Lecture 2 - Inventory Management

7/25/2019 Lecture 2 - Inventory Management

1/90

CHAPTER 2:

INVENTORY MANAGEMENT

AND RISK POOLING

E. Oldenkamp

Session 2April 5, 2016


2/90

AGENDA

PART I - Introduction1. What types of inventories? Where? Why do we

need inventories?

2. What does it cost to have inventories?

3. Impact of demand uncertainty on forecasting4. How to replenish products?

PART II Mathematical Modelling

1. Setting the order moment

2. Setting the order size

3. Risk Pooling

2


3/90

PART I

INTRODUCTION

3


4/90

AGENDA


need inventories?




1. Setting the order moment

2. Setting the order size

3. Risk Pooling

4


5/90

1. TYPES OF INVENTORY

INPUTS TRANSFORMATIONS OUTPUTS

Vendors

Purchasing

ReceivingFGI

Shipping

Distributors

Customers

Customers

Customers

Processes

Warehouse

Inventory

Raw Materials

Conversion

WIP5


6/90

WHY DO WE HOLD INVENTORY?

to hedge against uncertainty in supplyand demand to make use of economies of scale to hedge against lead time

because of capacity limitations

6


7/90

AGENDA


need inventories?




1. Setting the order moment2. Setting the order size

3. Risk Pooling

7


8/90

2. INVENTORY COST STRUCTURE

Order cost (straightforward computation)

product cost transportation cost

Holding cost (straightforward computation)

capital tied up

physical cost: warehouse space, storage tax,insurance, breakage, spoilage

Component devaluation cost (life cycle dependent)

Price protection cost (supply contract dependent)

Product return cost (also incur operational cost)

Obsolescence costs (FG inventory + components in thepipeline + probable discount/marketing)

Out-of-stock cost (difficult!)

8


9/90

AGENDA


need inventories?





3. Risk Pooling

12


10/90

3. IMPACT OF DEMAND UNCERTAINTY

Many companies treat the world as if itwere truly predictable: forecasts of demand made far in advance of

the selling season but they design planning process as if

forecast truly represents reality

13


11/90

FORECASTING METHODS

Quantitative methods

moving average

exponential smoothing

Qualitative methods

Principles of forecasts

1. The forecast is always wrong

2. The longer the forecast horizon the worse theforecast

3. Aggregate forecasts are more accurate

why?14


12/90

INCREASING DEMAND UNCERTAINTY

For many products demand uncertainty isincreasing over time

Possible reasons:

short product life increasing variety of similar products

competition

15


13/90

PRODUCT LIFE CYCLE

maturitygrowth

intro-duction

decline

time

dem

and

16


14/90

PRODUCT LIFE CYCLE

Source: Strategos17


15/90

AGENDA

PART I - Introduction1. What types of inventories? Where? Why do weneed inventories?


3. Impact of demand uncertainty on forecasts4. How to replenish products?



19


16/90

4. INVENTORY CONTROL POLICIES

Decisions: how often should the inventory status be checked? when to place a replenishment order?

how large should the order size be?

Objective: minimize total inventory costs whilemeeting a certain service level

Service level:

cycle service level (P1) = fraction of replenishment cycleswith no stock out

fill rate (P2) = fraction of demand satisfied from stockon hand

20


17/90

PART II

MATHEMATICAL MODELING

22


18/90

INVENTORY CONTROL POLICIES

Deterministic demand

Demand uncertainty single period

Demand uncertainty multi-period reorder level: threshold level to indicate that an order

should be placed

order size: the number of units to order

order moment

continuous review periodic review

ordersize fixed (R,Q) (R,Q)

variableno fixed cost: (S-1,S)fixed cost: (s,S)

no fixed cost: (S-1,S)fixed cost: (s,S)

23


19/90

DETERMINISTIC DEMAND

Economic lot size model: demand is known and constant at a rate of Ditems / time unit

order quantity is fixed at Q items per order

balance fixed order cost Kand inventory holdingcost h

receipt of inventory is instantaneous

no discounts no stock outs

24


20/90

ECONOMIC LOT SIZE MODEL

Q

0

cycle time T

- Consider time [0; T]

total cost = K + h2

- Cost per time unit

total cost = +h 2- Use T = Q/D

total cost =KDQ

+hQ2

How to find the optimal

order size Q?

Take the derivative w.r.t. Q

KDQ2

+h2

= !

Q = 2KDh

25


21/90


22/90

EXAMPLE - ECONOMIC LOT SIZE MODEL

D = 1,125 ! 50 = 56,250 per year

K = $20

h = $0.25 per item per year

Q= 2KDh

=2 ! 20! 56,250

0.25= 3,000units

What are the average costs?

C(Q) =KDQ

+hQ2

=20! 56,250

3 000

+0.25! 3,000

2

= $75027


23/90


24/90

ECONOMIC LOT SIZE SENSITIVITY (1)

Actual weekly demand turned out to be 1,445 units

What would have been the optimal order size?

Q=2KD

h =

2 ! 20! 72,250

0.25 = 3,400units

What is the difference in cost?

C(Q=3,000) = 20! 72,2503,000 + 0.25! 3,0002 = $856.67

C(Q=3,400) =20! 72,250

3,400+

0.25! 3,4002

= $850

29


25/90


If you order Q rather than Q*, the relative costincrease equals

C(Q)

C(Q)

=12

Q

Q

"Q

Q

If you are (1-b)% wrong in your order size, therelative cost increase equals

C(bQ)

C(Q) =

12

bQ

Q "

Q

bQ =

12 b"

1b

What happens when you order twice the optimal amount?30


26/90


If you order Q rather than Q*, the relative costincrease equals

C(Q)

C(Q)

=12

Q

Q

"Q

Q=

12

3,0003,400

"3,4003,000

= 1.0078

If you are (1-0.8824)% wrong in your order size, therelative cost increase equals

C(bQ)

C(Q) =

12 b"

1b =

12 0.8824"

10.8824 = 1.0078

EOQ is very robust is used when demand is stochastic31


27/90


Example continued: demand is in range [980; 1,620]

Step 1a: take D = 980 units/year

Q* = 2,800 units/order

Step 1b: take D = 1,620 units/year

Q* = 3,600 units/order

Step 2a: choose Q = 2,800 while Q* = 3,600

Q/Q* = 0.7778, cost ratio = 1.0317

Step 2b: choose Q = 3,600 while Q* = 2,800

Q/Q* = 1.2857, cost ratio = 1.0317

Never take extreme values but D=1,300 units/year

Maximum cost penalty ratio would be 1.010

32


28/90

OBSERVATIONS

The optimal order quantity is not necessarilyequal to forecast, or average, demand.

As the order quantity increases, average profittypically increases until the production quantityreaches a certain value, after which the averageprofit starts decreasing.

Risk/Reward trade-off: As we increase theproduction quantity, both risk and rewardincreases.


29/90





should be placed


order moment





34


30/90

SINGLE PERIOD MODEL

Selling Christmas trees

Cost per tree: $45 Sales price: $80

Loss of goodwill: $10

Salvage price: $2535


31/90


32/90

SINGLE PERIOD MODEL


$600 $1,700 profit (Q=80)

sell 60 units with a profit of $80 - $45 = $35

remain 20 units with a profit of $25 - $45 = $-2037


33/90


34/90

SINGLE PERIOD MODEL


$600 $1,700 $2,800 $2,600 profit (Q=80)


shortage 20 units with a loss of goodwill $-1039


35/90

SINGLE PERIOD MODEL


$600 $1,700 $2,800 $2,600 $2,400 profit (Q=80)




36/90

SINGLE PERIOD MODEL


$600 $1,700 $2,800 $2,600 $2,400 $2,200 profit (Q=80)




37/90

SINGLE PERIOD MODEL


$600 $1,700 $2,800 $2,600 $2,400 $2,200 $2,000 profit (Q=80)




38/90

SINGLE PERIOD MODEL


$600 $1,700 $2,800 $2,600 $2,400 $2,200 $2,000 $2,357 : profit (Q=80)

Expected profit = 0.04 ! $600 + 0.11 ! $1,700 +

43


39/90

SINGLE PERIOD MODEL


$600 $1,700 $2,800 $2,600 $2,400 $2,200 $2,000 $2,357 : profit (Q=80)

$200 $1,300 $2,400 $3,500 $3,300 $3,100 $2,900 $2,789 : profit (Q=100)

$-200 $900 $2,000 $3,100 $4,200 $4,000 $3,800 $2,857 : profit (Q=120)

$-600 $500 $1,600 $2,700 $3,800 $4,900 $4,700 $2,626 : profit (Q=140)

VERY TEDIOUSAPPROACH

44


40/90

SINGLE PERIOD MODEL

Notation

c = variable cost per unit p = selling price per unit

v = salvage value per unit

s = shortage penalty cost per unit

D = demand random variable

Q = order quantity decision variable

profit = ifD #Q (stock out)ifD

Q (excess inventory)

45


41/90

SINGLE PERIOD MODEL

Notation






profit = pc Q s(DQ) ifD #Q (stock out)ifD


46


42/90

SINGLE PERIOD MODEL

Notation






profit = pc Q s(DQ) ifD #Q (stock out)pD cQ +v(QD) ifD


Marginal profit / risk of ordering one extra unit?

47


43/90


44/90

SINGLE PERIOD MODEL the easy way

Marginal costs:

$ %&'( &) *+,-./0- 1'2&.(/0-3 $$ '/4-' 5.6%- 5-. *+6( %&'( 5-. *+6( " 5-+/4(7 %&'( 16) /+73$ "

$ %&'( &) &8-./0- 1&8-.'(&%96+03 $

$ %&'( 5-. *+6( '/48/0- 8/4*- 5-. *+6( 16) /+73$ 8

Service level = probability of not stocking out

$ " $ " " :because $ " /+, $

49


45/90

SINGLE PERIOD MODEL DETERMINE Q

Selling Christmas trees (continued)

Cost per tree (c) : $45 Sales price (p) : $80

Loss of goodwill (s): $10

Salvage price (v) : $25

1 3 $ "

" $ !;?

$ *+650


46/90

Single period model: how to determine Q?

All normal distributions (NDs) are characterized by two parameters,mean = and standard deviation =

All NDs are related to the standard normal with = 0 and = 1 Recipe:

1. Let be the order quantity, and 1:3 the parameters ofthe normal demand forecast .>; $ " $ ,3. Look up the Z score for the outcome of

1

3 in the

Standard Normal Distribution Function Table.

4. Set $" 51


47/90


48/90

$ !;? %&..-'5&+,6+0 $ !;@A $" $ ==;< "!;@A B!;!!> $ A>!;!!AA>!

$ B! !;!B " C " A>! !;>? " AB! !;!= "A

1

4099;

63

+1

6099;

63

+1

8099;

63

+1

10099;

63

+1

12099;

63

+1

14099;

63

+1

16099;

63

7

The Q for the Christmas trees

53


49/90

ALTERED SINGLE PERIOD MODEL

Selling Christmas trees:ALTERED MODEL

Loss of goodwill is just the lost opportunity of a possible sale,quantified as p c (you could otherwise consider s=0)

Cost per tree (c) : $45

Sales price (p) : $80

Salvage price (v) : $25

P(D < Q) =p cp v

= 0.6363

z = 0.35

Use the look-up table to determine z = 0.35, and then

setQ = + z = 9.6 +0.3540.001 =113.6007 114.

54


50/90





should be placed


order moment





55


51/90


52/90


53/90

CONTINUOUS (R,Q) POLICY

Given is the service level $ the probability of stock-outduring lead-time should be A ;demand P(DL R) , where DL is N(L,L)

$ " $ , " , where is the safety factor

(Look up in the standard normal table)If demand is normally distributed 1DEF: GHI3$ GHI!L and = STD ! L

58

CO O S ( Q) O C


54/90

R+Q


timeL

reorderpoint

actual leadtime demand

invento

rylevel

R

safety

stock

average on-hand inventory

=Q2

+ z! STD ! L

pipelinestock

59


55/90

EXAMPLE CONTINUOUS (R,Q) POLICY

Consider again the hardware supply warehouse thatwants to guarantee a service level of 95% to its retailstores. The weekly demand of the stores follows anormal distribution with an average of 1,445 units and astandard deviation of 300 units. The lead time of the

supplier is 3.5 days.

What should the reorder level be?

remember from the previous slide: R =AVG ! L + z ! STD ! L

60

EXAMPLE CONTINUOUS (R Q) POLICY


56/90


AVG = 1,445 units

STD = 300 units

L = 0.5 week

Safety factor z = find in look-up table

61

LOOK-UP TABLE STANDARD NORMAL


57/90

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

DISTRIBUTIONS

62



58/90


AVG = 1,445 units

STD = 300 units

L = 0.5 week

Safety factor z =

R = AVG ! L + z ! STD ! L= 1,445 ! 0.5 + 1.65 ! 300 ! 0.5

= 1,072.52

The reorder level should be 1,073 units.

always round up!

1.65 find in look-up table

63


59/90

CONTINUOUS (R Q) POLICY


60/90


timeL

reorderpoint

in

ventoryleve

l

R

safety stock

fill rate = 1 expected shortage in a replenishment cycle

expected demand in a replenishment cycle

pipeline stock

safety stock

65

CONTINUOUS (R Q) POLICY


61/90


timeL

reorderpoint

in

ventoryleve

l

R

safety stock

fill rate = 1 STD J L J L(z3

Q

pipeline stock

safety stock

66


62/90

LOOK-UP TABLE STANDARD NORMAL


63/90

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.3989 0.3940 0.3890 0.3841 0.3793 0.3744 0.3697 0.3649 0.3602 0.3556

0.1 0.3509 0.3464 0.3418 0.3373 0.3328 0.3284 0.3240 0.3197 0.3154 0.3111

0.2 0.3069 0.3027 0.2986 0.2944 0.2904 0.2863 0.2824 0.2784 0.2745 0.2706

0.3 0.2668 0.2630 0.2592 0.2555 0.2518 0.2481 0.2445 0.2409 0.2374 0.2339

0.4 0.2304 0.2270 0.2236 0.2203 0.2169 0.2137 0.2104 0.2072 0.2040 0.2009

0.5 0.1978 0.1947 0.1917 0.1887 0.1857 0.1828 0.1799 0.1771 0.1742 0.1714

0.6 0.1687 0.1659 0.1633 0.1606 0.1580 0.1554 0.1528 0.1503 0.1478 0.1453

0.7 0.1429 0.1405 0.1381 0.1358 0.1334 0.1312 0.1289 0.1267 0.1245 0.1223

0.8 0.1202 0.1181 0.1160 0.1140 0.1120 0.1100 0.1080 0.1061 0.1042 0.1023

0.9 0.1004 0.0986 0.0968 0.0950 0.0933 0.0916 0.0899 0.0882 0.0865 0.0849

1.0 0.0833 0.0817 0.0802 0.0787 0.0772 0.0757 0.0742 0.0728 0.0714 0.0700

1.1 0.0686 0.0673 0.0659 0.0646 0.0634 0.0621 0.0609 0.0596 0.0584 0.0573

1.2 0.0561 0.0550 0.0538 0.0527 0.0517 0.0506 0.0495 0.0485 0.0475 0.0465

1.3 0.0455 0.0446 0.0436 0.0427 0.0418 0.0409 0.0400 0.0392 0.0383 0.0375

1.4 0.0367 0.0359 0.0351 0.0343 0.0336 0.0328 0.0321 0.0314 0.0307 0.0300

1.5 0.0293 0.0286 0.0280 0.0274 0.0267 0.0261 0.0255 0.0249 0.0244 0.0238

1.6 0.0232 0.0227 0.0222 0.0216 0.0211 0.0206 0.0201 0.0197 0.0192 0.0187

1.7 0.0183 0.0178 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146

1.8 0.0143 0.0139 0.0136 0.0132 0.0129 0.0126 0.0123 0.0119 0.0116 0.0113

1.9 0.0111 0.0108 0.0105 0.0102 0.0100 0.0097 0.0094 0.0092 0.0090 0.0087

2.0 0.0085 0.0083 0.0080 0.0078 0.0076 0.0074 0.0072 0.0070 0.0068 0.0066

DISTRIBUTIONS L(z)

68



64/90


Consider again the hardware supply warehouse

where R = 1,073 and Q = 3,400.

AVG = 1,445 units

STD = 300 units

L = 0.5 week

L(z) = 0.0206

fill rate = 1 STD J L J L(z3

Q

= 1 300 J 0.5 J0.02063,400

= 99.87%69


65/90

PERIODIC (s S) POLICY


66/90

PERIODIC (s,S) POLICY

safety stock

reorder point

inventoryon hand inventoryposition

order-up-to level

timereview review review review

risk period

under-shoot

expecteddemand

leadtime

lead time

71

RISK POOLING


67/90

RISK POOLING

Products with high profit margin tend to havehave highly variable demand

Demand variability is reduced if oneaggregates demand across locations.

More likely that high demand from onecustomer will be offset by low demand fromanother.

Reduction in variability allows a decrease in

safety stock and therefore reduces averageinventory (while maintaining the sameservice level) HOW?

74

RISK POOLING


68/90

RISK POOLING

Consider regions Demand in each region is normally distributed average weekly demand in region : $ A: K :

standard deviation of weekly demand in region

: $ A: K : correlation of weekly demand between and

75

SQUARE ROOT LAW FOR RISK POOLING


69/90

SQUARE-ROOT LAW FOR RISK POOLING

If demand in

different geographic locations is

independent and

about the same size

Then aggregation reduces safety inventory by

about a factor of Disadvantages:

Increase in response time to customer order

Increase in transportation cost

76

SQUARE ROOT LAW: EXAMPLE


70/90

SQUARE-ROOT LAW: EXAMPLE

Italian coffee machine company, Shanghai branch

4 warehouses in 4 regions or only one in Ningbo?

Per region (north, east, south, west):

average weekly demand $ A:!!! units standard deviation $ ?!! units lead-time $ B weeks price$ LA:!!! per unit holding cost$ >!M transport cost$ LA!/unit within the region$ LA?/unit from centralized location

Demand for each region is independent77

SQUARE ROOT LAW: EXAMPLE


71/90

SQUARE-ROOT LAW: EXAMPLE

$ A:!!!, $ ?!!, $ B, $ LA:!!!, $ >!M$ LA!/unit within the region, $ LA?/unit centralized CSL = 95% (or 0.95) $ A;:?:B):

$

$ A;

?!! $ ==! units

total ss $ B $ ?=

$4

$3960

2 $ A=C!

Decrease in annual holding cost on aggregationL?=B:N


72/90

DEMAND VARIATION

Standard deviation measures how muchdemand tends to vary around the average

Gives an absolute measure of thevariability

Coefficient of variation is the ratio ofstandard deviation to average demand

Gives a relative measure of the variability,relative to the average demand

ACME RISK POOLING CASE


73/90

ACME RISK POOLING CASE

Electronic equipment manufacturer and distributor 2 warehouses for distribution in New York and New

Jersey (partitioning the northeast market into tworegions)

Customers (that is, retailers) receiving items fromwarehouses (each retailer is assigned a warehouse)

Warehouses receive material from Chicago

Current rule: 97 % cycle service level

Each warehouse operate to satisfy 97% of demand(3% probability of stock-out)


74/90

HISTORICAL DATA


75/90

HISTORICAL DATA

PRODUCT A

Week 1 2 3 4 5 6 7 8

Massachuse

tts33 45 37 38 55 30 18 58

New Jersey 46 35 41 40 26 48 18 55

Total 79 80 78 78 81 78 36 113

PRODUCT B

Week 1 2 3 4 5 6 7 8

Massachuse

tts0 3 3 0 0 1 3 0

New Jersey 2 4 3 0 3 1 0 0

Total 2 6 3 0 3 2 3 0

SUMMARY OF HISTORICAL DATA


76/90

SUMMARY OF HISTORICAL DATA

Statistics Product Average

Demand

Standard

Deviation of

Demand

Coefficient of

Variation

Massachusetts A 39.3 13.2 0.34

Massachusetts B 1.125 1.36 1.21

New Jersey A 38.6 12.0 0.31

New Jersey B 1.25 1.58 1.26

Total A 77.9 20.71 0.27

Total B 2.375 1.9 0.81

INVENTORY LEVELS


77/90

INVENTORY LEVELS

Product Average

Demand

During LeadTime

Safety Stock Reorder

Point

Q

Massachusett

s

A 39.3 25.08 65 132

Massachusett

s

B 1.125 2.58 4 25

New Jersey A 38.6 22.8 62 31

New Jersey B 1.25 3 5 24

Total A 77.9 39.35 118 186

Total B 2.375 3.61 6 33


78/90

CRITICAL POINTS


79/90

CRITICAL POINTS

The higher the coefficient of variation, the

greater the benefit from risk pooling The higher the variability, the higher the

safety stocks kept by the warehouses. Thevariability of the demand aggregated by thesingle warehouse is lower

The benefits from risk pooling depend on thebehavior of the demand from one marketrelative to demand from another risk pooling benefits are higher in situations

where demands observed at warehousesare negatively correlated

CENTRALIZED VS DECENTRALIZED SYSTEMS


80/90

CENTRALIZED VS. DECENTRALIZED SYSTEMS

Safety stock: lower with centralization

Service level: higher service level for thesame inventory investment with centralization

Overhead costs: higher in decentralized

system Customer lead time: response times lower in

the decentralized system

Transportation costs: not clear. Consider

outbound and inbound costs.

MANAGING INVENTORY IN THE SUPPLY CHAIN


81/90

MANAGING INVENTORY IN THE SUPPLY CHAIN

Inventory decisions are given by a single decision

maker whose objective is to minimize the system-wide cost

The decision maker has access to inventoryinformation at each of the retailers and at thewarehouse

Echelons and echelon inventory

Echelon inventory at any stage or level of the

system equals the inventory on hand at the echelon,plus all downstream inventory (downstream meanscloser to the customer)


82/90


83/90

4-STAGE SUPPLY CHAIN EXAMPLE


84/90

4 STAGE SUPPLY CHAIN EXAMPLE

Average weekly demand faced by the retailer:

DEI $ B@ Standard deviation of demand:

GHI $ ?>

At each stage, management is attempting tomaintain a service level of 97%:

$ A;CC Lead time between each of the stages, and

between the manufacturer and its suppliers is 1week: 1 $2 $3 $ A


85/90

REORDER POINTS AT EACH STAGE


86/90

REORDER POINTS AT EACH STAGE

For the retailer:

1 $ A J B@ " A;CC J ?> J A $ A!@ For the distributor:2 $ > J B@ " A;CC J ?> J > $ AN@ For the wholesaler:

3 $ ? J B@ " A;CC J ?> J ? $ >?= For the manufacturer:

4$ B J B@ " A;CC J ?> J B $ ?!!

MORE THAN ONE FACILITY AT EACH STAGE


87/90

MORE THAN ONE FACILITY AT EACH STAGE

Follow the same approach

Echelon inventory at the warehouse is theinventory at the warehouse, plus all of theinventory in transit to and in stock at each ofthe retailers.

Similarly, the echelon inventory position at thewarehouse is the echelon inventory at thewarehouse, plus those items ordered by thewarehouse that have not yet arrived minus allitems that are backordered.


88/90

SUMMARY


89/90

SU

Matching supply with demand a major

challenge

Forecast demand is always wrong

Longer the forecast horizon, less accurate the

forecast Aggregate demand more accurate than

disaggregated demand

Need the most appropriate technique

Need the most appropriate inventory policy

EXERCISE LECTURE


90/90

Thursday April 7

Prepare: read the document Introduction to inventorycontrol

During class

discuss problems

take home exercises with answers available later

For exam

a formula sheet is provided with the exam

no need to know the formulas by heart but you needto be able to explain them! (= understand them)

Lecture 2 - Inventory Management

Documents