bba 3274 qm week 7 inventory models

Inventory Control ModelsInventory Control ModelsInventory Control ModelsInventory Control Models

BBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESSBBA3274 / DBS1084 QUANTITATIVE METHODS for BUSINESS

byStephen Ong

Visiting Fellow, Birmingham City University Business School, UK

Visiting Professor, Shenzhen University

Today’s Overview Today’s Overview

Learning ObjectivesLearning Objectives1.1. Understand the importance of inventory control and Understand the importance of inventory control and

ABC analysis.ABC analysis.2.2. Use the economic order quantity (Use the economic order quantity (EOQEOQ) to ) to

determine how much to order.determine how much to order.3.3. Compute the reorder point (Compute the reorder point (ROPROP) in determining ) in determining

when to order more inventory.when to order more inventory.4.4. Handle inventory problems that allow quantity Handle inventory problems that allow quantity

discounts or non-instantaneous receipt.discounts or non-instantaneous receipt.5.5. Understand the use of safety stock.Understand the use of safety stock.6.6. Describe the use of material requirements planning Describe the use of material requirements planning

in solving dependent-demand inventory problems.in solving dependent-demand inventory problems.7.7. Discuss just-in-time inventory concepts to reduce Discuss just-in-time inventory concepts to reduce

inventory levels and costs.inventory levels and costs.8.8. Discuss enterprise resource planning systems.Discuss enterprise resource planning systems.

After completing this lecture, students will be able to:After completing this lecture, students will be able to:

OutlineOutline6.16.1 IntroductionIntroduction

6.26.2 Importance of Inventory ControlImportance of Inventory Control

6.36.3 Inventory DecisionsInventory Decisions

6.46.4 Economic Order Quantity: Determining How Much to Economic Order Quantity: Determining How Much to OrderOrder

6.56.5 Reorder Point: Determining When to OrderReorder Point: Determining When to Order

6.66.6 EOQEOQ Without the Instantaneous Receipt Assumption Without the Instantaneous Receipt Assumption

6.76.7 Quantity Discount ModelsQuantity Discount Models

6.86.8 Use of Safety StockUse of Safety Stock

6.96.9 Single-Period Inventory ModelsSingle-Period Inventory Models

6.106.10 ABC AnalysisABC Analysis

6.116.11 Dependent Demand: The Case for Material Dependent Demand: The Case for Material Requirements PlanningRequirements Planning

6.126.12 Just-in-Time Inventory ControlJust-in-Time Inventory Control

6.136.13 Enterprise Resource PlanningEnterprise Resource Planning

IntroductionIntroduction

Inventory is an expensive and important Inventory is an expensive and important asset to many companies.asset to many companies.

Inventory is any stored resource used to Inventory is any stored resource used to satisfy a current or future need.satisfy a current or future need.

Common examples are raw materials, work-Common examples are raw materials, work-in-process, and finished goods.in-process, and finished goods.

Most companies try to balance high and low Most companies try to balance high and low inventory levels with cost minimization as a inventory levels with cost minimization as a goal.goal. Lower inventory levels can reduce costs.Lower inventory levels can reduce costs. Low inventory levels may result in stockouts and Low inventory levels may result in stockouts and

dissatisfied customers.dissatisfied customers.


All organizations have some type of inventory All organizations have some type of inventory control system.control system.

Inventory planning helps determine what Inventory planning helps determine what goods and/or services need to be produced.goods and/or services need to be produced.

Inventory planning helps determine whether Inventory planning helps determine whether the organization produces the goods or the organization produces the goods or services or whether they are purchased from services or whether they are purchased from another organization.another organization.

Inventory planning also involves demand Inventory planning also involves demand forecasting.forecasting.

6-7

ControlliControlling ng

Inventory Inventory LevelsLevels


ForecastinForecasting g

Parts/ProdParts/Product uct

DemandDemand

Planning on Planning on What What

Inventory to Inventory to Stock and Stock and

How to How to Acquire ItAcquire It

Feedback Feedback Measurements to Measurements to Revise Plans and Revise Plans and

ForecastsForecastsFigure 6.1

Inventory planning and controlInventory planning and control

Importance of Inventory ControlImportance of Inventory Control

Five uses of inventory:Five uses of inventory: The decoupling functionThe decoupling function Storing resourcesStoring resources Irregular supply and demandIrregular supply and demand Quantity discountsQuantity discounts Avoiding stockouts and shortagesAvoiding stockouts and shortages

Decouple manufacturing processes.Decouple manufacturing processes. Inventory is used as a buffer between stages Inventory is used as a buffer between stages

in a manufacturing process.in a manufacturing process. This reduces delays and improves efficiency.This reduces delays and improves efficiency.

6-9

Importance of Inventory ControlImportance of Inventory Control

Storing resources.Storing resources. Seasonal products may be stored to satisfy off-Seasonal products may be stored to satisfy off-

season demand.season demand. Materials can be stored as raw materials, work-in-Materials can be stored as raw materials, work-in-

process, or finished goods.process, or finished goods. Labor can be stored as a component of partially Labor can be stored as a component of partially

completed subassemblies.completed subassemblies. Compensate for irregular supply and demand.Compensate for irregular supply and demand.

Demand and supply may not be constant over time.Demand and supply may not be constant over time. Inventory can be used to buffer the variability.Inventory can be used to buffer the variability.

Importance of Inventory ControlImportance of Inventory Control Take advantage of quantity discounts.Take advantage of quantity discounts.

Lower prices may be available for larger Lower prices may be available for larger orders.orders.

Extra costs associated with holding more Extra costs associated with holding more inventory must be balanced against lower inventory must be balanced against lower purchase price.purchase price.

Avoid stockouts and shortages.Avoid stockouts and shortages. Stockouts may result in lost sales.Stockouts may result in lost sales. Dissatisfied customers may choose to buy Dissatisfied customers may choose to buy

from another supplier.from another supplier.

Inventory DecisionsInventory Decisions

There are two fundamental decisions in There are two fundamental decisions in controlling inventory:controlling inventory:

How much to order.How much to order. When to order.When to order.

The major objective is to minimize total The major objective is to minimize total inventory costs.inventory costs.

Common inventory costs are:Common inventory costs are: Cost of the items (purchase or material cost).Cost of the items (purchase or material cost). Cost of ordering.Cost of ordering. Cost of carrying, or holding, inventory.Cost of carrying, or holding, inventory. Cost of stockouts.Cost of stockouts.

Inventory Cost FactorsInventory Cost Factors

ORDERING COST FACTORSORDERING COST FACTORS CARRYING COST FACTORSCARRYING COST FACTORS

Developing and sending purchase Developing and sending purchase ordersorders Cost of capitalCost of capital

Processing and inspecting incoming Processing and inspecting incoming inventoryinventory TaxesTaxes

Bill payingBill paying InsuranceInsurance

Inventory inquiriesInventory inquiries SpoilageSpoilage

Utilities, phone bills, and so on, for the Utilities, phone bills, and so on, for the purchasing departmentpurchasing department TheftTheft

Salaries and wages for the purchasing Salaries and wages for the purchasing department employeesdepartment employees ObsolescenceObsolescence

Supplies, such as forms and paper, for Supplies, such as forms and paper, for the purchasing departmentthe purchasing department

Salaries and wages for warehouse Salaries and wages for warehouse employeesemployees

Utilities and building costs for the Utilities and building costs for the warehousewarehouse

Supplies, such as forms and paper, for Supplies, such as forms and paper, for the warehousethe warehouseTable 6.1

Inventory Cost FactorsInventory Cost Factors

Ordering costs are generally independent of Ordering costs are generally independent of order quantity.order quantity.

Many involve personnel time.Many involve personnel time. The amount of work is the same no matter the The amount of work is the same no matter the

size of the order.size of the order. Carrying costs generally varies with the Carrying costs generally varies with the

amount of inventory, or the order size.amount of inventory, or the order size. The labour, space, and other costs increase as The labour, space, and other costs increase as

the order size increases.the order size increases. The actual cost of items purchased can vary The actual cost of items purchased can vary

if there are quantity discounts available.if there are quantity discounts available.

6-14

Economic Order QuantityEconomic Order Quantity The The economic order quantityeconomic order quantity

((EOQEOQ) model is one of the oldest ) model is one of the oldest and most commonly known and most commonly known inventory control techniques.inventory control techniques.

It is easy to use but has a It is easy to use but has a number of important number of important assumptions.assumptions.

Objective is to minimize total Objective is to minimize total cost of inventory.cost of inventory.

Economic Order QuantityEconomic Order QuantityAssumptions:Assumptions:

1.1. Demand is known and constant.Demand is known and constant.

2.2. Lead time is known and constant.Lead time is known and constant.

3.3. Receipt of inventory is instantaneous.Receipt of inventory is instantaneous.

4.4. Purchase cost per unit is constant throughout the Purchase cost per unit is constant throughout the year.year.

5.5. The only variable costs are the cost of placing an The only variable costs are the cost of placing an order, order, ordering costordering cost, and the cost of holding or , and the cost of holding or storing inventory over time, storing inventory over time, holdingholding or or carrying carrying costcost, and these are constant throughout the year., and these are constant throughout the year.

6.6. Orders are placed so that stockouts or shortages Orders are placed so that stockouts or shortages are avoided completely.are avoided completely.

Inventory Usage Over TimeInventory Usage Over Time

Time

InventoInventory ry LevelLevel

MinimuMinimum m InventorInventoryy 0

Order Quantity = Order Quantity = QQ = Maximum = Maximum Inventory LevelInventory Level

Figure 6.2

Inventory Costs in the EOQ Inventory Costs in the EOQ SituationSituation

Computing Average InventoryComputing Average Inventory

2level inventory Average

Q

INVENTORY LEVEL

DAY BEGINNING ENDING AVERAGE

April 1 (order received) 10 8 9

April 2 8 6 7

April 3 6 4 5

April 4 4 2 3

April 5 2 0 1Maximum level April 1 = 10 unitsTotal of daily averages = 9 + 7 + 5 + 3 + 1 = 25Number of days = 5Average inventory level = 25/5 = 5 units

Table 6.2

6-18

Inventory Costs in the Inventory Costs in the EOQEOQ SituationSituation

Mathematical equations can be Mathematical equations can be developed using:developed using:QQ = number of pieces to order= number of pieces to order

EOQEOQ = = QQ** = optimal number of pieces to order = optimal number of pieces to orderDD = annual demand in units for the inventory item= annual demand in units for the inventory itemCCoo = ordering cost of each order= ordering cost of each orderCChh = holding or carrying cost per unit per year= holding or carrying cost per unit per year

Annual ordering cost Annual ordering cost Number of Number of

orders orders placed per placed per

yearyear

Ordering Ordering cost per cost per

orderorder

oCQD


Mathematical equations can be Mathematical equations can be developed using:developed using:QQ = number of pieces to order= number of pieces to order

EOQEOQ = = QQ** = optimal number of pieces to order = optimal number of pieces to orderDD = annual demand in units for the inventory item= annual demand in units for the inventory itemCCoo = ordering cost of each order= ordering cost of each orderCChh = holding or carrying cost per unit per year= holding or carrying cost per unit per year

Annual holding cost Annual holding cost AveragAverag

e e inventoinvento

ryry

Carrying Carrying cost per cost per unit per unit per

yearyearhC

Q2


Minimum Total Cost

Optimal Order Quantity

Curve of Total Cost Curve of Total Cost of Carrying of Carrying and Orderingand Ordering

Carrying Cost CurveCarrying Cost Curve

Ordering Cost CurveOrdering Cost Curve

Cost

Order QuantityFigure 6.3

Total Cost as a Function of Order QuantityTotal Cost as a Function of Order Quantity

Finding the Finding the EOQEOQ

According to the graph, when the According to the graph, when the EOQEOQ assumptions assumptions are met, total cost is minimized when annual are met, total cost is minimized when annual ordering cost equals annual holding cost.ordering cost equals annual holding cost.

ho CQ

CQD

2

Solving for Solving for QQ ho CQDC 22

22Q

C

DC

h

o

*EOQ QQC

DC

h

o 2

Economic Order Quantity Economic Order Quantity ((EOQEOQ) Model) Model

hCQ2

cost holding Annual

oCQD

cost ordering Annual

h

o

C

DCQ

2 *EOQ

Summary of Summary of equations:equations:

Sumco Pump CompanySumco Pump Company Sumco Pump Company sells pump Sumco Pump Company sells pump

housings to other companies.housings to other companies. The firm would like to reduce inventory The firm would like to reduce inventory

costs by finding optimal order quantity.costs by finding optimal order quantity. Annual demand = 1,000 unitsAnnual demand = 1,000 units Ordering cost = $10 per orderOrdering cost = $10 per order Average carrying cost per unit per year = $0.50Average carrying cost per unit per year = $0.50

units 20000040500

10000122 ,

.))(,(*

h

o

C

DCQ

Sumco Pump CompanySumco Pump Company

Total annual cost = Order cost + Holding costTotal annual cost = Order cost + Holding cost

ho CQ

CQD

TC2

).()(,

502

20010

2000001

1005050 $$$

Sumco Pump CompanySumco Pump CompanyInput Data and Excel QM formulas Input Data and Excel QM formulas

for the Sumco Pump Company for the Sumco Pump Company ExampleExample

Sumco Pump CompanySumco Pump Company

Excel QM Excel QM Solution Solution for the for the Sumco Sumco Pump Pump Company Company ExampleExample

Purchase Cost of Inventory Purchase Cost of Inventory ItemsItems

Total inventory cost can be written to include the cost Total inventory cost can be written to include the cost of purchased items.of purchased items.

Given the Given the EOQEOQ assumptions, the annual purchase cost assumptions, the annual purchase cost is constant at is constant at DD CC no matter the order policy, where no matter the order policy, where CC is the purchase cost per unit. is the purchase cost per unit. DD is the annual demand in units. is the annual demand in units.

At times it may be useful to know the average dollar At times it may be useful to know the average dollar level of inventory:level of inventory:

2level dollar Average

)(CQ

Purchase Cost of Inventory Purchase Cost of Inventory ItemsItems

Inventory carrying cost is often expressed as an Inventory carrying cost is often expressed as an annual percentage of the unit cost or price of the annual percentage of the unit cost or price of the inventory.inventory.

This requires a new variable. This requires a new variable.

Annual inventory holding Annual inventory holding charge as a percentage of unit charge as a percentage of unit

price or costprice or cost

I

The cost of storing inventory The cost of storing inventory for one year is thenfor one year is thenICCh

thus,thus, IC

DCQ o2

*

Sensitivity Analysis with the Sensitivity Analysis with the EOQEOQ Model Model

The The EOQEOQ model assumes all values are know and model assumes all values are know and fixed over time.fixed over time.

Generally, however, some values are estimated or Generally, however, some values are estimated or may change.may change.

Determining the effects of these changes is Determining the effects of these changes is called called sensitivity analysis.sensitivity analysis.

Because of the square root in the formula, Because of the square root in the formula, changes in the inputs result in relatively small changes in the inputs result in relatively small changes in the order quantity.changes in the order quantity.

h

o

C

DC2EOQ

Sensitivity Analysis with the Sensitivity Analysis with the EOQEOQ Model Model

In the Sumco Pump example:In the Sumco Pump example:

units 200500

1000012

.))(,(

EOQ

If the ordering cost were increased four times from If the ordering cost were increased four times from $10 to $40, the order quantity would only double$10 to $40, the order quantity would only double

units 400500

4000012

.))(,(

EOQ

In general, In general, the the EOQEOQ changes by the square changes by the square root of the change to any of the inputsroot of the change to any of the inputs..

Reorder Point:Reorder Point:Determining When To OrderDetermining When To Order

Once the order quantity is determined, the Once the order quantity is determined, the next decision is next decision is when to order.when to order.

The time between placing an order and its The time between placing an order and its receipt is called the receipt is called the lead timelead time ( (LL) or ) or delivery time.delivery time.

When to order is generally expressed as aWhen to order is generally expressed as a reorder pointreorder point ( (ROPROP).).

Demand Demand per dayper day

Lead time for Lead time for a new order a new order

in daysin days

ROPROP

dd LL

Procomp’s Computer ChipsProcomp’s Computer Chips Demand for the computer chip is 8,000 per year.Demand for the computer chip is 8,000 per year. Daily demand is 40 units.Daily demand is 40 units. Delivery takes three working days.Delivery takes three working days.

ROPROP dd LL 40 units per day 40 units per day 3 days 3 days 120 units120 units An order based on the EOQ An order based on the EOQ

calculation is placed when the calculation is placed when the inventory reaches 120 units.inventory reaches 120 units.

The order arrives 3 days later just The order arrives 3 days later just as the inventory is depleted.as the inventory is depleted.

Reorder Point GraphsReorder Point Graphs

Figure 6.4

EOQ Without The Instantaneous EOQ Without The Instantaneous Receipt AssumptionReceipt Assumption

When inventory accumulates over time, the When inventory accumulates over time, the instantaneous receiptinstantaneous receipt assumption does not apply. assumption does not apply.

Daily demand rate must be taken into account.Daily demand rate must be taken into account. The revised model is often called the The revised model is often called the production production

run model.run model.

Figure 6.5

Annual Carrying Cost for Annual Carrying Cost for Production Run ModelProduction Run Model

In production runs, In production runs, setup costsetup cost replaces replaces ordering cost.ordering cost.

The model uses the following variables:The model uses the following variables:

QQ number of pieces per order, or number of pieces per order, or production runproduction run

CCss setup cost setup cost

CChh holding or carrying cost per holding or carrying cost per unit per yearunit per yearpp daily production rate daily production ratedd daily demand rate daily demand ratett length of production run in length of production run in daysdays


Maximum inventory levelMaximum inventory level (Total produced during the production run) (Total produced during the production run) – (Total used during the production run)– (Total used during the production run)

(Daily production rate)(Number of days production)(Daily production rate)(Number of days production)– (Daily demand)(Number of days production)– (Daily demand)(Number of days production)

((ptpt) – () – (dtdt))

sincesince Total produced Total produced QQ ptpt

we knowwe know pQ

t

MaximuMaximum m

inventorinventory levely level

pd

QpQ

dpQ

pdtpt 1


Since the average inventory is one-Since the average inventory is one-half the maximum: half the maximum:

pdQ

12

inventory Average

andand

hCpdQ

1

2cost holding Annual

Annual Setup Cost for Annual Setup Cost for Production Run ModelProduction Run Model

sCQD

cost setup Annual

Setup cost replaces ordering cost Setup cost replaces ordering cost when a product is produced over time. when a product is produced over time.

replacesreplaces

oCQD

cost ordering Annual

Determining the Optimal Determining the Optimal Production QuantityProduction Quantity

By setting setup costs equal to holding By setting setup costs equal to holding costs, we can solve for the optimal order costs, we can solve for the optimal order quantityquantity

Annual holding cost Annual setup cost

sh CQD

CpdQ

1

2

Solving for Q, we getSolving for Q, we get

pd

C

DCQ

h

s

1

2*

Production Run ModelProduction Run Model

Summary of Summary of equationsequations

pd

C

DCQ

h

s

1

2 quantity production Optimal *

sCQD

cost setup Annual

hCpdQ

1

2cost holding Annual

Brown ManufacturingBrown Manufacturing

Brown Manufacturing produces commercial Brown Manufacturing produces commercial refrigeration units in batches.refrigeration units in batches.

Annual demand D 10,000 unitsSetup cost Cs $100

Carrying cost Ch $0.50 per unit per yearDaily production rate p 80 units dailyDaily demand rate d 60 units daily

1.1. How many units should Brown produce in each batch?How many units should Brown produce in each batch?2.2. How long should the production part of the cycle last?How long should the production part of the cycle last?

Brown Manufacturing Brown Manufacturing ExampleExample

pd

C

DCQ

h

s

1

2*1. 2.

8060

150

100000102

.

,*Q

00000016

4150

0000002,,

.

,,

units 4,000

days 50800004

,

pQ

cycle Production

Brown ManufacturingBrown ManufacturingExcel QM Formulas and Input Data Excel QM Formulas and Input Data

for the Brown Manufacturing for the Brown Manufacturing ProblemProblem

Brown ManufacturingBrown Manufacturing

The Solution Results for the Brown The Solution Results for the Brown Manufacturing Problem Using Excel Manufacturing Problem Using Excel

QMQM

Quantity Discount Models Quantity Discount Models Quantity discounts are commonly available.Quantity discounts are commonly available. The basic The basic EOQEOQ model is adjusted by adding in the model is adjusted by adding in the

purchase or materials cost.purchase or materials cost.

Total cost Total cost Material cost + Ordering cost + Holding cost Material cost + Ordering cost + Holding cost

ho CQ

CQD

DC2

cost Total

wherewhereD annual demand in units

Co ordering cost of each orderC cost per unit

Ch holding or carrying cost per unit per year

Quantity Discount Models Quantity Discount Models Quantity discounts are commonly available.Quantity discounts are commonly available. The basic The basic EOQEOQ model is adjusted by adding in the model is adjusted by adding in the

purchase or materials cost.purchase or materials cost.

Total cost Material cost + Ordering cost + Holding cost

ho CQ

CQD

DC2

cost Total

wherewhereDD annual demand in units annual demand in units

CCoo ordering cost of each order ordering cost of each orderCC cost per unit cost per unit

CChh holding or carrying cost per unit per year holding or carrying cost per unit per year

Holding cost Holding cost CChh ICICII holding cost as a percentage of the unit cost ( holding cost as a percentage of the unit cost (CC))

Because unit cost is now variable,Because unit cost is now variable,

Quantity Discount Models Quantity Discount Models A typical quantity discount schedule can A typical quantity discount schedule can

look like the table below.look like the table below. However, buying at the lowest unit cost is However, buying at the lowest unit cost is

not always the best choice.not always the best choice.

DISCOUNT DISCOUNT NUMBERNUMBER

DISCOUNT DISCOUNT QUANTITYQUANTITY DISCOUNT (%)DISCOUNT (%)

DISCOUNT DISCOUNT COST ($)COST ($)

11 0 to 9990 to 999 00 5.005.00

22 1,000 to 1,9991,000 to 1,999 44 4.804.80

33 2,000 and over2,000 and over 55 4.754.75

Table 6.3

Quantity Discount Models Quantity Discount Models Total cost curve for the quantity discount modelTotal cost curve for the quantity discount model

Figure 6.6

TC Curve for Discount 1

TC Curve for Discount 3Total

Cost $

Order Quantity

0 1,000 2,000

TC Curve for Discount 2

EOQ for Discount 2

Brass Department StoreBrass Department Store

Brass Department Store stocks toy race cars.Brass Department Store stocks toy race cars. Their supplier has given them the quantity discount Their supplier has given them the quantity discount

schedule shown in Table 6.3.schedule shown in Table 6.3. Annual demand is 5,000 cars, ordering cost is $49, and Annual demand is 5,000 cars, ordering cost is $49, and

holding cost is 20% of the cost of the carholding cost is 20% of the cost of the car

The first step is to compute The first step is to compute EOQEOQ values for each values for each discount.discount.

order per cars 70000520

49000521

).)(.())(,)((

EOQ


49000522

).)(.())(,)((

EOQ


49000523

).)(.())(,)((

EOQ

Brass Department Store Brass Department Store ExampleExample

The second step is adjust quantities below the The second step is adjust quantities below the allowable discount range.allowable discount range.

The The EOQEOQ for discount 1 is allowable. for discount 1 is allowable. The The EOQEOQs for discounts 2 and 3 are outside the s for discounts 2 and 3 are outside the

allowable range and have to be adjusted to the allowable range and have to be adjusted to the smallest quantity possible to purchase and receive smallest quantity possible to purchase and receive the discount:the discount:

QQ11 700 700

QQ22 1,000 1,000

QQ33 2,000 2,000

Brass Department StoreBrass Department Store

The third step is to compute the total cost for each The third step is to compute the total cost for each quantity.quantity.

DISCOUNT DISCOUNT NUMBERNUMBER

UNIT UNIT PRICE PRICE

((CC))

ORDER ORDER QUANTITY QUANTITY

((QQ))

ANNUAL ANNUAL MATERIAL MATERIAL COST ($)COST ($)

= = DCDC

ANNUAL ANNUAL ORDERING ORDERING COST ($) COST ($) = (= (DD//QQ))CCoo

ANNUAL ANNUAL CARRYING CARRYING COST ($) COST ($) = (= (QQ//2)2)CChh TOTAL ($)TOTAL ($)

11 $5.00$5.00 700700 25,00025,000 350.00350.00 350.00350.00 25,700.0025,700.00

22 4.804.80 1,0001,000 24,00024,000 245.00245.00 480.00480.00 24,725.0024,725.00

33 4.754.75 2,0002,000 23,75023,750 122.50122.50 950.00950.00 24,822.5024,822.50

The final step is to choose The final step is to choose the alternative with the the alternative with the lowest total cost.lowest total cost.Table 6.4

Brass Department StoreBrass Department StoreExcel QM’s Formulas and the Input Data Excel QM’s Formulas and the Input Data for the Brass Department Store Quantity for the Brass Department Store Quantity

Discount ProblemDiscount Problem

Brass Department StoreBrass Department StoreExcel QM’s Solution to the Excel QM’s Solution to the Brass Department Store Brass Department Store

ProblemProblem

Use of Safety StockUse of Safety Stock If demand or the lead time are uncertain, If demand or the lead time are uncertain,

the exact the exact ROPROP will not be known with will not be known with certainty.certainty.

To prevent To prevent stockoutsstockouts, it is necessary to , it is necessary to carry extra inventory called carry extra inventory called safety stock.safety stock.

Safety stock can prevent stockouts Safety stock can prevent stockouts when demand is unusually high.when demand is unusually high.

Safety stock can be implemented by Safety stock can be implemented by adjusting the adjusting the ROP.ROP.

Use of Safety StockUse of Safety Stock

The basic The basic ROPROP equation is equation is

ROPROP dd LL

dd daily demand (or daily demand (or average daily demand)average daily demand)LL order lead time or the order lead time or the number of working days it number of working days it takes to deliver an order (or takes to deliver an order (or average lead time)average lead time) A safety stock variable is added to A safety stock variable is added to

the equation to accommodate the equation to accommodate uncertain demand during lead timeuncertain demand during lead time

ROP ROP dd L L ++ SS SSwherewhere

SSSS safety stock safety stock

Use of Safety StockUse of Safety Stock

Figure 6.7

ROP with Known Stockout ROP with Known Stockout CostsCosts

With a fixed With a fixed EOQEOQ and an and an ROPROP for placing for placing orders, stockouts can only occur during lead orders, stockouts can only occur during lead time.time.

Our objective is to find the safety stock Our objective is to find the safety stock quantity that will minimize the total of quantity that will minimize the total of stockout cost and holding cost.stockout cost and holding cost.

We need to know the stockout cost per unit We need to know the stockout cost per unit and the probability distribution of demand and the probability distribution of demand during lead time.during lead time.

Estimating stockout costs can be difficult as Estimating stockout costs can be difficult as there may be direct and indirect costs.there may be direct and indirect costs.

Safety Stock with Unknown Safety Stock with Unknown Stockout CostsStockout Costs

There are many situations when stockout There are many situations when stockout costs are unknown.costs are unknown.

An alternative approach to determining An alternative approach to determining safety stock levels is to use a safety stock levels is to use a service service levellevel..

A service level is the percent of time you A service level is the percent of time you will not be out of stock of a particular item.will not be out of stock of a particular item.

Service level Service level 1 – Probability of a 1 – Probability of a stockoutstockout

ororProbability of a stockout Probability of a stockout 1 – 1 –

Service levelService level

Safety Stock with the Normal Safety Stock with the Normal DistributionDistribution

ROP = (Average Demand During Lead Time) + ZROP = (Average Demand During Lead Time) + ZσσdLTdLT

Where:Where:

Z = number of standard Z = number of standard deviations for a given service deviations for a given service levellevelσσdLT dLT = standard deviation of = standard deviation of demand during lead timedemand during lead time

Safety Stock = ZSafety Stock = ZσσdLTdLT

Hinsdale CompanyHinsdale Company Inventory demand during lead time is normally Inventory demand during lead time is normally

distributed.distributed. Mean demand during lead time is 350 units with a Mean demand during lead time is 350 units with a

standard deviation of 10.standard deviation of 10. The company wants stockouts to occur only 5% of The company wants stockouts to occur only 5% of

the time.the time.

350

XX ? ?

SS

5% Area of 5% Area of Normal Normal CurveCurve

Figure 6.8

Mean demand Mean demand 350 350 dLTdLT Standard deviation Standard deviation 10 10

XX Mean demand + Safety stock Mean demand + Safety stockSSSS Safety stock Safety stock XX –– ZZ

X

Z

Hinsdale Company ExampleHinsdale Company Example

350 XX ? ?

SS

5% Area of Normal Curve

From Appendix A we find From Appendix A we find ZZ 1.65 1.65 SSX

Solving for safety Solving for safety stock:stock:SSSS 1.65(10) 1.65(10) 16.5 units, or 17 units 16.5 units, or 17 units

X = ROP = 350+16.5 = 366.5 unitsX = ROP = 350+16.5 = 366.5 units

Figure 6.9

Hinsdale CompanyHinsdale Company Different safety stock levels will be generated for Different safety stock levels will be generated for

different service levels.different service levels. However, the relationship is not linear.However, the relationship is not linear.

You should be aware of what a service level is costing You should be aware of what a service level is costing in terms of carrying the safety stock in inventory.in terms of carrying the safety stock in inventory.

The relationship between The relationship between ZZ and safety stock can and safety stock can be developed as follows:be developed as follows:

2. We also know that 2. We also know that SSSS XX ––

1. We know that1. We know that

XZ

3. Thus3. Thus SS

Z

4.4.So we So we have have SSSS

ZZ

ZZ(10)(10)

Hinsdale CompanyHinsdale CompanySafety Stock at different service levelsSafety Stock at different service levels

SERVICE SERVICE LEVEL (%)LEVEL (%)

ZZ VALUE FROM VALUE FROM NORMAL CURVE TABLENORMAL CURVE TABLE

SAFETY STOCK SAFETY STOCK (UNITS)(UNITS)

9090 1.281.28 12.812.8

9191 1.341.34 13.413.4

9292 1.411.41 14.114.1

9393 1.481.48 14.814.8

9494 1.551.55 15.515.5

9595 1.651.65 16.516.5

9696 1.751.75 17.517.5

9797 1.881.88 18.818.8

9898 2.052.05 20.520.5

9999 2.332.33 23.323.3

99.9999.99 3.723.72 37.237.2

Table 6.5

Hinsdale CompanyHinsdale Company

Figure 6.9

Service level versus annual carrying costsService level versus annual carrying costs

This graph This graph was was developed developed for a specific for a specific case, but the case, but the general general shape of the shape of the curve is the curve is the same for all same for all service-level service-level problems.problems.

Calculating Lead Time Demand Calculating Lead Time Demand and Standard Deviationand Standard Deviation

There are three situations to There are three situations to consider:consider: Demand is variable but lead time Demand is variable but lead time

is constant.is constant. Demand is constant but lead time Demand is constant but lead time

is variable.is variable. Both demand and lead time are Both demand and lead time are

variable.variable.


Demand is variable but lead time is Demand is variable but lead time is constant:constant:

Where:Where:


Demand is constant but lead time is variable:

Where:

6-68


Both demand and lead time are Both demand and lead time are variable.variable.

Notice that this is the most Notice that this is the most general case and that the other general case and that the other two cases can be derived from two cases can be derived from this formula.this formula.


Suppose for product SKU F5402, daily demand is Suppose for product SKU F5402, daily demand is normally distributed, with a mean of 15 units and a normally distributed, with a mean of 15 units and a standard deviation of 3. Lead time is exactly 4 days. standard deviation of 3. Lead time is exactly 4 days. To maintain a 97% service level, what is the ROP, To maintain a 97% service level, what is the ROP, and how much safety stock should be carried?and how much safety stock should be carried?

ROP = 15(4)+1.88(3*2)ROP = 15(4)+1.88(3*2)= 60 + 11.28= 60 + 11.28=71.28=71.28

So the average demand during So the average demand during lead time is 60 units, and lead time is 60 units, and safety stock is 11.28 units.safety stock is 11.28 units.


Suppose for product SKU B7319, daily demand is Suppose for product SKU B7319, daily demand is constant at 25 units per day, but lead time is constant at 25 units per day, but lead time is normally distributed, with a mean of 6 days and a normally distributed, with a mean of 6 days and a standard deviation of 3. To maintain a 98% service standard deviation of 3. To maintain a 98% service level, what is the ROP?level, what is the ROP?

ROP ROP = 25(6)+2.05(25*3)= 25(6)+2.05(25*3)= 150+153.75= 150+153.75=303.75=303.75

So the average demand during lead So the average demand during lead time is 150 units, and safety stock time is 150 units, and safety stock is 153.75 units.is 153.75 units.


Suppose for product SKU F9004, daily demand is normally Suppose for product SKU F9004, daily demand is normally distributed, with a mean of 20 units and a standard distributed, with a mean of 20 units and a standard deviation of 4. Lead time is normally distributed, with a deviation of 4. Lead time is normally distributed, with a mean of 5 days and a standard deviation of 2 days. To mean of 5 days and a standard deviation of 2 days. To maintain a 94% service level, what is the ROP?maintain a 94% service level, what is the ROP?

ROP ROP = 100+1.55(40.99)= 100+1.55(40.99)= 163.53= 163.53

Calculating Annual Holding Calculating Annual Holding Cost with Safety StockCost with Safety Stock

Under standard assumptions of Under standard assumptions of EOQ, average inventory is just EOQ, average inventory is just QQ/2./2.

So annual holding cost is: (So annual holding cost is: (QQ/2)*/2)*CChh.. This is not the case with safety This is not the case with safety

stock because safety stock is not stock because safety stock is not meant to be drawn down.meant to be drawn down.

Calculating Annual Holding Cost Calculating Annual Holding Cost with Safety Stockwith Safety Stock

Total annual holding cost = holding Total annual holding cost = holding cost of regular inventory + holding cost of regular inventory + holding cost of safety stockcost of safety stock

Where:Where:

THC = total annual holding costTHC = total annual holding costQQ = order quantity= order quantityCChh = holding cost per unit per year= holding cost per unit per yearSS SS = safety stock= safety stock

Excel QM Formulas and Input Data for Excel QM Formulas and Input Data for the Hinsdale Safety Stock Problemsthe Hinsdale Safety Stock Problems

Excel QM Solution to the Excel QM Solution to the Hinsdale Safety Stock ProblemHinsdale Safety Stock Problem

Single-Period Inventory ModelsSingle-Period Inventory Models Some products have no future value beyond the current Some products have no future value beyond the current

period.period. These situations are called These situations are called news vendornews vendor problems or problems or

single-period inventory models.single-period inventory models. Analysis uses marginal profit (Analysis uses marginal profit (MPMP) and marginal loss ) and marginal loss

((MLML) and is called marginal analysis.) and is called marginal analysis. With a manageable number of states of nature and With a manageable number of states of nature and

alternatives, discrete distributions can be used.alternatives, discrete distributions can be used. When there are a large number of alternatives or states When there are a large number of alternatives or states

of nature, the normal distribution may be used.of nature, the normal distribution may be used.

Marginal Analysis with Marginal Analysis with Discrete DistributionsDiscrete Distributions

We stock an additional unit only if the We stock an additional unit only if the expected marginal profit for that unit exceeds expected marginal profit for that unit exceeds the expected marginal loss.the expected marginal loss.

PP probability that demand will be probability that demand will be greater than or equal to a given greater than or equal to a given supply (or the probability of supply (or the probability of selling at least one additional selling at least one additional unit).unit).1 – 1 – PP probability that probability that

demand will be less than demand will be less than supply (or the probability that supply (or the probability that one additional unit will not one additional unit will not sell).sell).

Marginal Analysis with Marginal Analysis with Discrete DistributionsDiscrete Distributions

The expected marginal profit is The expected marginal profit is PP((MPMP) .) . The expected marginal loss is (1 – The expected marginal loss is (1 – PP)()(MLML).). The optimal decision rule is to stock the The optimal decision rule is to stock the

additional unit if:additional unit if:

PP((MPMP) ) ≥ (1 – ≥ (1 – PP))MLML With some basic With some basic

manipulation:manipulation:

PP((MPMP) ) ≥ ≥ MLML – – PP((MLML))PP((MPMP) + ) + PP((MLML) ≥ ) ≥ MLML

PP((MPMP + + MLML) ≥ ) ≥ MLML

oror MPMLML

P

Steps of Marginal Analysis Steps of Marginal Analysis with Discrete Distributionswith Discrete Distributions

1.1. Determine the value of for Determine the value of for the problem.the problem.

2.2. Construct a probability table and add a Construct a probability table and add a cumulative probability column.cumulative probability column.

3.3. Keep ordering inventory as long as the Keep ordering inventory as long as the probability (probability (PP) of selling at least one ) of selling at least one additionaladditional

unit is greater thanunit is greater than

MPMLML

MPMLML

CafCafé du Donuté du Donut

The cafThe café buys donuts each day for $4 per carton of é buys donuts each day for $4 per carton of 2 dozen donuts.2 dozen donuts.

Any cartons not sold are thrown away at the end of Any cartons not sold are thrown away at the end of the day.the day.

If a carton is sold, the total revenue is $6.If a carton is sold, the total revenue is $6. The marginal profit per carton is.The marginal profit per carton is.

MPMP Marginal profit Marginal profit $6 $6 –– $4 $4 $2 $2

The marginal loss is $4 per carton The marginal loss is $4 per carton since cartons can not be returned since cartons can not be returned or salvaged.or salvaged.

CafCafé du Donut’s Probability é du Donut’s Probability DistributionDistribution

DAILY SALES DAILY SALES (CARTONS OF DOUGHNUTS)(CARTONS OF DOUGHNUTS)

PROBABILITY (PROBABILITY (PP) THAT DEMAND ) THAT DEMAND WILL BE AT THIS LEVELWILL BE AT THIS LEVEL

44 0.050.05

55 0.150.15

66 0.150.15

77 0.200.20

88 0.250.25

99 0.100.10

1010 0.100.10

TotalTotal 1.001.00

Table 6.6

MPMLML

Step 1Step 1.. Determine the value of for the Determine the value of for the decision rule.decision rule.

CafCafé du Donut Exampleé du Donut Example

67064

244

.$$

$MPML

ML

P

670.P

Step 2Step 2..Add a new column to the table to Add a new column to the table to reflect the probability that doughnut reflect the probability that doughnut sales will be at each level or greater.sales will be at each level or greater.

Marginal Analysis for CafMarginal Analysis for Café é du Donutdu Donut

DAILY SALES DAILY SALES (CARTONS (CARTONS OF OF DOUGHNUTS)DOUGHNUTS)

PROBABILITY (PROBABILITY (PP) ) THAT DEMAND WILL THAT DEMAND WILL BE AT THIS LEVELBE AT THIS LEVEL

PROBABILITY (PROBABILITY (PP) THAT ) THAT DEMAND WILL BE AT DEMAND WILL BE AT THIS LEVEL OR THIS LEVEL OR GREATERGREATER

44 0.050.05 1.00 ≥ 0.661.00 ≥ 0.66

55 0.150.15 0.95 ≥ 0.660.95 ≥ 0.66

66 0.150.15 0.80 ≥ 0.660.80 ≥ 0.66

77 0.200.20 0.650.65

88 0.250.25 0.450.45

99 0.100.10 0.200.20

1010 0.100.10 0.100.10

TotalTotal 1.001.00Table 6.7

CafCafé du Donut Exampleé du Donut Example

Step 3. Keep ordering additional cartons as long as the probability of selling at least one additional carton is greater than P, which is the indifference probability.

PP at 6 cartons at 6 cartons 0.80 > 0.67 0.80 > 0.67

Marginal Analysis with the Marginal Analysis with the Normal DistributionNormal Distribution

We first need to find four values:We first need to find four values:1.1.The average or mean sales for the The average or mean sales for the

product, product, 2.2.The standard deviation of sales, The standard deviation of sales, 3.3.The marginal profit for the product, The marginal profit for the product,

MP.MP.4.4.The marginal loss for the product, The marginal loss for the product, ML.ML.We let We let XX ** optimal optimal stocking level.stocking level.

Steps of Marginal Analysis Steps of Marginal Analysis with the Normal Distributionwith the Normal Distribution

1.1. Determine the value of for Determine the value of for the problem.the problem.

2.2. Locate Locate PP on the normal distribution on the normal distribution (Appendix A) and find the associated (Appendix A) and find the associated ZZ-value.-value.

MPMLML

to solve for the resulting stocking policy:to solve for the resulting stocking policy:

ZX *

*X

Z

3.3.Find Find XX * * using the relationship: using the relationship:

Joe’s Stocking Decision for Joe’s Stocking Decision for the Chicago Tribunethe Chicago Tribune

Demand for the Demand for the Chicago TribuneChicago Tribune at Joe’s Newsstand at Joe’s Newsstand averages 60 papers a day with a standard deviation of averages 60 papers a day with a standard deviation of 10.10.

The marginal loss is 20 cents and the marginal profit is The marginal loss is 20 cents and the marginal profit is 30 cents.30 cents.

Step 1Step 1. Joe should stock the . Joe should stock the TribuneTribune as long as as long as the probability of selling the last unit is at least the probability of selling the last unit is at least MLML/(/(MLML + + MPMP): ):

4005020

cents 30cents 20cents 20

.MPML

ML

Let Let PP = 0.40. = 0.40.


Step 2. Using the normal distribution in Figure 6.10, we find the appropriate Z value

ZZ = 0.25 standard deviations from the mean = 0.25 standard deviations from the mean

50 X Demand

Area under the Curve is 0.40

Figure 6.10 X *

Optimal Stocking Policy (62 Newspapers)

Area under the Curve is 1 – 0.40 = 0.60(Z = 0.25) Mean Daily Sales


Step 3. In this problem, 60 and 10, so

1060

250

*

.X

oror

XX * * 60 + 0.25(10) 60 + 0.25(10) 62.5, or 62 newspapers 62.5, or 62 newspapers

Joe should order 62 Joe should order 62 newspapers since the newspapers since the probability of selling 63 probability of selling 63 newspapers is slightly less newspapers is slightly less than 0.40than 0.40


The procedure is the same when The procedure is the same when PP > 0.50. > 0.50. Joe also stocks the Joe also stocks the Chicago Sun-Times.Chicago Sun-Times. Marginal loss is 40 cents and marginal Marginal loss is 40 cents and marginal

profit is 10 cents.profit is 10 cents. Daily sales average 100 copies with a Daily sales average 100 copies with a

standard deviation of 10 papers.standard deviation of 10 papers.

8005040

cents 10cents 40cents 40

.MPML

ML

ZZ = = – – 0.84 standard deviations from the mean0.84 standard deviations from the mean

From Appendix From Appendix A:A:


With With 100 and 100 and 10 10

10100

840

*

.X

or

XX * * 100 – 0.84(10) 100 – 0.84(10) 91.6, or 91 newspapers91.6, or 91 newspapers

100 X Demand

Area under Area under the Curve is the Curve is 0.400.40

Figure 6.11X *

Optimal Stocking Policy (91 Newspapers)

(Z = – 0.84)

ABC AnalysisABC Analysis

The purpose of ABC analysis is to divide the The purpose of ABC analysis is to divide the inventory into three groups based on the overall inventory into three groups based on the overall inventory value of the items.inventory value of the items.

Group A items account for the major portion of Group A items account for the major portion of inventory costs.inventory costs. Typically about 70% of the dollar value but only 10% of the Typically about 70% of the dollar value but only 10% of the

quantity of items.quantity of items. Forecasting and inventory management must be done Forecasting and inventory management must be done

carefully.carefully.

Group B items are more moderately priced.Group B items are more moderately priced. May represent 20% of the cost and 20% of the quantity.May represent 20% of the cost and 20% of the quantity.

Group C items are very low cost but high volume.Group C items are very low cost but high volume. It is not cost effective to spend a lot of time managing It is not cost effective to spend a lot of time managing

these items.these items.

Summary of ABC AnalysisSummary of ABC Analysis

INVENTORY INVENTORY GROUPGROUP

DOLLAR DOLLAR USAGE (%)USAGE (%)

INVENTORY INVENTORY ITEMS (%)ITEMS (%)

ARE QUANTITATIVE ARE QUANTITATIVE CONTROL TECHNIQUES CONTROL TECHNIQUES USED?USED?

AA 7070 1010 YesYes

BB 2020 2020 In some casesIn some cases

CC 1010 7070 NoNo

Table 6.8

6-94

Dependent Demand: The Case for Dependent Demand: The Case for Material Requirements PlanningMaterial Requirements Planning

All the inventory models discussed so far All the inventory models discussed so far have assumed demand for one item is have assumed demand for one item is independent of the demand for any other independent of the demand for any other item.item.

However, in many situations items demand is However, in many situations items demand is dependent on demand for one or more other dependent on demand for one or more other items.items.

In these situations, In these situations, Material Requirements Material Requirements Planning (MRP)Planning (MRP) can be employed effectively. can be employed effectively.

Dependent Demand: The Case for Dependent Demand: The Case for Material Requirements PlanningMaterial Requirements Planning

Some of the benefits of MRP are:Some of the benefits of MRP are:1.1. Increased customer service levels.Increased customer service levels.

2.2. Reduced inventory costs.Reduced inventory costs.

3.3. Better inventory planning and scheduling.Better inventory planning and scheduling.

4.4. Higher total sales.Higher total sales.

5.5. Faster response to market changes and shifts.Faster response to market changes and shifts.

6.6. Reduced inventory levels without reduced Reduced inventory levels without reduced customer service.customer service.

Most MRP systems are computerized, but Most MRP systems are computerized, but the basic analysis is straightforward.the basic analysis is straightforward.

6-96

Material Structure TreeMaterial Structure Tree

The first step is to develop a The first step is to develop a bill of materials bill of materials ((BOMBOM).).

The BOM identifies components, descriptions, The BOM identifies components, descriptions, and the number required for production of one and the number required for production of one unit of the final product.unit of the final product.

From the BOM we can develop a material From the BOM we can develop a material structure tree.structure tree.

We use the following data:We use the following data: Demand for product A is 50 units.Demand for product A is 50 units. Each A requires 2 units of B and 3 units of C.Each A requires 2 units of B and 3 units of C. Each B requires 2 units of D and 3 units of E.Each B requires 2 units of D and 3 units of E. Each C requires 1 unit of E and 2 units of F.Each C requires 1 unit of E and 2 units of F.


Material structure tree for Item AMaterial structure tree for Item A

ALevel

0

1

2

B(2) C(3)

D(2) E(3) F(2)E(1)

Figure 6.12


It is clear from the three that the demand for B, C, It is clear from the three that the demand for B, C, D, E, and F is completely dependent on the D, E, and F is completely dependent on the demand for A.demand for A.

The material structure tree has three levels: 0, 1, The material structure tree has three levels: 0, 1, and 2.and 2.

Items above a level are called Items above a level are called parents.parents. Items below any level are called Items below any level are called components.components. The number in parenthesis beside each item The number in parenthesis beside each item

shows how many are required to make the item shows how many are required to make the item above it.above it.

Material Structure TreeMaterial Structure TreeWe can use the material structure tree and the demand We can use the material structure tree and the demand for Item A to compute demands for the other items.for Item A to compute demands for the other items.

Part B: 2 number of A’s 2 50 100.

Part C: 3 number of A’s 3 50 150.

Part D: 2 number of B’s 2 100 200.

Part E: 3 number of B’s + 1 number of C’s 3 100 + 1 150 450.

Part F: 2 number of C’s 2 150 300.

Gross and Net Material Gross and Net Material Requirements PlanRequirements Plan

Once the materials structure tree is done, we Once the materials structure tree is done, we construct a gross material requirements plan.construct a gross material requirements plan.

This is a time schedule that shows:This is a time schedule that shows: when an item must be ordered when there is no when an item must be ordered when there is no

inventory on hand, or inventory on hand, or when the production of an item must be started in order when the production of an item must be started in order

to satisfy the demand for the finished product at a to satisfy the demand for the finished product at a particular date.particular date.

We need lead times for each of the items.We need lead times for each of the items.

Item A – 1 week Item D – 1 weekItem B – 2 weeks Item E – 2 weeksItem C – 1 week Item F – 3 weeks

Gross Material Requirements Gross Material Requirements Plan for 50 Units of APlan for 50 Units of A

Week

1 2 3 4 5 6

ARequired Date 50

Lead Time = 1 WeekOrder Release 50

BRequired Date 100

Lead Time = 2 WeeksOrder Release 100

CRequired Date 150


DRequired Date 200


ERequired Date 300 150

Lead Time = 2 WeeksOrder Release 300 150

FRequired Date 300

Lead Time = 3 WeeksOrder Release 300 Figure 6.13

Net Material Requirements PlanNet Material Requirements Plan

A net material requirements plan can be constructed A net material requirements plan can be constructed from the gross materials requirements plan and the from the gross materials requirements plan and the following on-hand inventory information:following on-hand inventory information:

ITEM ON-HAND INVENTORY

A 10

B 15

C 20

D 10

E 10

F 5Table 6.9

Net Material Requirements PlanNet Material Requirements Plan

Using this data we can construct a plan Using this data we can construct a plan that includes:that includes: Gross requirements.Gross requirements. On-hand inventory.On-hand inventory. Net requirements.Net requirements. Planned-order receipts.Planned-order receipts. Planned-order releases.Planned-order releases.

The net requirements plan is constructed The net requirements plan is constructed like the gross requirements plan.like the gross requirements plan.

Net Material Requirements Net Material Requirements Plan for 50 Units of APlan for 50 Units of A

WeekLead TimeItem 1 2 3 4 5 6

A Gross 50 1

On-Hand 10 10

Net 40

Order Receipt 40

Order Release 40

B Gross 80A 2

On-Hand 15 15

Net 65

Order Receipt 65

Order Release 65Figure 6.14(a)



C Gross 120A 1

On-Hand 20 10

Net 100

Order Receipt 100

Order Release 100

D Gross 130B 1

On-Hand 10 10

Net 120

Order Receipt 120

Order Release 120Figure 6.14(b)



E Gross 195B 100C 2

On-Hand 10 10 0

Net 185 100

Order Receipt 185 100

Order Release 185 100

F Gross 200C 3

On-Hand 5 5

Net 195

Order Receipt 195

Order Release 195

Figure 6.14(c)

Two or More End ProductsTwo or More End Products

Most manufacturing companies have more than Most manufacturing companies have more than one end item.one end item.

In this example, the second product is AA and it In this example, the second product is AA and it has the following material structure tree:has the following material structure tree:

AA

D(3) F(2)

If we require 10 units of AA, the gross If we require 10 units of AA, the gross requirements for parts D and F can be requirements for parts D and F can be computed:computed:

Part D: 3 number of AA’s 3 10 30

Part F: 2 number of AA’s 2 10 20

Two or More End ProductsTwo or More End Products

The lead time for AA is one week.The lead time for AA is one week. The gross requirement for AA is 10 units in week 6 The gross requirement for AA is 10 units in week 6

and there are no units on hand.and there are no units on hand. This new product can be added to the MRP process.This new product can be added to the MRP process. The addition of AA will only change the MRP The addition of AA will only change the MRP

schedules for the parts contained in AA.schedules for the parts contained in AA.

MRP can also schedule spare parts MRP can also schedule spare parts and components.and components.

These have to be included as gross These have to be included as gross requirements.requirements.

6-109

Net Material Requirements Plan, Net Material Requirements Plan, Including AAIncluding AA

Figure 6.15

Just-in-Time (JIT) Inventory ControlJust-in-Time (JIT) Inventory Control

To achieve greater efficiency in the To achieve greater efficiency in the production process, organizations have production process, organizations have tried to have less in-process inventory on tried to have less in-process inventory on hand.hand.

This is known as This is known as JIT inventory.JIT inventory. The inventory arrives just in time to be used The inventory arrives just in time to be used

during the manufacturing process.during the manufacturing process. One technique of implementing JIT is a One technique of implementing JIT is a

manual procedure called manual procedure called kanban.kanban.

Just-in-Time Inventory ControlJust-in-Time Inventory Control

Kanban in Japanese means “card.” Kanban in Japanese means “card.” With a dual-card kanban system, there is a With a dual-card kanban system, there is a

conveyance kanban, or C-kanban, and a conveyance kanban, or C-kanban, and a production kanban, or P-kanban.production kanban, or P-kanban.

Kanban systems are quite simple, but they Kanban systems are quite simple, but they require considerable discipline.require considerable discipline.

As there is little inventory to cover As there is little inventory to cover variability, the schedule must be followed variability, the schedule must be followed exactly.exactly.

4 Steps of Kanban4 Steps of Kanban

1.1. A user takes a container of parts or inventory A user takes a container of parts or inventory along with its C-kanban to his or her work area.along with its C-kanban to his or her work area.

When there are no more parts or the container is When there are no more parts or the container is empty, the user returns the container along with empty, the user returns the container along with the C-kanban to the producer area.the C-kanban to the producer area.

2.2. At the producer area, there is a full container of At the producer area, there is a full container of parts along with a P-kanban.parts along with a P-kanban.

The user detaches the P-kanban from the full The user detaches the P-kanban from the full container and takes the container and the C-container and takes the container and the C-kanban back to his or her area for immediate use.kanban back to his or her area for immediate use.

4 Steps of Kanban4 Steps of Kanban

3.3. The detached P-kanban goes back to the The detached P-kanban goes back to the producer area along with the empty containerproducer area along with the empty container

The P-kanban is a signal that new parts are to be The P-kanban is a signal that new parts are to be manufactured or that new parts are to be placed manufactured or that new parts are to be placed in the container and is attached to the container in the container and is attached to the container when it is filled .when it is filled .

4.4. This process repeats itself during the typical This process repeats itself during the typical workday.workday.

The Kanban SystemThe Kanban System

ProducProducer Areaer Area

StoraStorage ge

AreaArea

UseUser r

AreAreaa

P-kanban P-kanban and and

ContaineContainerr

C-kanban C-kanban and and

ContaineContainerr

4

3 2

1

Figure 6.16

MRP has evolved to include not only the materials MRP has evolved to include not only the materials required in production, but also the labor hours, required in production, but also the labor hours, material cost, and other resources related to material cost, and other resources related to production.production.

In this approach the term MRP II is often used and In this approach the term MRP II is often used and the word the word resourceresource replaces the word replaces the word requirements.requirements.

As this concept evolved and sophisticated software As this concept evolved and sophisticated software was developed, these systems became known aswas developed, these systems became known as enterprise resource planning enterprise resource planning ((ERPERP) systems.) systems.

Enterprise Resource PlanningEnterprise Resource Planning

The objective of an ERP System is to reduce costs The objective of an ERP System is to reduce costs by integrating all of the operations of a firm.by integrating all of the operations of a firm.

Starts with the supplier of materials needed and Starts with the supplier of materials needed and flows through the organization to include invoicing flows through the organization to include invoicing the customer of the final product.the customer of the final product.

Data are entered only once into a database where it Data are entered only once into a database where it can be quickly and easily accessed by anyone in can be quickly and easily accessed by anyone in the organization.the organization.

Benefits include:Benefits include: Reduced transaction costs.Reduced transaction costs. Increased speed and accuracy of Increased speed and accuracy of

information.information.


6-117

Drawbacks to ERP:Drawbacks to ERP: The software is expensive to buy and costly to The software is expensive to buy and costly to

customize. customize. Small systems can cost hundreds of thousands of Small systems can cost hundreds of thousands of

dollars.dollars. Large systems can cost hundreds of millions.Large systems can cost hundreds of millions.

The implementation of an ERP system may The implementation of an ERP system may require a company to change its normal require a company to change its normal operations.operations.

Employees are often resistant to change.Employees are often resistant to change. Training employees on the use of the new Training employees on the use of the new

software can be expensive.software can be expensive.


TutorialTutorial

Lab Practical : Spreadsheet Lab Practical : Spreadsheet

1 - 118

Further ReadingFurther Reading

Render, B., Stair Jr.,R.M. & Hanna, M.E. (2013) Quantitative Analysis for Management, Pearson, 11th Edition

Waters, Donald (2007) Quantitative Methods for Business, Prentice Hall, 4th Edition.

Anderson D, Sweeney D, & Williams T. (2006) Quantitative Methods For Business Thompson Higher Education, 10th Ed.

QUESTIONS?QUESTIONS?

bba 3274 qm week 7 inventory models

Business

inventory cost factors

total cost of inventory

common inventory costs

total inventory costs

lower inventory levels

low inventory levels

time inventory concepts

handle inventory problems