,000,000 B

1 2,500 360 900,000 B

4 1,500 100 150,000 C

63.3 6.5

10 500 200 100,000 C

9 8,000 10 80,000 C

2 1,000 70 70,000 C

5 700 70 49,000 C

7 200 210 42,000 C

18,800 7,591,000 100 100

ABC Classification System


ABC Classification: Cycle Counting

• Cycle counting– A physical count of items in inventory

• Cycle counting management– How much accuracy is needed?

• A items: ± 0.2 percent• B items: ± 1 percent• C items: ± 5 percent

– When should cycle counting be performed?– Who should do it?

Inventory Models

• Economic Order Quantity models:– identify the optimal order quantity

• by minimizing total annual costs that vary with order size and frequency

1. The basic Economic Order Quantity model (EOQ)2. The Quantity Discount model3. The Economic Production Quantity model (EPQ)4. Reorder Point Ordering (uncertainty, when to order)5. Fixed-Order-Interval model6. Single Period model (perishable items)


Basic EOQ Model• The basic EOQ model:

– used to find a fixed order quantity that will minimize total annual inventory costs

– continuous monitoring system

• Assumptions:1. Only one product is involved2. Annual demand requirements are known3. Demand is even throughout the year4. Lead time does not vary5. Each order is received in a single delivery6. There are no quantity discounts


The Inventory CycleProfile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usagerate

Time

Discussion

• What costs are associated with this model?– (Hint: Recall the 5 types of costs)Purchase costHolding (carrying) costOrdering costSetup costShortage cost (Backorder/Backlog cost)

Instructor Slides 21


Total Annual Cost

• Total Cost = Annual Holding Cost + Annual Ordering Cost (TC)

where• Q = order quantity in units• H = holding (carrying) cost per unit, usually per year• D = demand, usually in units per year• S = ordering cost per order

=Q

H +D

S2 Q

Number of orders

Average number of units in inventory


Goal: Total Cost Minimization

• The Total-Cost Curve is U-Shaped– There is a tradeoff between holding costs and

ordering costs

Order Quantity (Q)

Ordering Costs

Q*

Annu

al C

ost

(optimal order quantity)

Holding Costs

SQ

DH

QTC

2


Deriving EOQ

• Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

• The total cost curve reaches its minimum where the carrying and ordering costs are equal.

𝑄∗=√ 2𝐷𝑆𝐻

=√ 2 (𝑎𝑛𝑛𝑢𝑎𝑙𝑑𝑒𝑚𝑎𝑛𝑑 ) (𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 )𝑎𝑛𝑛𝑢𝑎𝑙𝑝𝑒𝑟𝑢𝑛𝑖𝑡 h𝑜𝑙𝑑𝑖𝑛𝑔𝑐𝑜𝑠𝑡

𝑇 𝐶′=𝐻2

+(−1 ) 𝐷𝑆𝑄2

=0→𝐷𝑆𝑄2

=𝐻2

→𝐷𝑆𝑄

=𝐻𝑄2


Example: Deriving EOQ

• Tire distributer• D (Demand)=9,600 tires per year• H (Holding cost)=$16 per unit per year• S (Ordering cost) = $75 per order


=√ 2∗9,600∗7516

=300 𝑡𝑖𝑟𝑒𝑠

𝑇𝐶=𝑄2𝐻+

𝐷𝑄𝑆=

3002∗16+

9,600300

∗75=2,400+2,400=4,800


Example: Deriving EOQ• D (Demand)=9,600 tires per year• H (Holding cost)=$16 per unit per year• S (Ordering cost) = $75 per order • Q*=300 tires• TCmin = 4,800

880,4880,2000,275250

600,916

2

250

2250 S

Q

DH

QTC

000,5800,1200,375400

600,916

2

400

2400 S

Q

DH

QTC

Let’s verify whether the Q* indeed gives the lowest cost.

Exercise

• A local distributor for a national tire company expects to sell approximately 9,600 tires per year. Annual carrying cost is $16 per tire, and ordering cost is $75 per order. The distributor operates 288 working days a year.

• a. What is the optimal order size? • b. How many times per year the store reorder?• c. What is the length of an order cycle?• d. What is the total annual cost if EOQ is placed?


Solution

• a

• b

• c

• d


)(30016

75(9,600)2S2EOQ tires

H

D

)(32300

600,9times

EOQ

D

932

288

reorder#

#

timesof

daysworkingofLength

4800$

75)300/600,9(162300/

)/()2/(

）（

SQDHQCostTotal

Economic Production Quantity (EPQ)

• The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate)– Assumptions

1. Only one item is involved

2. Annual demand requirements are known

3. Usage rate is constant (= even demand throughout the year)

4. Usage occurs continually, but production occurs periodically (batch production)

5. The production rate is constant

6. Production rate is greater than usage rater

7. Lead time does not vary

8. There are no quantity discounts

Instructor Slides13-29

EPQ: Inventory Cycle

Instructor Slides

Q

Qp

Imax

Productionand usage

Productionand usage

Productionand usage

Usageonly

Usageonly

Cumulativeproduction

Amounton hand

Time

13-30

Discussion

• What costs are associated with this model?– (Hint: Recall the 5 types of costs)Purchase costHolding (carrying) costOrdering costSetup costShortage cost (Backorder/Backlog cost)

• Our decision making in EPQ model is to determine the size of order (Q) each time. Why?


EPQ Model


day)per(unit rate usageu

day)per(unit rate production p

orderper cost Setup

Demand

yearper unit per cost (carrying) Holding

B

S

AnnualD

H

LevelInventoryMaximumI

productionforsizeatchQ

EPQ – Total Cost

rate Usage

ratedelivery or Production

inventory Maximum

where

2

Cost SetupCost CarryingTC

max

max

min

u

p

upp

Q

I

SQ

DH

I

p

Instructor Slides13-33

EPQ

up

p

H

DSQp

2

Instructor Slides 13-34

Optimal Batch size a.k.a Economic Produciton Quantity (EPQ)

Exercise

• A toy manufacturer uses 48,000 wheels per year for toy trucks. The firm produces its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost is $45 per production run. The firm operates 240 days per year.

• a. What is the optimal batch size? • b. What is the total annual cost if EPQ is produced each

run?• c. What is cycle time (production stage + usage stage)?• d. What is the production cycle time?


Solution

• a

• b


,8001$

45)400,2/000,48(121,800/

)/()2/(

)(800,1)200800(800

400,2)(

max

max

）（SQDHICostTotal

wheelsupp

EPQI

)(400,2200800

800

1

45(48,000)2S2EPQ wheels

up

p

H

D

dayperwheelsu 200240/000,48

Solution

• c

• d


)(12200

400,2days

u

EPQCycleTime

)(3800

400,2Pr days

p

EPQcleoductionCy

Quantity Discount Model

• Quantity discount– Price reduction for larger orders offered to

customers to induce them to buy in large quantities

Instructor Slides

priceUnit

where

2

Cost PurchasingCost OrderingCost CarryingCost Total

P

PDSQ

DH

Q

13-38


When to Reorder

• If delivery is not instantaneous, but there is a lead time:When to order?

Receive

order

Time

Inve

nto

ry

OrderQuantity

Q

Lead Time

Placeorder


When to Reorder

• EOQ answers the “how much” question• The reorder-point (ROP) tells “when” to order

• Reorder-Point– When the quantity on hand of an item drops to this amount

(quantity-trigger), the item is reordered.

– Determinants of the Reorder-Point1. The rate of demand2. The lead time3. The extent of demand and/or lead time variability4. The degree of stockout risk acceptable to management


Reorder-Point

ROP = (Demand per day) * (Lead time for a new order in days)= d * L

where d = (Demand per year) / (Number of working days in a year)

Example:– Demand = 12,000 iPads per year– 300 working day year– Lead time for orders is 3 working days

In other words, the manager should place the order when only 120 units

left in the inventory.

d = 12,000 / 300 = 40 unitsROP = d * L = 40 units per day * 3 days of leading time = 120 units


The Inventory CycleProfile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usagerate

Time

ROP = LxD

D: demand per periodL: Lead time in periods

Q: When shall we order? A: When inventory = ROPQ: How much shall we order? A: Q = EOQ

• Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? (Assuming that the lead time to receive cars is 10 days and that there are 365 working days in a year)

ROP = (Demand per day) * (Lead time for a new order in days)= d * L

where d = (Demand per year) / (Number of working days in a year)


=√ 2 (𝑎𝑛𝑛𝑢𝑎𝑙𝑑𝑒𝑚𝑎𝑛𝑑 ) (𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 )𝑎𝑛𝑛𝑢𝑎𝑙𝑝𝑒𝑟𝑢𝑛𝑖𝑡 h𝑜𝑙𝑑𝑖𝑛𝑔𝑐𝑜𝑠𝑡

EOQ =

Recall:

Exercise: EOQ & ROP

• Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size?

548500

)000,5)(000,15(2* Q

Since d is given in years, first convert: 5000/365 =13.7 cars per working day

So, ROP = 13.7 * 10 = 137

So, when the number of cars on the lot reaches 137, order 548 more cars.

Exercise: EOQ & ROP


But demand is rarely predictable!

Time

Inventory Level

OrderQuantity

Receive order

Placeorder Lead Time

Inventory at time of receipt

ROP

Lead Time Demand

When Actual Demand < Expected Demand



Time

Inventory Level

OrderQuantity

Receive order


ROP

When Actual Demand > Expected Demand

Unfilled demand

Stockout Point



Time

Inventory Level

OrderQuantity

ROP = Expected Demand

Average

If ROP = expected demand, inventory left 50% of the time, stock outs 50% of the time.

Uncertain Demand


Safety Stock

Time

Inventory Level

OrderQuantity

Expected

Lead-time

Demand

To reduce stockouts we add safety stock

Receive order


Order QuantityQ = EOQROP =

Safety Stock +

Expected LT

Demand

ExpectedLT Demand

Safety Stock


How Much Safety Stock?

• The amount of safety stock that is appropriate for a given situation depends upon:1. The average demand rate and average lead time2. Demand and lead time variability3. The desired service level

• Service level = probability of NOT stocking out

• Reorder point (ROP) = Expected demand during lead time + z*σdLT

Where z = number of standard deviationsσdLT = the standard deviation of lead time demand


Reorder Point

• The ROP based on a normal distribution of lead time demand

Safety Stock

Risk of stockout

ROP

Quantity

Expected demand

Service level

(probability of not stockout)

Z scaleZ0

inventory management

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