Download Chapter 2 - SUNY New Paltz

CASE: Steel Works
Chapter 2
Background of case and intent
Overview of business
z What does data tell you about Specialty?
z How much inventory might you expect?
z What opportunities are there for Custom?
z Wrap up
z
z
Inventory
Management
and Risk Pooling
McGraw-Hill/Irwin
Stephen C. Graves Copyright 2003
All Rights Reserved
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Background & Intent
Custom Products
Abstraction from summer consulting job
z Intent is to examine a realistic, but
simplified inventory context and perform a
diagnosis of problem – poor service and
too much inventory
Rapid growth, 1/3 of total sales ($133 MM)
z One customer per product
z Very high margins
z High service level
z 3 plants, co-located with R&D center
z Each product produced at a single plant
z
Stephen C. Graves Copyright 2003
All Rights Reserved
z
Stephen C. Graves Copyright 2003
All Rights Reserved
2-3
Specialty Products
z
z
z
z
z
z
z
2-4
Consultant Recommendation
Rapid growth, 2/3 of total sales ($267 MM)
6 product families
3 plants, each producing 2 product families
130 customers, 120 products
Few big customers
Highly volatile demand
High service level
Stephen C. Graves Copyright 2003
All Rights Reserved
2-2
Drop low volume products
z Improve forecasts
z Consolidate warehouses
z
2-5
Stephen C. Graves Copyright 2003
All Rights Reserved
2-6
1
What Does Data Tell You?
What Does Data Tell You?
μ
σ
cv
DB R10
15.5
13.2
0.85
DB R12
1008
256
0.25
DB R15
2464
494
0.20
z
z
DF R10
97
92.5
0.95
DF R12
18.5
11.4
0.62
DF R15
55
80
1.46
DF R23
35.5
45.9
1.29
Stephen C. Graves Copyright 2003
All Rights Reserved
z
Durabend R12:
z
7 products:
z
One customer accounts for 97% of demand
High volume (2) is not very volatile
Low volume (5) is very volatile
Stephen C. Graves Copyright 2003
All Rights Reserved
2-7
How Much Inventory Should
You Expect?
Assume base stock model with periodic
review
z Review period = r = ?
z Lead time = L = ?
z
E [I ] = r
μ
2
μ
σ
DB R10
15.5
13.2
8
26
34
72
DB R12
1008
256
504
510
1014
740
DB R15
2464
494
1232
990
2222
1875
DF R10
97
92.5
49
185
234
604
DF R12
18.5
11.4
9
23
32
55
DF R15
55
80
28
160
188
388
DF R23
35.5
45.9
6
+ zσ r + L
Saf.
stock
E[I]
Act.
Inv.
18
92
110
190
1848
1986
3834
3824
Safety stock = z σ √r+L
Stephen C. Graves Copyright 2003
All Rights Reserved
2-9
What Are the Opportunities at
Custom?
2-10
Wrap Up
Combine production and inventory for
common items, e. g. DF R23
z Produce monthly: reduce setups by half
and pool safety stocks
z Produce twice a month: same number of
setups but cut cycle stock and review
period in half
Realistic diagnostic exercise
z In real life: not as clean, more data and
more considerations
z Yet simple models and principles can
provide valuable guidance
z
Stephen C. Graves Copyright 2003
All Rights Reserved
Cycle
stock
Assumes r = 1; L=0.25; and z = 1.8
Cycle stock = r μ/2
Stephen C. Graves Copyright 2003
All Rights Reserved
2-8
z
2-11
Stephen C. Graves Copyright 2003
All Rights Reserved
2-12
2
2.1 Introduction
Why Is Inventory Important?
Why Is Inventory Important?
z
Distribution and inventory (logistics) costs
are quite substantial
GM’s production and distribution network
z
z
z
Total U.S. Manufacturing Inventories ($m):
z 1992-01-31: $m 808,773
z 1996-08-31: $m 1,000,774
z 2006-05-31: $m 1,324,108
Inventory-Sales Ratio (U.S. Manufacturers):
z 1992-01-01: 1.56
z 2006-05-01: 1.25
z
20,000 supplier plants
133 parts plants
31 assembly plants
11,000 dealers
z
Freight transportation costs: $4.1 billion (60% for
material shipments)
GM inventory valued at $7.4 billion (70%WIP; Rest
Finished Vehicles)
Decision tool to reduce:
z
26% annual cost reduction by adjusting:
z
z
z
z
z
combined corporate cost of inventory and transportation.
Shipment sizes (inventory policy)
Routes (transportation strategy)
2-13
2-14
Holding the right amount at the
right time is difficult!
Why Is Inventory Required?
z
Uncertainty in customer demand
Shorter product lifecycles
z More competing products
z
Dell Computer’s was sharply off in its forecast of
demand, resulting in inventory write-downs
z
Liz Claiborne’s higher-than-anticipated excess
inventories
z
IBM’s ineffective inventory management
z
Cisco’s declining sales
z
z
z
Uncertainty in supplies
z
Quality/Quantity/Costs/Delivery Times
z
Delivery lead times
z Incentives for larger shipments
z
z
z
1993 stock plunge
1993 unexpected earnings decline,
1994 shortages in the ThinkPad line
2001 $ 2.25B excess inventory charge
2-15
2-16
Inventory Management-Demand
Forecasts
z
Supply Chain Factors in Inventory
Policy
z
Uncertain demand makes demand
forecast critical for inventory related
decisions:
z
z
z
z
What to order?
z When to order?
z How much is the optimal order quantity?
z
z
z
Order cost:
z
z
z
z
z
INVENTORY POLICY!!
z
z
2-17
Product cost
Transportation cost
Inventory holding cost, or inventory carrying cost:
z
Approach includes a set of techniques
z
Estimation of customer demand
Replenishment lead time
The number of different products being considered
The length of the planning horizon
Costs
State taxes, property taxes, and insurance on inventories
Maintenance costs
Obsolescence cost
Opportunity costs
Service level requirements
2-18
3
2.2.1. Economic Lot Size Model
2.2 Single Stage Inventory
Control
z
z
Single supply chain stage
Variety of techniques
z
z
z
z
z
z
z
z
z
Economic Lot Size Model
Demand Uncertainty
Single Period Models
Initial Inventory
Multiple Order Opportunities
Continuous Review Policy
Variable Lead Times
Periodic Review Policy
Service Level Optimization
FIGURE 2-3: Inventory level as a function of time
2-19
2-20
Assumptions
z
z
z
z
z
z
z
Deriving EOQ
D items per day: Constant demand rate
Q items per order: Order quantities are fixed, i.e., each
time the warehouse places an order, it is for Q items.
K, fixed setup cost, incurred every time the warehouse
places an order.
h, inventory carrying cost accrued per unit held in
inventory per day that the unit is held (also known as,
holding cost)
Lead time = 0
(the time that elapses between the placement of an
order and its receipt)
Initial inventory = 0
Planning horizon is long (infinite).
z
Total cost at every cycle:
K
hTQ
2
+
Average inventory holding cost in a cycle: Q/2
z Cycle time T =Q/D
KD
hQ
+
z Average total cost per unit time:
Q
2
z
2 KD
h
Q* =
2-21
2-22
EOQ: Costs
Sensitivity Analysis
Total inventory cost relatively insensitive to order quantities
Actual order quantity: Q
Q is a multiple b of the optimal order quantity Q*.
For a given b, the quantity ordered is Q = bQ*
b
.5
.8
.9
1
1.1
1.2
1.5
2
Increase
in cost
25%
2.5%
0.5%
0
.4%
1.6%
8.9%
25%
FIGURE 2-4: Economic lot size model: total cost per unit time
2-23
2-24
4
2.2.2. Demand Uncertainty
z
It is difficult to match supply and demand
The longer the forecast horizon, the worse the
forecast
z
z
Short lifecycle products
z One ordering opportunity only
z Order quantity to be decided before
demand occurs
The forecast is always wrong
z
z
2.2.3. Single Period Models
It is even more difficult if one needs to predict
customer demand for a long period of time
Aggregate forecasts are more accurate.
z
z
z
More difficult to predict customer demand for
individual SKUs
Much easier to predict demand across all SKUs
within one product family
z
Order Quantity > Demand => Dispose excess
inventory
Order Quantity < Demand => Lose sales/profits
2-25
2-26
Single Period Models
z
z
z
z
identify a variety of demand scenarios
determine probability each of these scenarios will
occur
Given a specific inventory policy
z
z
determine the profit associated with a particular
scenario
given a specific order quantity
z
z
z
Single Period Model Example
Using historical data
weight each scenario’s profit by the likelihood that it will occur
determine the average, or expected, profit for a particular
ordering quantity.
FIGURE 2-5: Probabilistic forecast
Order the quantity that maximizes the average
profit.
2-27
2-28
Two Scenarios
Additional Information
z
Fixed production cost: $100,000
z Variable production cost per unit: $80.
z During the summer season, selling price:
$125 per unit.
z Salvage value: Any swimsuit not sold
during the summer season is sold to a
discount store for $20.
z
z
2-29
Manufacturer produces 10,000 units while
demand ends at 12,000 swimsuits
Profit
= 125(10,000) - 80(10,000) - 100,000
= $350,000
Manufacturer produces 10,000 units while
demand ends at 8,000 swimsuits
Profit
= 125(8,000) + 20(2,000) - 80(10,000) - 100,000
= $140,000
2-30
5
Probability of Profitability Scenarios
with Production = 10,000 Units
z
Order Quantity that Maximizes
Expected Profit
Probability of demand being 8000 units =
11%
z
Probability of profit of $140,000 = 11%
z
Probability of demand being 12000 units =
27%
z
Total profit = Weighted average of profit
scenarios
z
Probability of profit of $140,000 = 27%
FIGURE 2-6: Average profit as a function of production quantity
2-31
2-32
Relationship Between Optimal
Quantity and Average Demand
z
For the Swimsuit Example
Compare marginal profit of selling an additional unit and
marginal cost of not selling an additional unit
z
z
z
Marginal profit/unit =
Selling Price - Variable Ordering (or, Production) Cost
z
Marginal cost/unit =
Variable Ordering (or, Production) Cost - Salvage Value
z
If Marginal Profit > Marginal Cost => Optimal Quantity >
Average Demand
If Marginal Profit < Marginal Cost => Optimal Quantity <
Average Demand
z
z
z
z
Average demand = 13,000 units.
Optimal production quantity = 12,000 units.
Marginal profit = $45
Marginal cost = $60.
Thus, Marginal Cost > Marginal Profit
=> optimal production quantity < average
demand.
2-33
Risk-Reward Tradeoffs
2-34
Risk-Reward Tradeoffs
Optimal production quantity maximizes
average profit is about 12,000
z Producing 9,000 units or producing 16,000
units will lead to about the same average
profit of $294,000.
z If we had to choose between producing
9,000 units and 16,000 units, which one
should we choose?
z
FIGURE 2-7: A frequency histogram of profit
2-35
2-36
6
Observations
Risk-Reward Tradeoffs
z
z
Profit is:
z
z
z
either $200,000 with probability of about 11 %
or $305,000 with probability of about 89 %
Production quantity = 16,000 units.
z
z
z
z
The optimal order quantity is not
necessarily equal to forecast, or average,
demand.
z As the order quantity increases, average
profit typically increases until the
production quantity reaches a certain
value, after which the average profit starts
decreasing.
z Risk/Reward trade-off: As we increase the
production quantity, both risk and reward
increases.
z
Production Quantity = 9000 units
Distribution of profit is not symmetrical.
Losses of $220,000 about 11% of the time
Profits of at least $410,000 about 50% of the time
With the same average profit, increasing the production
quantity:
z
z
Increases the possible risk
Increases the possible reward
2-37
2-38
2.2.4. What If the Manufacturer
Has an Initial Inventory?
z
Initial Inventory Solution
Trade-off between:
Using on-hand inventory to meet demand and
avoid paying fixed production cost: need
sufficient inventory stock
z Paying the fixed cost of production and not
have as much inventory
z
FIGURE 2-8: Profit and the impact of initial inventory
2-39
2-40
Manufacturer Initial Inventory =
10,000
Manufacturer Initial Inventory =
5,000
z
z
z
If nothing is produced, average profit =
225,000 (from the figure) + 5,000 x 80 = 625,000
If the manufacturer decides to produce
z
z
No need to produce anything
z
z
Production should increase inventory from 5,000 units
to 12,000 units.
Average profit =
If we produce, the most we can make on
average is a profit of $375,000.
z
z
371,000 (from the figure) + 5,000 • 80 = 771,000
z
2-41
average profit > profit achieved if we produce to
increase inventory to 12,000 units
Same average profit with initial inventory of 8,500
units and not producing anything.
If initial inventory < 8,500 units => produce to raise
the inventory level to 12,000 units.
If initial inventory is at least 8,500 units, we should not
produce anything
(s, S) policy or (min, max) policy
2-42
7
2.2.5. Multiple Order
Opportunities
2.2.6. Continuous Review Policy
REASONS
z To balance annual inventory holding costs and annual fixed order
costs.
z To satisfy demand occurring during lead time.
z To protect against uncertainty in demand.
z
z
TWO POLICIES
z Continuous review policy
z
z
z
z
z
inventory is reviewed continuously
an order is placed when the inventory reaches a particular level or reorder point.
inventory can be continuously reviewed (computerized inventory systems are
used)
z
z
Periodic review policy
z
z
z
inventory is reviewed at regular intervals
appropriate quantity is ordered after each review.
it is impossible or inconvenient to frequently review inventory and place orders if
necessary.
z
Daily demand is random and follows a normal
distribution.
Every time the distributor places an order from the
manufacturer, the distributor pays a fixed cost, K, plus an
amount proportional to the quantity ordered.
Inventory holding cost is charged per item per unit time.
Inventory level is continuously reviewed, and if an order
is placed, the order arrives after the appropriate lead
time.
If a customer order arrives when there is no inventory on
hand to fill the order (i.e., when the distributor is stocked
out), the order is lost.
The distributor specifies a required service level.
2-43
2-44
Continuous Review Policy
z
z
z
z
z
z
Continuous Review Policy
AVG = Average daily demand faced by the
distributor
STD = Standard deviation of daily demand faced
by the distributor
L = Replenishment lead time from the supplier to
the
distributor in days
h = Cost of holding one unit of the product for
one day at the distributor
α = service level. This implies that the
probability of stocking out is 1 - α
(Q,R) policy – whenever inventory level
falls to a reorder level R, place an order for
Q units
z What is the value of R?
z
2-45
Continuous Review Policy
Service Level & Safety Factor, z
Average demand during lead time: L x
AVG
z × STD × L
z Safety stock:
z
z
Reorder Level, R: L × AVG + z × STD × L
z
Order Quantity, Q: Q =
2-46
Service
Level
90% 91% 92% 93% 94%
95% 96% 97% 98% 99% 99.9%
z
1.29
1.65
1.34
1.41
1.48
1.56
1.75
1.88
2.05
2.33
3.08
z is chosen from statistical tables to ensure
that the probability of stockouts during lead time is exactly 1 - α
2K × AVG
h
2-47
2-48
8
Inventory Level Over Time
Continuous Review Policy Example
FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy
A distributor of TV sets that orders from a
manufacturer and sells to retailers
z Fixed ordering cost = $4,500
z Cost of a TV set to the distributor = $250
z Annual inventory holding cost = 18% of
product cost
z Replenishment lead time = 2 weeks
z Expected service level = 97%
z
Inventory level before receiving an order = z × STD × L
Inventory level after receiving an order = Q + z × STD × L
Average Inventory =
Q
2
+ z × STD × L
2-49
2-50
Continuous Review Policy
Example
Continuous Review Policy
Example
Month
Sept
Oct
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug
Sales
200
152
100
221
287
176
151
198
246
309
98
156
Average monthly demand = 191.17
Standard deviation of monthly demand = 66.53
Average weekly demand = Average Monthly Demand/4.3
Standard deviation of weekly demand = Monthly standard deviation/√4.3
Parameter
Average weekly
demand
Standard
deviation of
weekly demand
Average
demand
during lead
time
Safety
stock
Reorder
point
Value
44.58
32.08
89.16
86.20
176
Weekly holding cost =
0.18 × 250
= 0 .87
52
Optimal order quantity =
Q=
2 × 4,500 × 44 .58
= 679
.87
Average inventory level = 679/2 + 86.20 = 426
2-51
2-52
2.2.7. Variable Lead Times
2.2.8. Periodic Review Policy
Average lead time, AVGL
z Standard deviation, STDL.
z Reorder Level, R:
z
z
z
z
Inventory level is reviewed periodically at regular
intervals
An appropriate quantity is ordered after each review
Two Cases:
z
R = AVG× AVGL+ z AVGL× STD2 + AVG2 × STDL2
Short Intervals (e.g. Daily)
z
z
z
2
2
2
Amount of safety stock= z AVGL× STD + AVG × STDL
z
Longer Intervals (e.g. Weekly or Monthly)
z
z
Order Quantity =
Q =
z
2 K × AVG
h
z
z
2-53
Define two inventory levels s and S
During each inventory review, if the inventory position falls below s,
order enough to raise the inventory position to S.
(s, S) policy
May make sense to always order after an inventory level review.
Determine a target inventory level, the base-stock level
During each review period, the inventory position is reviewed
Order enough to raise the inventory position to the base-stock level.
Base-stock level policy
2-54
9
(s,S) policy
Base-Stock Level Policy
z
Calculate the Q and R values as if this
were a continuous review model
z Set s equal to R
z Set S equal to R+Q.
z
z
z
Determine a target inventory level, the basestock level
Each review period, review the inventory
position is reviewed and order enough to raise
the inventory position to the base-stock level
Assume:
r = length of the review period
L = lead time
AVG = average daily demand
STD = standard deviation of this daily demand.
2-55
2-56
Base-Stock Level Policy
z
z
Base-Stock Level Policy
Average demand during an interval of r + L
days= ( r + L ) × AVG
Safety Stock= z × STD × r + L
FIGURE 2-10: Inventory level as a function of time in a periodic
review policy
2-57
2-58
Base-Stock Level Policy
Example
z
z
z
distributor places an order for TVs every 3 weeks
Lead time is 2 weeks
Base-stock level needs to cover 5 weeks
z
Average demand = 44.58 x 5 = 222.9
Safety stock = 1.9 × 32.8 × 5
Base-stock level = 223 + 136 = 359
Average inventory level = 3×442 .58 + 1.9 × 32.08 × 5 = 203.17
z
Distributor keeps 5 (= 203.17/44.58) weeks of supply.
z
z
Optimal inventory policy assumes a
specific service level target.
z What is the appropriate level of service?
z
Assume:
z
z
2.2.9. Service Level
Optimization
z
May be determined by the downstream
customer
z Retailer
may require the supplier, to maintain a
specific service level
z Supplier will use that target to manage its own
inventory
z
2-59
Facility may have the flexibility to choose the
appropriate level of service
2-60
10
Service Level Optimization
Trade-Offs
z
Everything else being equal:
the higher the service level, the higher the
inventory level.
z for the same inventory level, the longer the
lead time to the facility, the lower the level of
service provided by the facility.
z the lower the inventory level, the higher the
impact of a unit of inventory on service level
and hence on expected profit
z
FIGURE 2-11:
Service level
inventory versus
inventory level as
a function of lead
time
2-61
2-62
Profit Optimization and Service
Level
Retail Strategy
Given a target service level across all
products determine service level for each
SKU so as to maximize expected profit.
z Everything else being equal, service level
will be higher for products with:
z
high profit margin
high volume
z low variability
z short lead time
z
z
FIGURE 2-12: Service level optimization by SKU
2-63
2-64
Profit Optimization and Service
Level
2.3 Risk Pooling
Target inventory level = 95% across all
products.
z Service level > 99% for many products
with high profit margin, high volume and
low variability.
z Service level < 95% for products with low
profit margin, low volume and high
variability.
Demand variability is reduced if one
aggregates demand across locations.
z More likely that high demand from one
customer will be offset by low demand
from another.
z Reduction in variability allows a decrease
in safety stock and therefore reduces
average inventory.
z
z
2-65
2-66
11
Acme Risk Pooling Case
Demand Variation
z
Standard deviation measures how much
demand tends to vary around the average
z
z
z
z
Gives an absolute measure of the variability
Coefficient of variation is the ratio of
standard deviation to average demand
z
z
Gives a relative measure of the variability,
relative to the average demand
z
z
z
Electronic equipment manufacturer and
distributor
2 warehouses for distribution in New York and
New Jersey (partitioning the northeast market
into two regions)
Customers (that is, retailers) receiving items
from warehouses (each retailer is assigned a
warehouse)
Warehouses receive material from Chicago
Current rule: 97 % service level
Each warehouse operate to satisfy 97 % of
demand (3 % probability of stock-out)
2-67
2-68
New Idea
z
z
z
Historical Data
PRODUCT A
Replace the 2 warehouses with a single
warehouse (located some suitable place) and
try to implement the same service level 97 %
Delivery lead times may increase
But may decrease total inventory investment
considerably.
Week
1
2
3
4
5
6
7
8
Massachusetts
33
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
Massachusetts
0
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
2-69
2-70
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
2-71
Product
Average
Demand
During Lead
Time
Safety Stock
Reorder
Point
Q
Massachusetts
A
39.3
25.08
65
132
Massachusetts
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
2-72
12
Critical Points
Savings in Inventory
z
Average inventory for Product A:
z
z
z
z
z
z
At NJ warehouse is about 88 units
At MA warehouse is about 91 units
In the centralized warehouse is about 132 units
Average inventory reduced by about 36 percent
z
Average inventory for Product B:
z
z
z
z
At NJ warehouse is about 15 units
At MA warehouse is about 14 units
In the centralized warehouse is about 20 units
Average inventory reduced by about 43 percent
z
The higher the coefficient of variation, the greater the
benefit from risk pooling
z The higher the variability, the higher the safety stocks
kept by the warehouses. The variability of the demand
aggregated by the single warehouse is lower
The benefits from risk pooling depend on the behavior of
the demand from one market relative to demand from
another
z risk pooling benefits are higher in situations where
demands observed at warehouses are negatively
correlated
Reallocation of items from one market to another
easily accomplished in centralized systems. Not
possible to do in decentralized systems where
they serve different markets
2-73
2-74
2.5 Managing Inventory in the
Supply Chain
2.4 Centralized vs.
Decentralized Systems
z
z
z
z
z
z
Safety stock: lower with centralization
Service level: higher service level for the same
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.
z
z
2-75
Inventory decisions are given by a single
decision maker whose objective is to
minimize the system-wide cost
The decision maker has access to inventory
information at each of the retailers and at the
warehouse
Echelons and echelon inventory
z Echelon inventory at any stage or level of
the system equals the inventory on hand
at the echelon, plus all downstream
inventory (downstream means closer to
the customer)
2-76
Reorder Point with Echelon
Inventory
Echelon Inventory
z
Le = echelon lead time,
z
lead time between the retailer and the
distributor plus the lead time between the
distributor and its supplier, the wholesaler.
AVG = average demand at the retailer
STD = standard deviation of demand at
the retailer
e
e
z Reorder point R = L × AVG + z × STD × L
z
z
FIGURE 2-13: A serial supply chain
2-77
2-78
13
4-Stage Supply Chain Example
Costs and Order Quantities
Average weekly demand faced by the
retailer is 45
z Standard deviation of demand is 32
z At each stage, management is attempting
to maintain a service level of 97% (z=1.88)
z Lead time between each of the stages,
and between the manufacturer and its
suppliers is 1 week
z
K
D
H
Q
retailer
250
45
1.2
137
distributor
200
45
.9
141
wholesaler
205
45
.8
152
manufacturer
500
45
.7
255
2-79
2-80
More than One Facility at Each
Stage
Reorder Points at Each Stage
For the retailer, R=1*45+1.88*32*√1 =
105
z For the distributor, R=2*45+1.88*32*√2 =
175
z For the wholesaler, R=3*45+1.88*32*√3
= 239
z For the manufacturer,
R=4*45+1.88*32*√4 = 300
z
z
z
z
Follow the same approach
Echelon inventory at the warehouse is the
inventory at the warehouse, plus all of the
inventory in transit to and in stock at each of the
retailers.
Similarly, the echelon inventory position at the
warehouse is the echelon inventory at the
warehouse, plus those items ordered by the
warehouse that have not yet arrived minus all
items that are backordered.
2-81
2-82
2.6 Practical Issues
Warehouse Echelon Inventory
Periodic inventory review.
Tight management of usage rates, lead times, and
safety stock.
z Reduce safety stock levels.
z Introduce or enhance cycle counting practice.
z ABC approach.
z Shift more inventory or inventory ownership to
suppliers.
z Quantitative approaches.
FOCUS: not reducing costs but reducing inventory levels.
Significant effort in industry to increase inventory turnover
z
z
Inventory_ Turnover_ Ratio =
FIGURE 2-14: The warehouse echelon inventory
2-83
Annual_ Sales
Average_ Inventory_ Level
2-84
14
Inventory Turnover Ratios for
Different Manufacturers
Industry
Upper quartile
Median
Lower quartile
Electronic components
and accessories
8.1
4.9
3.3
Electronic computers
22.7
7.0
2.7
Household audio and
video equipment
6.3
3.9
2.5
Paper Mills
11.7
8.0
5.5
Industrial chemicals
14.1
6.4
4.2
Bakery products
39.7
23.0
12.6
Books: Publishing and
printing
7.2
2.8
1.5
2.7 Forecasting
RULES OF FORECASTING
z The forecast is always wrong.
z The longer the forecast horizon, the
worse the forecast.
z Aggregate forecasts are more accurate.
2-85
2-86
Techniques
Utility of Forecasting
z
Judgment Methods
z
Part of the available tools for a manager
z Despite difficulties with forecasts, it can be
used for a variety of decisions
z Number of techniques allow prudent use
of forecasts as needed
z
z
z
z
z
Market research/survey
Time Series
z
z
z
z
z
z
Moving Averages
Exponential Smoothing
Trends
z
z
Sales-force composite
Experts panel
Delphi method
Regression
Holt’s method
Seasonal patterns – Seasonal decomposition
Trend + Seasonality – Winter’s Method
Causal Methods
2-87
2-88
The Most Appropriate
Technique(s)
SUMMARY
Purpose of the forecast
z How will the forecast be used?
z Dynamics of system for which forecast will
be made
z How accurate is the past history in
predicting the future?
z
z
z
z
z
z
z
2-89
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
2-90
15