Title: Chapter 3 Inventory Management and Risk Pooling
1Chapter 3 Inventory Management and Risk Pooling
2Outline of the contents
- Introduction to Inventory Management
- The Effect of Demand Uncertainty
- (s,S) Policy
- Periodic Review Policy
- Supply Contracts
- Risk Pooling
- Centralized vs. Decentralized Systems
- Practical Issues in Inventory Management
3Inventory
- Where do we hold inventory?
- Suppliers and manufacturers
- Warehouses and distribution centers
- Retailers
- Types of Inventory
- Raw materials
- WIP
- Finished goods
- Why do we hold inventory?
- Economies of scale
- Uncertainty in supply and demand
- Lead Time, Capacity limitations
4Inventory
- Managing inventory in complex supply chains is
typically difficult, and may have a significant
impact on the customer service level and supply
chain system-wide cost. - Inventory in three types
- Raw material inventory (where?)
- Work-in-process inventory (where?)
- Finished product inventory (where?)
5Why hold Inventory?
- Unexpected changes in customer demand.
- The short life cycle of an increasing number of
products. Thus, historical data may not be
available or may be quite limited. - The presence of many competing products in the
marketplace. (Discussed in Chapters 5 and 9) - The presence in many situations of a significant
uncertainty in the quantity and quality of the
supply, supplier costs, and delivery times. - A need to hold inventory due to delivery lead
times even if there is no uncertainty in supply
or demand. - Economies of scale offered by transportation
companies that encourage firms to transport large
quantities of items, and therefore hold large
inventories.
6Managing inventory examples
- By effectively managing inventory
- Xerox eliminated 700 million inventory from its
supply chain. - Wal-Mart became the largest retail company
utilizing efficient inventory management. - GM has reduced parts inventory and transportation
costs by 26 annually .
7Managing inventory examples
- By not managing inventory successfully
- In 1993, Dells stock plunged after the company
predicted a loss. (sharply off in its forecast of
demand) - In 1994, IBM continues to struggle with
shortages in their ThinkPad line (WSJ, Oct 7,
1994) - In 1993, Liz Claiborne said its unexpected
earning decline is the consequence of higher than
anticipated excess inventory (WSJ, July 15,
1993) - In 2001, Cisco took a 2.25B excess inventory
charge due to declining scales.
8Two important issues in inventory management
- Demand forecasting
- Forecast demand is a critical element in
determining order quantity. - What is the relationship between forecast demand
and the optimal order quantity? - Should the order quantity or gt or lt the
forecast demand? - ..
- Order quantity calculation
9A single warehouse inventory example
10Key factors affecting inventory policy?
- Customer demand
- Known in advance or may be random (forecasting
tools can be used). - Replenishment lead time
- May be known at the time we place the order or
may be uncertain. - The number of different products
- High-mix and low volume?
- The length of the planning horizon
11Key factors affecting inventory policy?
- Costs (order cost and inventory holding cost)
- Order cost the cost of the product and the
transportation cost - Inventory holding cost
- State taxes, property taxes, and insurance on
inventories - Maintenance costs
- Obsolescence cost (an item will lose some of its
value because of changes in the market.) - Opportunities costs (the return on investment
that one would receive had money been invested in
something else (e.g. stock market) instead of
inventory.
12Key factors affecting inventory policy?
- Service level requirements
- It is not possible to meat customer orders 100
percent of the time. Managements need to specify
an acceptable level of service
133.2.1 The Economic Lot Size model
- Economic lot size model is used to trade-off the
costs between ordering and storage. - Assumptions (for a single item and has a
unlimited quantity of the product) - Demand is constant at a rate of D items per day.
- Order quantities are fixed at Q items per order.
- A fixed cost (setup cost) K, incurred every time
the warehouse places an order. - An inventory carrying cost, h, also referred to
as a holding cost, is accrued per unit held in
inventory per day that the unit is held. - The lead time, the time that elapses between the
placement of an order and its receipt, is zero - Initial inventory is zero.
- The planning horizon is long (infinite).
143.2.1 The Economic Lot Size model
- Goal
- Find the optimal order policy that minimizes
annual purchasing and carrying costs while
meeting all demand. - Realistic system?
- A known fixed demand over a long horizon is clear
unrealistic. - This model will help us to develop inventory
policies that are effective for more complex
realistic systems.
153.2.1 The Economic Lot Size model
Notes No Stockouts Order when no inventory
Order Size determines policy
Inventory
Order Size
Avg. Inven
Time
Saw-toothed inventory pattern
163.2.1 The Economic Lot Size model
- Total costs
- Purchase Cost is Constant
- Holding Cost (Avg. Inven) (Holding Cost)
- Ordering (Setup Cost)
- Number of Orders Order Cost
- Goal Find the order Quantity that minimizes
these costs.
173.2.1 The Economic Lot Size model
- Total inventory cost in a cycle of length T
-
- Average total cost per unit of time
- EOQ model
An inventory holding cost
Q/2 average inventory Level.
A fixed cost (setup cost)
QTD -gt TQ/D
Setup cost/unit
Holding/unit
183.2.1 The Economic Lot Size model
Total Cost
Holding Cost
Order Cost
19Economic Lot Size model Important Observations
- Tradeoff between set-up costs and holding costs
when determining order quantity. In fact, we
order so that these costs are equal per unit time - Total Cost is not particularly sensitive to the
optimal order quantity
Q bQ
See page. 48.
20The Effect of Demand Uncertainty
- Most companies treat the world as if it were
predictable - Production and inventory planning are based on
forecasts of demand made far in advance of the
selling season - Companies are aware of demand uncertainty when
they create a forecast, but they design their
planning process as if the forecast truly
represents reality - Recent technological advances have increased the
level of demand uncertainty - Short product life cycles
- Increasing product variety
21Demand Forecasts
- The three principles of all forecasting
techniques - Forecasting is always wrong
- The longer the forecast horizon the worst is the
forecast - Aggregate forecasts are more accurate
22Swimsuit production
- (Read the case on page 49)
- Fashion items have short life cycles, high
variety of competitors - Swimsuit
- New designs are completed
- One production opportunity
- Based on past sales, knowledge of the industry,
and economic conditions, the marketing department
has a probabilistic forecast - The forecast averages about 13,000, but there is
a chance that demand will be greater or less than
this.
23Probabilistic forecast
24Data
- 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
25Example scenarios
- Scenario One
- Suppose you make 12,000 swimsuits and demand ends
up being 13,000 swimsuits. - Profit 125(12,000) - 80(12,000) - 100,000
440,000 - Scenario Two
- Suppose you make 12,000 swimsuits and demand ends
up being 11,000 swimsuits. - Profit 125(11,000) - 80(12,000) - 100,000
20(1000) 335,000
26What to make?
- Find order quantity that maximizes weighted
average profit. - Question Will this quantity be less than, equal
to, or greater than average demand?
See Excel Spreadsheet for Chapter 3
27What to Make?
- Average demand is 13,100
- Look at marginal cost vs. marginal profit
- if extra swimsuit sold, profit is 125-80 45
- if not sold, cost is 80-20 60
- So we will make less than average demand
28Expected Profit
29Expected Profit
30Important Observations
- Tradeoff between ordering enough to meet demand
and ordering too much - Several quantities have the same average profit
- Average profit does not tell the whole story
- Question 9000 and 16000 units lead to about the
same average profit, so which do we prefer?
31Probability of Outcomes
32Key Points from this case study
- 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 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
33The effect of Initial Inventory
- Suppose that one of the swimsuit 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
- From Figure 3-6, the profit can be obtained
- 225000500080625,000
34Initial Inventory and Profit
Fix production costs
225000
35Questions
- If there are 7000 units remaining, what should
the company do? - What should they do if there are 10,000 remaining?
36Initial Inventory and Profit
37(s, S) Policies
- For some starting inventory levels, it is better
to not start production - If we start, we always produce to the same level
- Thus, we use an (s,S) policy. If the inventory
level is below s, we produce up to S. - s is the reorder point, and S is the order-up-to
level - The difference between the two levels is driven
by the fixed costs associated with ordering,
transportation, or manufacturing - Swimsuit case s 8,500 and S 12,000
38Supply contracts
- In as supply contract, the buyer and supplier may
agree on - Pricing and volume discounts
- Maximum and minimum purchase quantities
- Delivery lead times
- Product or material quality
- Product return policies
- Refer to the Excel spreadsheet (supply contract).
39Swimsuit example again
- (Read the case of example 3-2 on page 53)
- Sequential supply chain
- each party determines its own course of action
independent of the other parties. - For the earlier example, the retailer assumes all
of the risk, of having more inventory than sales,
while the manufacturer takes no risk. - Larger the order is, better it is for the
manufacturer but it has a reverse impact to the
retailer.
40Buy-back contracts
- In a buy-back contract, the seller agrees to buy
back unsold goods from the buyer for some
agreed-upon price. - Study example 3-3 on page 54 and explain how does
it work?
41Revenue-sharing contracts
- For the swimsuit example, if the manufacturer is
willing to give discounts, the retailer will have
an incentive to order more. - Study example 3-4 and explain how does it works.
42Quantity-flexibility contracts
- The supplier provides full unsold items as long
as the number of returns is no larger than a
certain quantity. - How is it different from buy-back contracts?
43Sales rebate contracts
- Sales rebate (discounts) contacts provide a
direct incentive to the retailer to increase
sales by means of a rebate paid by the supplier
for any item sold above a certain quantity.
44Global optimization
- What is the best strategy for the entire supply
chain? - The difficulty with global optimization is that
it requires the firm to surrender decision-making
power to an unbiased decision maker. - See example 3-5 on page 56
- Its main drawback is that it does not provide a
mechanism to allocate supply chain profit between
the partners. - See example 3-6 on page 57
45Multiple reorder opportunities
- Consider a central distribution facility which
orders from a manufacturer and delivers to
retailers. The distributor periodically places
orders to replenish its inventory - Continuous review policy and periodic review
policy
46The Multi-Period Inventory Model
- Normally distributed random demand
- Fixed order cost plus a cost proportional to
amount ordered. - Inventory cost is charged per item per unit time
- If an order arrives and there is no inventory,
the order is lost - The distributor has a required service level.
This is expressed as the the likelihood that the
distributor will not stock out during lead time. - Intuitively, what will a good policy look like?
47Continuous review policy
- Known parameters
- 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 - ? service level
48Continuous review policy
- Inventory position
- The actual inventory at the warehouse plus items
ordered by the distributor that have not yet
arrived minus items that are backordered.
49The (s,S) Policy
- (s, S) Policy Whenever the inventory position
drops below a certain level, s, we order to raise
the inventory position to level S. - The reorder point is a function of
- The Lead Time
- Average demand
- Demand variability
- Service level
50A View of (s, S) Policy
S
Inventory Position
Inventory Level
Lead Time
s
0
Time
51Analysis
- The reorder point has two components
- To account for average demand during lead
time - L ? AVG
- To account for deviations from average (we call
this safety stock) z ? STD ? ?L - where z is chosen from statistical tables to
ensure that the probability of stockouts during
leadtime is (1-?).
52Analysis
- Reorder level (s)
- L ? AVG z ? STD ? ?L
- It needs to satisfy
- Probability Demand during lead time ? L ? AVG
z ? STD ? ?L (1-?) - Refer to Table 3-2 on page 59 for z values.
53Analysis
- Use EOQ model
- Q
- S Q s
- Average inventory level (S s)
-
-
54Reminder The Normal Distribution
Standard Deviation 5
Standard Deviation 10
Average 30
55The distributor holds inventory to
- Satisfy demand during lead time
- Protect against demand uncertainty
- Balance fixed costs and holding costs
56Distributor of the TV sets
- The distributor has historically observed weekly
demand of AVG 44.6 STD 32.1 - Replenishment lead time is 2 weeks, and desired
service level SL 97 - Average demand during lead time is 44.6 ? 2
89.2 - Safety Stock is 1.88 ? 32.1 ? ?2 85.3
- Reorder point is thus 175, or about 3.9 weeks of
supply at warehouse and in the pipeline
57Distributor of the TV sets
- In addition to previous costs, a fixed cost K is
paid every time an order is placed. - We have seen that this motivates an (s,S) policy,
where reorder point and order quantity are
different. - The reorder point will be the same as the
previous model, in order to meet the service
requirement - s LT?AVG z ? AVG ? ?L
- What about the order up to level?
58Distributor of the TV sets
- We have used the EOQ model to balance fixed,
variable costs Q?(2 ?K ?AVG)/h - If there was no variability in demand, we would
order Q when inventory level was at L ?AVG. Why? - There is variability, so we need safety stock
- z ? STD ? ?L
59Distributor of the TV sets
- Consider the previous example, but with the
following additional info - fixed cost of 4500 when an order is placed
- 250 product cost
- holding cost 18 of product
- Weekly holding cost h (.18 ? 250) / 52 0.87
- Order quantity Q?(2 ?4500 ? 44.6 / 0.87 679
- Order-up-to level s Q 175 679 855
60Periodic review policy
- Base-stock level
- Each review period, the inventory position is
reviewed and the warehouse orders enough to raise
the inventory position to the base-stock level. - Assume that orders are placed every r period of
time.
61Periodic review policy
62Periodic review policy
- Average demand during an interval of r L(r
L) ? AVG - Safety stock
- z ? STD ? ? (r L)
- Expected level of inventory after receiving an
order - r ? AVG z ? STD ? ? (r L)
- Example 3-8 on page 63
63Risk Pooling
- Consider these two systems
Market One
Warehouse One
Supplier
Market Two
Warehouse Two
Market One
Warehouse
Supplier
Market Two
64Risk Pooling
- For the same service level, which system will
require more inventory? Why? - For the same total inventory level, which system
will have better service? Why? - What are the factors that affect these answers?
65Risk Pooling Example
- Compare the two systems (Read the case on page.
64-66) - two products
- maintain 97 service level
- 60 order cost
- .27 weekly holding cost
- 1.05 transportation cost per unit in
decentralized system, 1.10 in centralized system - 1 week lead time
66Risk Pooling Example
67Risk Pooling Example
68Risk Pooling Example
69Risk PoolingImportant Observations
- Centralizing inventory control reduces both
safety stock and average inventory level for the
same service level. - This works best for
- High coefficient of variation, which reduces
required safety stock. - Negatively correlated demand. Why?
- What other kinds of risk pooling will we see?
70Risk Pooling Types of Risk Pooling
- Risk Pooling Across Markets
- Risk Pooling Across Products
- Risk Pooling Across Time
- Daily order up to quantity is
- LT?AVG z ? AVG ? ?L
Orders
10
12
11
13
14
15
Demands
71To Centralize or not to Centralize
- Safety stock
- Safety stock decreases as a firm moves from a
decentralized to a centralized system. - Depend on CV and correlation
- Service level
- Given the same total safety stock, the service
level provided by the centralized system is
higher. - Overhead
- Typically, these costs are much greater in a
decentralized system.
72To Centralize or not to Centralize
- Lead time
- The response time for a decentralized system is
much shorter. - Transportation Costs
- Outbound costs are higher for the centralized
system. - Inbound costs are higher for the decentralized
system.
73Centralized Systems
Supplier
Warehouse
Retailers
74Centralized Distribution Systems
- Question How much inventory should management
keep at each location? - A good strategy
- The retailer raises inventory to level s each
period - The supplier raises the sum of inventory in the
retailer and supplier warehouses and in transit
to S - If there is not enough inventory in the warehouse
to meet all demands from retailers, it is
allocated so that the service level at each of
the retailers will be equal.
75Practical issues
- Periodic inventory review policy
- Tight management of usage rates, lead times and
safety stock - Reduced safety stock levels
- Introduce or enhance cycle counting practice
- ABC approach
- Shift more inventory, or inventory ownership, to
suppliers - Quantitative approaches inventory turnover rate
76Practical issues
Practical issues
77Forecasting
- Three rules of forecasting
- The forecast is always wrong.
- The longer the forecast horizon, the worse the
forecast. - Aggregate forecasts are more accurate.
78Forecasting
- Categories (See section 3.7)
- Judgment methods
- Market research methods
- Time-series methods
- Causal methods
79Summary
- Matching supply and demand in the supply chain is
a critical challenge. - Unfortunately, the existence the three
forecasting rules. - Globally optimal inventory policies, in which the
best possible policy for the entire supply chain
is implemented, are the best course of action. - Well-designed supply contracts frequently make
this global optimization possible.