chapter 4 inventory management. learning objectives define inventory and functions of inventory...

CHAPTER 4CHAPTER 4

INVENTORY INVENTORY MANAGEMENTMANAGEMENT

LEARNING OBJECTIVESLEARNING OBJECTIVES

Define inventory and functions of inventory

Conduct an ABC analysis.

Explain and apply the EOQ and POQ model to solve typical problems.

Compute a ROP and safety stock

Inventory

A stock or store of goodsA stock of item kept to meet demand

Inventory Management How much

When

Classified

Accuracy

Objective of Inventory Control

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

To keep enough inventory to meet customer demand and also be cost effective. Level of customer service

Costs of ordering and carrying inventory

Functions of Inventory

To meet anticipated demand

To decouple operations

To protect against stock-outs

To take advantage of order cycles

To help hedge against price increases

To take advantage of quantity discounts

Types of Inventory

Types of Inventory

Raw material Purchased but not processed

Work-in-process Undergone some change but not

completed A function of cycle time for a product

Maintenance/repair/operating (MRO) Necessary to keep machinery and

processes productive

Types of Inventory

Finished-goods inventories (manufacturing firms) or merchandise

(retail stores)Goods in transit

Completed product awaiting shipment

The Material Flow Cycle

InputInput Wait forWait for Wait toWait to MoveMove Wait in queueWait in queue SetupSetup RunRun OutputOutputinspectioninspection be movedbe moved timetime for operatorfor operator timetime timetime

Cycle timeCycle time

95%95% 5%5%

Effective Inventory Management

A system to keep track of inventory

A reliable forecast of demand

Knowledge of lead times

Reasonable estimates ofo Holding costs

o Ordering costs

o Shortage costs

A classification system

Inventory Counting Systems

Periodic Systemo Physical count of items made at periodic

intervals

Perpetual Inventory System o keeps track of removals from inventory

continuously, thus monitoring current levels of each item

Inventory Counting Systems

Two-Bin System Two containers of inventory; reorder when

the first is empty

Universal Bar Code printed on a label that has

information about the item to which it is attached

0

214800 232087768

Key Inventory TermsLead time: time interval between ordering and

receiving the order Item cost: Cost per item plus any other direct

costs associated with getting the item to the plant

Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year

Ordering costs: costs of ordering and receiving inventory

Shortage costs: costs when demand exceeds supply

Independent Versus Dependent Demand Independent Demand

A

B(4) C(2)

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

Dependent Demand

Independent demand is uncertain. Dependent demand is certain.

ABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

AA - very important

BB - moderately important

CC - least important

Annual $ value of items

AA

BB

CC

High

Low

Low HighPercentage of Items

ABC Analysis

A ItemsA Items

B ItemsB ItemsC ItemsC Items

Pe

rce

nt

of

an

nu

al d

olla

r u

sa

ge

Pe

rce

nt

of

an

nu

al d

olla

r u

sa

ge

80 80 –

70 70 –

60 60 –

50 50 –

40 40 –

30 30 –

20 20 –

10 10 –

0 0 – | | | | | | | | | |

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percent of inventory itemsPercent of inventory items

ABC Analysis Example

Data Results - sorted by dollar volume

Dollar Volume Rank Item Volume Unit Cost Dollar volume

Dollar Volume Rank Item Volume Unit Cost Dollar Volume

Percent of Dollar Volume

Cum Percent of Dollar Volume Category

2 Item 1 1200 5.84 7,008.00$ 1 Item 4 1104 74.54 82,292.16$ 81.87% 81.87% A3 Item 2 1110 5.4 5,994.00$ 2 Item 1 1200 5.84 7,008.00$ 06.97% 88.84% B6 Item 3 896 1.12 1,003.52$ 3 Item 2 1110 5.4 5,994.00$ 05.96% 94.80% B1 Item 4 1104 74.54 82,292.16$ 4 Item 5 1110 2 2,220.00$ 02.21% 97.01% C4 Item 5 1110 2 2,220.00$ 5 Item 6 961 2.08 1,998.88$ 01.99% 99.00% C5 Item 6 961 2.08 1,998.88$ 6 Item 3 896 1.12 1,003.52$ 01.00% 100.00% C

Total 100,516.56$

Inventory Models for Independent Demand

Need to determine when and how much to order Basic economic order quantity Production order quantity Quantity discount model

Basic EOQ Model

Demand is known, constant, and independent

Lead time is known and constant Receipt of inventory is instantaneous and

complete Quantity discounts are not possible Only variable costs are setup and

holding Stockouts can be completely avoided

Cycle-Inventory Levels

Inventory depletion Inventory depletion (demand rate)(demand rate)

Receive Receive orderorder

1 cycle1 cycle

On

-han

d i

nve

nto

ry (

un

its)

On

-han

d i

nve

nto

ry (

un

its)

TimeTime

QQ

AverageAveragecyclecycleinventoryinventory

QQ——22

Total Annual Cycle-Inventory Costs

Objective is to minimize total costs

Table 11.5Table 11.5

An

nu

al c

ost

An

nu

al c

ost

Order quantityOrder quantity

Curve for total Curve for total cost of holding cost of holding

and setupand setup

Holding cost Holding cost curvecurve

Setup (or order) Setup (or order) cost curvecost curve

Minimum Minimum total costtotal cost

Optimal order Optimal order quantity (Q*)quantity (Q*)

Total cost = (Total cost = (HH) + () + (SS))DDQQ

QQ22

Holding cost = (Holding cost = (HH))QQ22

Ordering cost = (Ordering cost = (SS))DDQQ

Minimum Total Cost The total cost curve reaches its minimum where

the carrying and ordering costs are equal.

Q2

H DQ

S=

Cost Holding AnnualCost) Setupor der Demand)(Or 2(Annual

=

H

2DS = Q

Example

Bird feeder sales are 18 units per week, and the supplier charges $60 per unit. The cost of placing an order (S) with the supplier is $45.

Annual holding cost (H) is 25% of a feeder’s value, based on operations 52 weeks per year.

Management chose a 390-unit lot size (Q) so that new orders could be placed less frequently.

What is the annual cycle-inventory cost (C) of the current policy of using a 390-unit lot size?

Costing out a Lot Sizing Policy

What is the annual cycle-inventory cost (C) of the current policy of using a 390-unit lot size?

D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15

C = $2925 + $108 = $3033

C = (H) + (S) = (15) + (45) Q2

DQ

936390

3902

Museum of Natural History Gift Shop:

Would a lot size of 468 be better?

Lot Sizing at the Museumof Natural History Gift Shop

D = 936 units; H = $15; S = $45; Q = 390 units; C = $3033

C = (H) + (S) = (15) + (45) Q2

DQ

936468

4682

Q = 468 units; C = ?

C = $3510 + $90 = $3600

Q = 468 is a more expensive option.

The best lot size (EOQ) is the lowest point on the total annual cost curve!

3000 3000 —

2000 2000 —

1000 1000 —

0 0 —| | | | | | | |

5050 100100 150150 200200 250250 300300 350350 400400

Lot Size (Q)

Ann

ual c

ost

(dol

lars

)A

nnua

l cos

t (d

olla

rs) Total costTotal cost

Holding costHolding cost

Ordering costOrdering cost

Currentcost

CurrentQ

Lowestcost

Best Q (EOQ)

Lot Sizing at the Museumof Natural History Gift Shop

Computing the EOQ

C = (H) + (S)Q2

DQ

EOQ = 2DS

H

D = annual demandS = ordering or setup costs per lotH = holding costs per unit

D = 936 unitsH = $15S = $45

EOQ = 2(936)4515

= 74.94 or 75 units

C = (15) + (45)752

93675

C = $1,124.10

Bird Feeders:

Computing EOQ using the Excel Solver

= T == T =Expected Expected

time between time between ordersorders

Number of working Number of working days per yeardays per year

NN

= N = == N = =Expected Expected number of number of

ordersorders

DemandDemandOrder quantityOrder quantity

DDQ*Q*

TBOEOQ =EOQ

D

Understanding the Effect of Changes

A Change in the Demand Rate (D): When demand rises, the lot size also rises, but more slowly than actual demand.

A Change in the Setup Costs (S): Increasing S increases the EOQ and, consequently, the average cycle inventory.

A Change in the Holding Costs (H): EOQ declines when H increases.

EOQ: Robust Model ?

Errors in Estimating D, H, and S: Total cost is fairly insensitive to errors, even when the estimates are wrong by a large margin. The reasons are that errors tend to cancel each other out and that the square root reduces the effect of the error.

When to Reorder with EOQ Ordering

Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered

Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.

Service Level - Probability that demand will not exceed supply during lead time.

Determinants of the Reorder Point

The rate of demandThe lead timeDemand and/or lead time variabilityStockout risk (safety stock)

Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stockSafety stock reduces risk ofstockout during lead time

Reorder Point

ROP ROP ==Lead time for a Lead time for a

new order in daysnew order in daysDemand Demand per dayper day

== d x L d x L

d = d = DDNumber of working days in a yearNumber of working days in a year

Q*Q*

ROP ROP (units)(units)In

ven

tory

lev

el (

un

its)

Inve

nto

ry l

evel

(u

nit

s)

Time (days)Time (days)Lead time = LLead time = L

Slope = units/day = dSlope = units/day = d

Production Order Quantity Model

Used when inventory builds up over a Used when inventory builds up over a period of time after an order is placedperiod of time after an order is placed

Used when units are produced and sold Used when units are produced and sold simultaneouslysimultaneously

Inve

nto

ry l

evel

Inve

nto

ry l

evel

TimeTime

Demand part of cycle Demand part of cycle with no productionwith no production

Part of inventory cycle during Part of inventory cycle during which production (and usage) which production (and usage) is taking placeis taking place

tt

Maximum Maximum inventoryinventory


Q =Q = Number of pieces per orderNumber of pieces per order p = p = Daily production rateDaily production rateH =H = Holding cost per unit per yearHolding cost per unit per year d = d = Daily demand/usage rateDaily demand/usage ratet =t = Length of the production run in daysLength of the production run in days

= –= –Maximum Maximum inventory levelinventory level

Total produced during Total produced during the production runthe production run

Total used during Total used during the production runthe production run

== pt – dt pt – dt

H

2

IS

Q

DTC MAX

EPQ

= –= –Maximum Maximum inventory levelinventory level

Total produced during Total produced during the production runthe production run

Total used during Total used during the production runthe production run

== pt – dt pt – dt

However, Q = total produced = pt ; thus t = Q/pHowever, Q = total produced = pt ; thus t = Q/p

Maximum Maximum inventory levelinventory level = p – d = Q = p – d = Q 1 –1 –QQ

ppQQpp

ddpp

Holding cost = Holding cost = ((HH)) = = 1 –1 – H H ddpp

QQ22

Maximum inventory levelMaximum inventory level

22


QQ22 = =22DSDS

HH[1 - ([1 - (dd//pp)])]

QQ* =* =22DSDS

HH[1 - [1 - ((dd//pp)])]

pp

Setup cost Setup cost == ((DD//QQ))SS

Holding cost Holding cost == HQ HQ[1 - ([1 - (dd//pp)])]1122

((DD//QQ))S = HQS = HQ[1 - ([1 - (dd//pp)])]1122


EPQ.xls

Quantity Discount Models

Reduced prices are often available when larger quantities are purchased

Trade-off is between reduced product cost and increased holding cost

Total cost = Setup cost + Holding cost + Product costTotal cost = Setup cost + Holding cost + Product cost

TC = S + H + PDTC = S + H + PDDDQQ

QQ22

Total Cost With PDC

ost

EOQ/POQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing costdoesn’t change EOQ


Discount Number Discount Quantity Discount (%)

Discount Price (P)

1 0 to 999 no discount $5.00

2 1,000 to 1,999 4 $4.80

3 2,000 and over 5 $4.75


A typical quantity discount scheduleA typical quantity discount schedule

1. For each discount, calculate Q*

2. If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount

3. Compute the total cost for each Q* or adjusted value from Step 2

4. Select the Q* that gives the lowest total cost

Steps in analyzing a quantity discountSteps in analyzing a quantity discount


1,0001,000 2,0002,000

To

tal

cost

$T

ota

l co

st $

00

Order quantityOrder quantity

Q* for discount 2 is below the allowable range at point a Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point band must be adjusted upward to 1,000 units at point b

aabb

1st price 1st price breakbreak

2nd price 2nd price breakbreak

Total cost Total cost curve for curve for

discount 1discount 1

Total cost curve for discount 2Total cost curve for discount 2

Total cost curve for discount 3Total cost curve for discount 3

Figure 12.7Figure 12.7


Calculate Q* for every discountCalculate Q* for every discount Q* =2DSIP

QQ11* * = = 700= = 700 cars/order cars/order2(5,000)(49)2(5,000)(49)

(.2)(5.00)(.2)(5.00)


(.2)(4.80)(.2)(4.80)


(.2)(4.75)(.2)(4.75)


Calculate Q* for every discountCalculate Q* for every discount Q* =2DSIP


(.2)(5.00)(.2)(5.00)


(.2)(4.80)(.2)(4.80)


(.2)(4.75)(.2)(4.75)

1,0001,000 — adjusted — adjusted

2,0002,000 — adjusted — adjusted


Discount Number

Unit Price

Order Quantity

Annual Product

Cost

Annual Ordering

Cost

Annual Holding

Cost Total

1 $5.00 700 $25,000 $350 $350 $25,700

2 $4.80 1,000 $24,000 $245 $480 $24,725

3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50


Choose the price and quantity that gives Choose the price and quantity that gives the lowest total costthe lowest total cost

Buy Buy 1,0001,000 units at units at $4.80$4.80 per unit per unit


Quantity Discount Example: Collin’s Sport store is considering going to a different hat supplier. The present supplier charges $10 each and requires minimum quantities of 490 hats. The annual demand is 12,000 hats, the ordering cost is $20, and the inventory carrying cost is 20% of the hat cost, a new supplier is offering hats at $9 in lots of 4000. Who should he buy from?

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

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

$101,66012,000$9$1.802

4000$20

4000

12,000C

$120,98012,000$10$22

490$20

490

12,000C

$9

$10

Probabilistic Models and Safety Stock

Used when demand is not constant or certain

Use safety stock to achieve a desired service level and avoid stockouts

ROP ROP == d x L d x L + + ssss

Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit

x the number of orders per year

Safety Stock Example

Number of Units Probability

30 .2

40 .2

ROP 50 .3

60 .2

70 .1

1.0

ROP ROP = 50= 50 units units Stockout cost Stockout cost = $40= $40 per frame per frameOrders per year Orders per year = 6= 6 Carrying cost Carrying cost = $5= $5 per frame per year per frame per year

ROP ROP = 50= 50 units units Stockout cost Stockout cost = $40= $40 per frame per frameOrders per year Orders per year = 6= 6 Carrying cost Carrying cost = $5= $5 per frame per year per frame per year

Safety Stock

Additional Holding Cost Stockout Cost

Total Cost

20 (20)($5) = $100 $0 $100

10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290

0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960

A safety stock of A safety stock of 2020 frames gives the lowest total cost frames gives the lowest total cost

ROP ROP = 50 + 20 = 70= 50 + 20 = 70 frames frames

Safety Stock Example

Safety stock 16.5 units

ROP ROP

Place Place orderorder

Probabilistic DemandIn

ven

tory

lev

elIn

ven

tory

lev

el

TimeTime00

Minimum demand during lead timeMinimum demand during lead time

Maximum demand during lead timeMaximum demand during lead time

Mean demand during lead timeMean demand during lead time

Normal distribution probability of Normal distribution probability of demand during lead timedemand during lead time

Expected demand during lead time Expected demand during lead time (350(350 kits kits))

ROP ROP = 350 += 350 + safety stock of safety stock of 16.5 = 366.516.5 = 366.5

Receive Receive orderorder

Lead Lead timetime


Safety Safety stockstock

Probability ofProbability ofno stockoutno stockout

95% of the time95% of the time

Mean Mean demand demand

350350

ROP = ? kitsROP = ? kits QuantityQuantity

Number of Number of standard deviationsstandard deviations

00 zz

Risk of a stockout Risk of a stockout (5% of area of (5% of area of normal curve)normal curve)

Probabilistic Demand

Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined

ROP = demand during lead time + ZROP = demand during lead time + ZdLTdLT

where Z =number of standard deviations

dLT =standard deviation of demand during lead time

Probabilistic Demand

Average demand = = 350 kitsStandard deviation of demand during lead time = dLT = 10 kits5% stockout policy (service level = 95%)

Using Appendix I, for an area under the curve of 95%, the Z = 1.65

Safety stock Safety stock == Z ZdLTdLT = 1.65(10) = 16.5= 1.65(10) = 16.5 kits kits

Reorder point =expected demand during lead time + safety stock=350 kits + 16.5 kits of safety stock=366.5 or 367 kits

Probabilistic Example

Other Probabilistic Models

1. When demand is variable and lead time is constant

2. When lead time is variable and demand is constant

3. When both demand and lead time are variable

When data on demand during lead time is not available, there are other models available

Demand is variable and lead time is constantDemand is variable and lead time is constant

ROP ROP == ((average daily demand average daily demand x lead time in daysx lead time in days) +) + Z ZdLTdLT

wherewhere dd == standard deviation of demand per day standard deviation of demand per day

dLTdLT = = dd lead timelead time


Variance = daily variance x no. of days of lead time

Standard D . (sum of daily variance during lead time)LL

L

dd

d

2

2

Average daily demand (normally distributed) = 15Standard deviation = 5Lead time is constant at 2 days90% service level desired

Z for Z for 90%90% = 1.28= 1.28From Appendix IFrom Appendix I

ROPROP = (15 = (15 units x units x 22 days days) +) + Z Zdltdlt

= 30 + 1.28(5)( 2)= 30 + 1.28(5)( 2)

= 30 + 9.02 = 39.02 ≈ 39= 30 + 9.02 = 39.02 ≈ 39

Safety stock is about 9 iPods


Lead time is variable and demand is constantLead time is variable and demand is constant

ROP ROP ==((daily demand x average daily demand x average lead time in dayslead time in days) + ) + Z xZ x ( (daily daily demanddemand) ) xx LTLT

wherewhere LTLT == standard deviation of lead time in days standard deviation of lead time in days



Daily demand (constant) = 10Average lead time = 6 daysStandard deviation of lead time = LT = 398% service level desired

Z for Z for 98%98% = 2.055= 2.055From Appendix IFrom Appendix I

ROPROP = (10 = (10 units x units x 66 days days) + 2.055(10) + 2.055(10 units units)(3))(3)

= 60 + 61.65 = 121.65= 60 + 61.65 = 121.65

Reorder point is about 122 cameras

Both demand and lead time are variableBoth demand and lead time are variable

ROP ROP == ((average daily demand average daily demand x average lead timex average lead time) +) + Z ZdLTdLT

where d = standard deviation of demand per day

LT = standard deviation of lead time in days

dLT = (average lead time x d2)

+ (average daily demand)2 x LT2



Average daily demand (normally distributed) = 150Standard deviation = d = 16Average lead time 5 days (normally distributed)Standard deviation = LT = 1 day95% service level desired Z for Z for 95%95% = 1.65= 1.65

From Appendix IFrom Appendix I

ROPROP = (150 = (150 packs x packs x 55 days days) + 1.65) + 1.65dLTdLT

= (150 x 5) + 1.65 (5 days x 16= (150 x 5) + 1.65 (5 days x 1622) + (150) + (15022 x 1 x 122))

= 750 + 1.65(154) = 1,004 = 750 + 1.65(154) = 1,004 packspacks

Total Q System Costs

Total cost = Annual Holding Cost +

Annual setup/ordering Cost +

Annual safety stock holding cost

dLTHs

QD

HQ

TC 2

Fixed-Period (P) Systems

Orders placed at the end of a fixed period

Inventory counted only at end of period

Order brings inventory up to target level

Only relevant costs are ordering and holding

Lead times are known and constant

Items are independent from one another

On

-han

d i

nve

nto

ryO

n-h

and

in

ven

tory

TimeTime

QQ11

QQ22

Target quantity Target quantity ((TT))

PP

QQ33

QQ44

PP

PP



Order amount Order amount ((QQ)) = Target = Target ((TT)) - On- - On-hand inventory - Earlier orders not yet hand inventory - Earlier orders not yet

received (SR)+ Back ordersreceived (SR)+ Back orders

Q = 50 - 0 - 0 + 3 = 53 jackets

3 jackets are back ordered No jackets are in stockIt is time to place an order Target value = 50

Fixed-Period (P) Example

Periodic Review Systems: Calculations for TI

Targeted Inventory level:

TI = d(p + LT) + SS

d = average period demand

p = order interval (days, wks)

LT = lead time (days, wks)

SS = zσd

Replenishment Quantity (Q)=TI-OH

TLp

Periodic Review Systems Example

The KVS Pharmacy stocks a popular brand of over-the-counter flu and cold medicine. The average demand for the medicine is 6 packages per day, with a standard deviation of 1.2 packages. A vendor for the pharmaceutical company checks KVS’s stock every 60 days. During one visit the store had 8 packages in stock. The lead time to receive an order is 5 days. Determine the order size for this order period that will enable KVS to maintain a 95% service level.

Q = d(p + LT) + zσd - OH

= 6(60 + 5) + 1.65(1.2) - 8

= 397.96

TLp

560

Total P System Costs

Same three cost element as Q systemOrder quantity, Q will be the average

consumption of inventory during the p periods between order; Q =dP

TLpdZHS

dPD

HdP

TC

2

Q System Example

dLT = d LT = 5 2 = 7.1

Safety stock = zdLT = 1.28(7.1) = 9.1 or 9 units

Reorder point = dL + safety stock = 2(18) + 9 = 45 units

Suppose that the average demand for bird feeders is 18 units per week with a standard deviation of 5 units. The lead time is constant at 2 weeks. Determine the safety stock and reorder point for a 90% cycle-service level. What is the total cost of the Q system?

C = ($15) + ($45) + 9($15)75

2

936

75

C = $562.50 + $561.60 + $135 = $1259.10

P System ExampleBird feeder demand is normally distributed with a mean of 18 units per week and a standard deviation in weekly demand of 5 units, operating 52 weeks a year. Lead time (L) is 2 weeks and EOQ is 75 units with a safety stock of 9 units and a cycle-service level of 90%. Annual demand (D) is 936 units. What is the equivalent P system and total cost?

P = (52) = (52) = 4.2 or 4 weeksEOQ

D75

936Time between reviews =

d(P+LT) = P + LT = 5 6 = 12 units Standard deviation of demand over the protection period

T = Average demand during the protection interval + Safety stock

= d (P + LT) + zd(P + LT)

= (18 units/week)(6 weeks) + 1.28(12 units) = 123 units

© 2007 Pearson Education

D = (18 units/week)(52 weeks) = 936 units Safety Stock during P = 15 Holding Costs = $15/unit Ordering Costs = $45

d = 18 units L = 2 weeks Cycle/service level = 90% EOQ = 75 units

The time between reviews (P) = 4 weeks Average demand during P + Safety stock = T = 123 units

C = ($15) + ($45) + 15($15) 4(18)

2936

4(18)

C = $540 + $585 + $225 = $1350

P System Example continued

The total P-system cost for the bird feeders is:

The P system requires 15 units in safety stock, while the Q system only needs 9 units. If cost were the only criterion, the Q system would be the choice.

Inventory is only counted at each review period

May be scheduled at convenient times

May require only periodic checks of inventory levels

May result in stockouts between periods

May require increased safety stock


Comparison of Q and P SystemsComparison of Q and P Systems

P Systems

Convenient to administer Orders for multiple items from the same supplier

may be combined Inventory Position (IP) only required at review

Systems in which inventory records are always current are called Perpetual Inventory Systems

Review frequencies can be tailored to each item Possible quantity discounts Lower, less-expensive safety stocks

Q Systems

Single Period Inventory Model

The SPI model is designed for products that share the following characteristics: Sold at their regular price only during a single-time period Demand is highly variable but follows a known probability

distribution Salvage value is less than its original cost so money is lost when

these products are sold for their salvage value

Objective is to balance the gross profit of the sale of a unit with the cost incurred when a unit is sold after its primary selling period

SPI Model Example: Tee shirts are purchase in multiples of 10 for a charity event for $8 each. When sold during the event the selling price is $20. After the event their salvage value is just $2. From past events the organizers know the probability of selling different quantities of tee shirts within a range from 80 to 120

Payoff TableProb. Of Occurrence .20 .25 .30 .15 .10Customer Demand 80 90 100 110 120# of Shirts Ordered Profit

80 $960 $960 $960 $960 $960 $96090 $900 $1080 $1080 $1080 $1080 $1040

Buy 100 $840 $1020 $1200 $1200 $1200 $1083 110 $780 $ 960 $1140 $1320 $1320 $1068 120 $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

chapter 4 inventory management. learning objectives define inventory and functions of inventory...

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