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Chapter 12 IndependentDemand Inventory Management

Operations Management

by

R. Dan Reid & Nada R. Sanders4th Edition Wiley 2010

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Learning Objectives Describe the different types and uses of inventory

Describe the objectives of inventory management

Calculate inventory performance measures

Understand relevant costs associated withinventory

Perform ABC inventory control & analysis Understand the role of cycle counting in inventory

record accuracy

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Learning Objectivescont Understand inventorys role in service organizations

Calculate order quantities

Evaluate the total relevant costs of differentinventory policies

Understand why companies dont always use theoptimal order quantity

Understand how to justify smaller order sizes Calculate appropriate safety stock inventory

policies

Calculate order quantities for single-period

inventory

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Types of InventoryInventory comes in many shapes and sizes such as:

Raw materials purchased items or extracted materialstransformed into components or products

Components parts or subassemblies used in finalproduct

Work-in-process items in process throughout theplant

Finished goods products sold to customers Distribution inventory finished goods in the

distribution system

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Types of Inventory

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How Companies Use Their

Inventory1. Anticipation or seasonal inventory2. Fluctuation Inventory or Safety stock: buffer

demand fluctuations3. Lot-size or cycle stock: take advantage of

quantity discounts or purchasing efficiencies4. Transportation or Pipeline inventory5. Speculative or hedge inventory protects against

some future event, e.g. labor strike6. Maintenance, repair, and operating (MRO)

inventories

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Objectives of Inventory

ManagementProvide desired customer service level

Customer service is the ability to satisfy

customer requirements Percentage of orders shipped on schedule

Percentage of line items shipped on schedule

Percentage of $ volume shipped on schedule

Idle time due to material and componentshortages

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Inventory Objectives contProvide for cost-efficient operations:

Buffer stock for smooth production flow

Maintain a level work force

Allowing longer production runs & quantity discounts

Minimum inventory investments: Inventory turnover

Weeks, days, or hours of supply

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Customer Service Level Examples Percentage of Orders Shipped on Schedule

Good measure if orders have similar value. Does not capture value.

If one company represents 50% of your business but only 5% of

your orders, 95% on schedule could represent only 50% of value Percentage of Line Items Shipped on Schedule

Recognizes that not all orders are equal, but does not capture

$ value of orders. More expensive to measure. Ok for finished goods.

A 90% service level might mean shipping 225 items out of the total250 line items totaled from 20 orders scheduled

Percentage Of Dollar Volume Shipped on Schedule Recognizes thedifferences inorders in terms of both line items and

$ value

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Inventory Investment Measures Example: The Coach MotorHome Company has annual cost of goods sold of $10,000,000. Theaverage inventory value at any point in time is $384,615. Calculate

inventory turnover and weeks/days of supply.

Inventory Turnover:

Weeks/Days of Supply:

turnsinventory26

$384,615

0$10,000,00

valueinventoryaverage

soldgoodsofcostannualTurnover

2weeks

0/52$10,000,00

$384,615

dollarsinusageweeklyaverage

dollarsinhandoninventoryaverageSupplyofWeeks

days100/260$10,000,00

$384,615SupplyofDays

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Relevant Inventory CostsItem Cost Includes price paid for the item plus

other direct costs associated with thepurchase

HoldingCosts

Include the variable expenses incurredby the plant related to the volume ofinventory held (15-25%)

CapitalCosts

The higher of the cost of capital or theopportunity cost for the company

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Relevant Inventory CostsOrderingCost

Fixed, constant dollar amount incurredfor each order placed

ShortageCosts

Loss of customer goodwill, back orderhandling, and lost sales

Risk costs Obsolescence, damage, deterioration,

theft, insurance and taxesStoragecosts

Included the variable expenses forspace, workers, and equipment relatedto the volume of inventory held

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Determining Order QuantitiesLot-for-lot Order exactly what is needed

Fixed-orderquantity Specifies the number of units to orderwhenever an order is placed

Min-maxsystem

Places a replenishment order whenthe on-hand inventory falls below the

predetermined minimum level.

Order nperiods

Order quantity is determined by totaldemand for the item for the next n

periods

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ABC Inventory ClassificationABC classification is a method for determining level of

control and frequency of review of inventory items

A Pareto analysis can be done to segment items into

value categories depending on annual dollar volume A Items typically 20% of the items accounting for

80% of the inventory value-use Q system

B Items typically an additional 30% of the items

accounting for 15% of the inventory value-use Q or P C Items Typically the remaining 50% of the items

accounting for only 5% of the inventory value-use P

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The AAU Corp. is considering doing an ABC analysis onits entire inventory but has decided to test thetechnique on a small sample of 15 of its SKUs. Theannual usage and unit cost of each item is shown below

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(A) First calculate the annual dollarvolume for each item

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B) List the items in descending order based on annual dollarvolume. (C) Calculate the cumulative annual dollar volume as apercentage of total dollars. (D) Classify the items into groups

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Graphical solution for AAU Corp showingthe ABC classification of materials

TheA items (106 and 110) account for 60.5% of the value and 13.3% of theitems

The B items (115,105,111,and 104) account for 25% of the value and 26.7%of the items

The C items make up the last 14.5% of the value and 60% of the items

How might you control each item classification? Different ordering rules foreach?

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Inventory Record Accuracy

Inaccurate inventory records cancause:

Lost sales

Disrupted operations

Poor customer service

Lower productivity Planning errors and expediting

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Inventory Record Accuracy

Two methods for checking record accuracy:

Periodic counting - physical inventory is takenperiodically, usually annually

Cycle counting - daily counting of prespecified itemsprovides the following advantages:

Timely detection and correction of inaccurate records

Elimination of lost production time due to unexpected stock outs

Structured approach using employees trained in cycle counting

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Inventory in ServiceOrganizations

Achieving good inventory control mayrequire the following:

Select, train and discipline personnel

Maintain tight control over incomingshipments

Maintain tight control over outgoingshipments

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Determining Order Quantities

Inventory management and control aremanaged with SKU (stock control units)

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Mathematical Models forDetermining Order Quantity

Economic Order Quantity (EOQ)

An optimizing method used for determining order

quantity and reorder points Part ofcontinuous review system which tracks on-

hand inventory each time a withdrawal is made

Economic Production Quantity (EPQ)

A model that allows for incremental product delivery

Quantity Discount Model

Modifies the EOQ process to consider cases wherequantity discounts are available

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EOQ Assumptions

Demand is known & constant - nosafety stock is required

Lead time is known & constant

No quantity discounts areavailable

Ordering (or setup) costs areconstant

All demand is satisfied (noshortages)

The order quantity arrives in asingle shipment

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Total Annual Inventory Costwith EOQ Model

Total annual cost= annual ordering cost + annual

holding costs

H2DSQandH;

2QS

QDTCQ

C ti (Q) R i S t E l A t h

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Continuous (Q) Review System Example: A computer company hasannual demand of 10,000. They want to determine EOQ for circuitboards which have an annual holding cost (H) of $6/unit, and anordering cost (S) of $75. They want to calculate TC and the reorderpoint (R) if the purchasing lead time is 5 days.

EOQ (Q)

Reorder Point (R)

Total Inventory Cost (TC)

units500$6

$75*10,000*2

H

2DSQ

units200days5*

days250

10,000TimeLeadxDemandDailyR

$3000$1500$1500$62

500$75

500

10,000TC

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Economic ProductionQuantity (EPQ)

Same assumptions as the EOQ except: inventoryarrives in increments & draws down as it arrives

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Calculating EPQ

Total cost:

Maximum inventory:

d=avg. daily demand rate

p=daily production rate

Calculating EPQ

H

2

IS

Q

DTC MAXEPQ

p

d1QIMAX

p

d1H

2DSEPQ

EPQ P bl HP Ltd P d i l t f d i 50# b

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EPQ Problem:HP Ltd. Produces premium plant food in 50# bags.Demand is 100,000 lbs/week. They operate 50 wks/year; HPproduces 250,000 lbs/week. Setup cost is $200 and the annualholding cost rate is $.55/bag. Calculate the EPQ. Determine themaximum inventory level. Calculate the total cost of using the

EPQ policy.

H

2

IS

Q

DTC MAXEPQ

p

d1H

2DSEPQ

p

d1QIMAX

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EPQ Problem Solution

p

d1H

2DSEPQ BagsEPQ 850,77

250000

000,100155.

)200)(000,100)(50(2

p

d1QIMAX

H

2

ISQ

DTC MAXEPQ

bagsMAXI 710,46000,250

000,1001850,77

690,25$55.2710,46200

850,77000,000,5

TC

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Quantity Discount Model

Same as the EOQ model, except:

Unit price depends upon the quantity ordered

The total cost equation becomes:

H2

QS

Q

DTCQD CD

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Quantity Discount Procedure

Calculate the EOQ at the lowest price

Determine whether the EOQ is feasible

at that price Will the vendor sell that quantity at that

price?

If yes, stop if no, continue

Check the feasibility of EOQ at the nexthigher price

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QD Procedure cont

Continue until you identify a feasible EOQ

Calculate the total costs (including total item

cost) for the feasible EOQ model Calculate the total costs of buying at the

minimum quantity required for each of thecheaper unit prices

Compare the total cost of each option &choose the lowest cost alternative

Any other issues to consider?

Quantity Discount Example: Collins Sport store is considering

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Quantity Discount Example: Collin s Sport store is consideringgoing to a different hat supplier. The present supplier charges$10/hat and requires minimum quantities of 490 hats. The annualdemand is 12,000 hats, the ordering cost is $20, and the inventorycarrying cost is 20% of the hat cost, a new supplier is offering hats

at $9 in lots of 4000. Who should he buy from?

EOQ at lowest price $9. Is it feasible?

Since the EOQ of 516 is not feasible, calculate the totalcost (C) for each price to make the decision

4000 hats at $9 each saves $19,320 annually. Space?

hats516$1.80

20)2(12,000)(EOQ$9

$101,66012,000$9$1.8024000

$204000

12,000C

$120,98012,000$10$22

490$20

490

12,000C

$9

$10

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Why Companies DontAlwaysUse Optimal Order Quantity

It is not unusual for companies to order lessor more than the EOQ for several reasons:

They may not have a known uniformdemand;

Some suppliers have minimum order

quantity that are beyond the demand.

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Justifying Smaller OrderQuantities

JIT or Lean Systems would recommend reducing order quantities to thelowest practical levels

Benefits from reducing Qs:

Improved customer responsiveness (inventory = Lead time) Reduced Cycle Inventory

Reduced raw materials and purchased components

Justifying smaller EOQs:

Reduce Qs by reducing setup time (S).Setup reduction is a welldocumented, structured approach to reducing S

H

2DSQ

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Determining Safety Stock and ServiceLevels

If demand or lead time is uncertain,safety stock can be added toimprove order-cycle service levels R = dL +SS

Where SS =zdL, and Z is thenumber of standard deviations

and dL is standard deviation ofthe demand during lead time

Order-cycle service level The probability that demand

during lead time will not exceedon-hand inventory

A 95% service level (stockout

risk of 5%) has a Z=1.645

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Periodic Review Systems

Orders are placed at specified, fixed-time intervals(e.g. every Friday), for a order size (Q) to bringon-hand inventory (OH) up to the target

inventory (TI), similar to the min-max system. Advantages are:

No need for a system to continuously monitor item Items ordered from the same supplier can be reviewed

on the same day saving purchase order costs

Disadvantages: Replenishment quantities (Q) vary Order quantities may not quality for quantity discounts On the average, inventory levels will be higher than Q

systems-more stockroom space needed

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Periodic Review Systems:Calculations for TI

Targeted Inventory level:

TI = d(RP + L) + SS

d = average period demandRP = review period (days, wks)

L = lead time (days, wks)

SS = zRP+L

Replenishment Quantity (Q)=TI-OH

P System: an auto parts store calculated the EOQ for Drive Belts at

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P System: an auto parts store calculated the EOQ for Drive Belts at236 units and wants to compare the Total Inventory Costs for a Qvs. a PReview System. Annual demand (D) is 2704, avg. weeklydemand is 52, weekly is 1.77 belts, and lead time is 3 weeks. Theannual TC for the Q system is $229; H=$97, S=$10.

Review Period Target Inventory for 95% Service Level

Average On-Hand

OHavg= TI-dL=424-(52belts)(3wks) = 268 belts

Annual Total Cost (P System)

5wksx522704

23652weeksx

D

QRP

belts4248416351.771.64535units52TIzL)d(RPSSL)d(RPTI LRP

$16$229$245DifferenceCostAnnual

$245130115$0.972

268$10

5

52TCp

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Single Period Inventory Model

The SPI model is designed for products that sharethe following characteristics:

Sold at their regular price only during a single-time period

Demand is highly variable but follows a known probabilitydistribution

Salvage value is less than its original cost so money is lost whenthese products are sold for their salvage value

Objective is to balance the gross profit of the saleof a unit with the cost incurred when a unit is soldafter its primary selling period

SPI Model Example: T-shirts are purchase in multiples of 10 for

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SPI Model Example: T shirts are purchase in multiples of 10 fora charity event for $8 each. When sold during the event the sellingprice is $20. After the event their salvage value is just $2. Frompast events the organizers know the probability of selling differentquantities of t-shirts within a range from 80 to 120

Payoff Table

Prob. Of Occurrence .20 .25 .30 .15 .10Customer Demand 80 90 100 110 120

# of Shirts Ordered Profit80 $960 $960 $960 $960 $960 $96090 $900 $1080 $1080 $1080 $1080 $1040

Buy 100 $840 $1020 $1200 $1200 $1200 $1083110 $780 $ 960 $1140 $1320 $1320 $1068120 $720 $ 900 $1080 $1260 $1440 $1026

Sample calculations:Payoff (Buy 110)= sell 100($20-$8)((110-100) x ($8-$2))= $1140Expected Profit (Buy 100)= ($840 X.20)+($1020 x .25)+($1200 x .30) +

($1200 x .15)+($1200 x .10) = $1083

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Inventory management withinOM: How it all fits together

Inventory management provides the materials and supplies needed tosupport actual manufacturing or service operations. Inventoryreplenishment policies guide the master production scheduler whendetermining which jobs and what quantity should be scheduled(Supplement D).

Inventory management policies also affect the layout of the facility. Apolicy of small lot sizes and frequent shipments reduces the spaceneeded to store materials (Ch 7).

Longer throughput times reduce an organizations ability to respondquickly to changing customer demands (Ch 4).

Good inventory management assures continuous supply andminimizes inventory investment while achieving customer serviceobjectives.

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Inventory Management Acrossthe Organization

Inventory management policies affectfunctional areas throughout

Accounting is concerned of the costimplications of inventory

Marketing is concerned as stocking decision

affect the level of customer service Information Systems tracks and controls

inventory records

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Chapter 12 Highlights Raw materials, purchased components,

work-in-process, finished goods,distribution inventory and maintenance,

repair and operating supplies are alltypes of inventory.

The objectives of inventory

management are to provide the desiredlevel of customer service, to allow cost-efficient operations, and to minimizeinventory investment.

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Chapter 12 Highlights cont

Inventory investment is measured ininventory turnover and/or level ofsupply. Inventory performance iscalculated as inventory turnover orweeks, days, or hours of supply.

Relevant inventory costs include itemcosts, holding costs, and shortagecosts.

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Chapter 12 Highlights cont

Retailers, wholesalers, & food serviceorganizations use tangible inventory eventhough they are service organizations.

The ABC classification system allows acompany to assign the appropriate level ofcontrol & frequency of review of an item

based on its annual $ volume. Cycle counting is a method for maintaining

accurate inventory records. Determining whatand when to count are the major decisions.

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Chapter 12 Highlights cont

Lot-for-lot, fixed-order quantity, min-maxsystems, order n periods, periodic review

systems, EOQ models, quantity discountmodels, and single-period models can beused to determine order quantities.

Ordering decisions can be improved by

analyzing total costs of an inventory policy.Total costs include ordering cost, holdingcost, and material cost.

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Chapter 12 Highlights cont

Practical considerations can cause acompany to not use the optimal order

quantity, that is, minimum orderrequirements.

Smaller lot sizes give a company flexibility

and shorter response times. The key toreducing order quantities is to reduceordering or setup costs.

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Chapter 12 Highlights cont

Calculating the appropriate safety stock policyenables companies to satisfy their customer

service objective at minimum costs. Thedesired customer service level determines theappropriate z value.

Inventory decisions about perishable productscan be made using the single-period inventorymodel. The expected payoff is calculated toassist the quantity decision.

Chapter 12 Homework Hints

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Chapter 12 Homework Hints Problem12.3: calculate inventory turnover, weekly,

and daily supply Problem 12.12: calculate EOQ. TC is based on

ordering + holding costs. Calculate reorder point.

Problem 12.13: use data from problem 12.12.

Quantity discount model. Use steps from slides orbook. Choose best Q based on lowest TC.

Problem 12.14: use data from problem 12.2.Determine Q based on period needs, then compare

using TC for each option. Problem 12.20: ordering and holding costs are

not needed for this problem. Follow example12.15 (p. 449) which uses four steps to do an ABC