3 inventory management and risk pooling
TRANSCRIPT
Inventory Management &
Risk Pooling
Introduction
General Motors in 1984:
Logistic network consisted of 20,000 supplier plants, 133
parts plants, 31 assembly plants, and 11,000 dealers.
Freight transportation costs were about $4.1 billion, of
which 60 percent for material shipments.
GM inventory was valued at $7.4 billion, of which 70
percent was WIP and the rest was finished vehicles.
Response:-Inventory Management in Supply Chain
Goals of Inventory Management
By effectively managing inventory: GM has reduced parts inventory and transportation costs
by 26% annually Xerox eliminated $700 million inventory from its supply
chain Wal-Mart became the largest retail company utilizing
efficient inventory management
Reduce Cost, Improve Service
Inventory Levels FinancialInvestment
Operational Need
Inventory
Where do we hold inventory?
Suppliers and manufacturers
warehouses and distribution centers
retailers
Types of Inventory: General classification
WIP
raw materials
finished goods
Functions of Inventory
To meet anticipated demand
To smooth production requirements
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
Factors Affecting Inventory Policy
Demand Characteristics: known in advance or random
Lead Time
Number of Different Products Stored in the Warehouse
Economies of scale offered by suppliers & transport
companies
Length of Planning Horizon
Service level desired
1000 2000 3000 4000 5000 6000
0
50
100
150
200
250
300
350
Ordering (Acquisition)Costs
Holding or Carry
ing CostsTotal CostsEconomic Order Quantity
Economic Order Quantity Model
Assuming demand certainty
Trade-offs between setup costs and inventory holding costs, but ignores issues such as demand uncertainty and forecasting.
Single Period Model Without Initial Inventory
Case: Swimsuit Production
A company designs, produces, and sells summer fashion
items such as swimsuits.
The company has to commit itself six months before summer
to specific production quantities for all its products
– predicting demand for each product.
The trade-offs are clear: overestimating customer demand
will result in unsold inventory while underestimating
customer demand will lead to inventory stockouts and
loss of potential customers.
Demand forecast
forecast averages about 13,000
The marketing department uses historical data from the last five years, current economic conditions, and other factors to construct a probabilistic forecast of the demand.
11% 11%
28%
22%
18%
10%
0%
5%
10%
15%
20%
25%
30%
8000 10000 12000 14000 16000 18000
Unit sales
Swimsuit Costs
Production cost per unit (C): $80
Selling price per unit (S): $125
Salvage value per unit (V): $20
Fixed production cost (F): $100,000
Q is production quantity, D: demand
Profit = Revenue - Variable Cost - Fixed Cost + Salvage
Swimsuit Two Scenarios
Scenario One: Suppose you make 12,000 jackets and demand ends up
being 13,000 jackets. Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000
Scenario Two: Suppose you make 12,000 jackets and demand ends up
being 11,000 jackets. Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000) =
$ 335,000
Swimsuit Best Questions ?
Find order quantity that maximizes weighted average profit?
Will this quantity be less than, equal to, or greater than average demand?
How much to Make?
Marginal cost Vs. marginal profit if extra jacket sold, profit is 125-80 = 45 if not sold, cost is 80-20 = 60
So we will make less than average
Swimsuit Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
If Quantity ordered is 12000, hence the Profit is
= (0.78)*12000*125+ 0.11*8000*125+0.11* 10000*125+4000*0.11*20+2000*0.11*20-80*12000-100000= 1170000+247500 – 960000 -100000 + 13200= 3070700
Swimsuit : Important Observations
Tradeoff between ordering enough to meet demand and ordering too much
Several quantities have the same estimated profit Estimated profit does not tell the whole story 9000 and 16000 units lead to about the same
estimated profit, so which do we prefer?
Swimsuit Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
Case: Swimsuit Production
But Need to understand risk associated with certain
decisions.
A frequency histogram provides information about
potential profit for the two given production
quantities, 9,000 units and 16,000 units. The
possible risk and possible reward increases as we
increase the production size.
Probability of Outcomes
0 0 0 0 0
0.11
0.89
0 00
0.11 0.11
0 0
0.28
0
0.22
0
0.28
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
-3E
+0
5
-2E
+0
5
-1E
+0
5
0
10
00
0
20
00
0
30
00
0
40
00
0
50
00
0
60
00
0
Cost
Pro
ba
bil
ity
Q =9000
Q =16000
Key Points from this Case
The optimal order quantity is not necessarily equal to
average forecast demand
The optimal quantity depends on the relationship between
marginal profit and marginal cost
As order quantity increases, average estimated profit first
increases and then decreases
As production quantity increases, risk increases. In other
words, the probability of large gains and of large losses
increases
Single Period Model With Initial Inventory
Initial Inventory
Suppose that one of the jacket designs is a model produced last year.
Some inventory is left from last year Assume the same demand pattern as before If only old inventory is sold, no setup cost
Question: If there are 7000 units remaining, what should the company do? What should they do if there are 10,000 remaining?
Initial Inventory and Profit
0
100000
200000
300000
400000
500000
5000
6000
7000
8000
9000
1000
0
1100
0
1200
0
1300
0
1400
0
1500
0
1600
0
Production Quantity
Prof
it
The case motivates a powerful (s,S) inventory policy (or a min max policy): s is the reorder point and S is the order-up-to-level
Assuming Inventory holding cost is negligible.
Multi-Order Opportunities under Uncertainties
Inventory Policies
Continuous review policy in which inventory is reviewed every day (or every unit of
time) and a decision is made about whether and how
much to order.
Periodic review policy in which the inventory level is reviewed at regular
intervals and an appropriate quantity is ordered after
each review.
Variable Demand with a Fixed ROP
Reorderpoint, R
Q
LT
Time
LT
Inve
nto
ry le
vel
0
Result of uncertainty
Reorder Point with a Safety Stock
Reorderpoint, R
Q
LT
Time
LT
Inve
nto
ry le
vel
0
Safety Stock
The amount of safety stock needed is based on the degree of uncertainty in the lead time demand and desired customer service level
Determinants of the Reorder Point
The rate of demand
The lead time
Demand and/or lead time variability
Stockout risk (safety stock)
Continuous Review Policy
AVG = Average daily demand faced STD = Standard deviation of daily demand faced L = Replenishment lead time h = Cost of holding one unit of the product per unit timeα = service level (the probability of stocking out is 1 – α)
hp
p
p =shortage cost
Continuous Review Policy
The inventory position at any point in time is the actual inventory at the warehouse plus items ordered by the distributor that have not yet arrived minus items that are backordered.
The reorder level, R consists of two components: the average inventory during lead time, which is the product of average daily demand and the lead time; and the safety stock, which is the amount of inventory that the distributor needs to keep at the warehouse and in the pipeline to protect against deviations from average demand during lead time.
Continuous Review Policy –Variable demand & fixed lead time
Average demand during lead time is exactly
Safety stock is
where z is a constant, referred to as the safety factor.
This constant is associated with the service level.
The reorder level is
Economic lot size is
LSTDz
AVGL
LSTDzAVGL
h
AVGKQ
2
Continuous Review Policy –Variable demand & fixed lead time
The expected level of inventory before receiving the order
is (lowest level i.e. Safety
Stock)
The expected level of inventory immediately after
receiving the order is (highest
level)
The average inventory level is the average of these two
values
LSTDzQ
LSTDzQ
2
LSTDz
In many situation, the lead time to the warehouse must be assumed to be normally distributed with average lead time denoted by AVGL and standard deviation denoted by STDL. In this case, the reorder point is calculated as
where AVG x AVGL represents average demand during lead time, &
is the standard deviation of demand during lead time. The amount of safety stock that has to be kept is equal to
222 STDLAVGSTDAVGLz
222 STDLAVGSTDAVGL
Continuous Review Policy –Variable demand & lead time
Periodic Review Policy
Inventory level is reviewed periodically at regular
intervals and an appropriate quantity so as to arrive at
base stock level is ordered after each review . Since inventory levels are reviewed at a periodic interval, the fixed
cost of placing an order is a sunk cost and hence can be ignored.
This level of the inventory position should be enough to
protect the warehouse against shortages until the next order
arrives, that is to cover demand during a period of r + L
days, with r being the length of review period and L being
the lead time.
Periodic Review Policy
Thus, the base-stock level should include two components: average demand during an interval of r + L days, which is equal to
and the safety stock, which is calculated as
where z is a safety factor.
AVGLr )(
LrSTDz
Periodic Review Policy (with SS)
Periodic Review Policy
Maximum inventory level is achieved immediately after receiving an order, while the minimum level of inventory is achieved just before receiving an order.
It is easy to see that the expected level of inventory after receiving an order is
while the expected level of inventory before an order arrives is just the safety stock
Hence, the average inventory level is the average of these two values
LrSTDzAVGr
LrSTDz
LrSTDzAVGr
2
RISK POOLING
Risk Pooling Consider these two systems:
Market Two
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier Warehouse
Market One
Questions: Q1: For the same service level, which system will require more inventory?Q2: For the same total inventory level, which system will have better service?
What is Risk Pooling?
The idea behind risk pooling is to redesign the supply chain,
the production process, or the product to either reduce the
uncertainty the firm faces or to hedge uncertainty so that
the firm is in a better position to mitigate the consequence
of uncertainty.
• Location pooling
• Product pooling
• Lead Time pooling
• Capacity pooling
Lead Time Pooling
Store 1
Sup
plie
r
Store 100
8-week lead time
Lead Time Pooling
Store 1
Sup
plie
r
Store 100
8-week lead time
Retail DC
1-week lead time
Capacity Pooling
3 Links – no flexibility
Capacity Pooling
9 Links – Total Flexibility
Advantages / Disadvantages
Advantages Disadvantages
Location Pooling reduce demand variabilitycreates distance between inventory and
customers
reduce expected inventory investment needed to achieve a target service level
Product Pooling reduction in demand variability potentially degrades product functionality
better performance in terms of
matching supply and demand
Lead Time Pooling decrease lead time extra costs of operating distribution center
keep inventory closer to customer additional transportation costs
reduce inventory investment
Capacity Pooling accommodate demand uncertainty large costs to have flexibility
Summary Risk Pooling
Risk-pooling strategies are most effective when demands
are negatively correlated because then the uncertainty with
total demand is much less than the uncertainty with any
individual item/location
Risk-pooling strategies do not help reduce pipeline
inventory
Risk-pooling strategies can be used to reduce inventory
while maintaining the same service or they can be used to
increase service while holding the same inventory
Example
Decentralized system: total SS = 47.88
total avg. invent. = 179
Safety Stock SS = z ·STD · L
Reorder Point R = AVG·L + SSOrder Quantity Q = sqrt(2*C0*AVG/h)Order-up-to-level R + QAverage Inventory SS + Q/2
AVG STD SS R QOrder-
up-to LevelAverage
Inventory
Warehouse 1 39.3 13.2 25.08 65 132 197 91
Warehouse 2 38.6 12.0 22.8 62 131 193 88
CentralizedWarehouse
77.9 20.7 39.35 118 186 304 132
Service Level:97% k=1.88Lead Time= 1 week
Q/2+SS
Risk Pooling – Effect of Correlation
The benefits of risk pooling depend on the behavior of demand from one market relative to the demand from another market.
WarehouseMarket 1
Market 2
D1+D2: (, 2)
Calculating demand variability of centralized system
Warehouse 1
Warehouse 2
Market 1
Market 2
D1: (1, 12)
D2: (2, 22)
2 = 1
2 + 22 + 212,
where -1 12
= 12 + 2
2 + 212,
where -1 1
: correlation coefficient of D1, D2
1+ 2 1+ 2
Conclusions: 1. Stdev of aggregated demand is less than the sum of stdev of individual demands2. If demands are independent or negatively correlated, the std of aggregated demand is much less
Conclusions: 1. Stdev of aggregated demand is less than the sum of stdev of individual demands2. If demands are independent or negatively correlated, the std of aggregated demand is much less
1. If D1, D2 positively correlated, > 02. If D1, D2 are independent, = 03. If D1, D2 negatively correlated, < 0
= 1 + 2
= ??
1+2
10-1
22
21
P.C.N.C. Ind.As (safety) stock is based on standard deviation
Square Root Law:Square Root Law: stock for combined demands usually less than the combined stocks
Risk Pooling – Effect of Coefficient of Variation
The higher the C.V. of demand observed in one market, the greater the benefit from risk pooling
COV= Standard deviation/Avg. demand
DecentralizedCentralized
Inbound transportation cost (from factories to warehouses)
Facility/Labor cost
Outbound transportation cost (from warehouses to retailers)
Safety Stock
Responsiveness to customers (lead time)
Centralized vs. Decentralized
Overhead Costs
Service Level
Case Study
# below stage = processing time # in white box = CST In this solution, inventory is held of finished
product and its raw materials
PART 1DALLAS ($260)
157
8
PART 2CHARLESTON ($7)
14
PART 4BALTIMORE ($220)
5
PART 3AUSTIN ($2)
14
6
8
5
PART 5CHICAGO ($155)
45
PART 7CHARLESTON ($30)
14
PART 6CHARLESTON ($2)
32
8
0
14
55
1445
14
32
(Adapted from Simchi-Levi, Chen, and Bramel, The Logic of Logistics, Springer, 2004)
A Pure Pull System
Produce to orderLong CST to customerNo inventory held in system
PART 1DALLAS ($260)
157
8
PART 2CHARLESTON ($7)
14
PART 4BALTIMORE ($220)
5
PART 3AUSTIN ($2)
14
6
8
5
PART 5CHICAGO ($155)
45
PART 7CHARLESTON ($30)
14
PART 6CHARLESTON ($2)
32
8
77
14
55
1445
14
32
A Pure Push System
Produce to forecastZero CST to customerHold lots of finished goods inventory
PART 1DALLAS ($260)
157
8
PART 2CHARLESTON ($7)
14
PART 4BALTIMORE ($220)
5
PART 3AUSTIN ($2)
14
6
8
5
PART 5CHICAGO ($155)
45
PART 7CHARLESTON ($30)
14
PART 6CHARLESTON ($2)
32
8
0
14
55
1445
14
32
A Hybrid Push-Pull System
Part of system operated produce-to-stock, part produce-to-order
Moderate lead time to customer
PART 1DALLAS ($260)
157
8
PART 2CHARLESTON ($7)
14
PART 4BALTIMORE ($220)
5
PART 3AUSTIN ($2)
14
6
8
5
PART 5CHICAGO ($155)
45
PART 7CHARLESTON ($30)
14
PART 6CHARLESTON ($2)
32
8
27
7
5
945
14
32
push/pull boundary
CST vs. Inventory Cost
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
0 10 20 30 40 50 60 70 80
Committed Lead Time to Customer (days)
Inve
nto
ry C
ost
($/
year
)
Push System
Pull System
Push-Pull System
Echelon Inventory System
Supplier
Warehouse
Retailers
Warehouse echelon
inventoryWarehouse
echelon lead time
Managing Inventory in the Supply Chain
How should the reorder point associated with the warehouse
echelon inventory position be calculated? The reorder point
is
where Le = echelon lead time, defined as the lead time between the
retailers and the warehouse plus the lead time between the
warehouse and its supplier
AVG = average demand across all retailers (i.e., the
average of the aggregate demand)
STD = standard deviation of (aggregate) demand across
all retailers
ee LSTDzAVGLs
Forecasting
Is never accurateNevertheless, forecast is criticalGeneral Overview:
Judgment methodsMarket research methodsTime Series methodsCausal methods
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