inventory management, supply contracts and risk pooling
DESCRIPTION
Inventory Management, Supply Contracts and Risk Pooling. Phil Kaminsky [email protected]. February 1, 2007. Issues. Inventory Management The Effect of Demand Uncertainty (s,S) Policy Periodic Review Policy Supply Contracts Risk Pooling Centralized vs. Decentralized Systems - PowerPoint PPT PresentationTRANSCRIPT
Issues
• 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
Supply
Sources:plantsvendorsports
RegionalWarehouses:stocking points
Field Warehouses:stockingpoints
Customers,demandcenterssinks
Production/purchase costs
Inventory &warehousing costs
Transportation costs Inventory &
warehousing costs
Transportation costs
Inventory• Where do we hold inventory?
– Suppliers and manufacturers– warehouses and distribution centers– retailers
• Types of Inventory– WIP– raw materials– finished goods
• Why do we hold inventory?– Economies of scale– Uncertainty in supply and demand– Lead Time, Capacity limitations
Goals: Reduce Cost, Improve Service
• 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
Goals: Reduce Cost, Improve Service
• By not managing inventory successfully– 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 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993)
Understanding Inventory
• The inventory policy is affected by:– Demand Characteristics– Lead Time– Number of Products– Objectives
• Service level• Minimize costs
– Cost Structure
Cost Structure
• Order costs – Fixed– Variable
• Holding Costs– Insurance– Maintenance and Handling– Taxes– Opportunity Costs– Obsolescence
EOQ: A Simple Model*
• Book Store Mug Sales– Demand is constant, at 20 units a week– Fixed order cost of $12.00, no lead time– Holding cost of 25% of inventory value
annually– Mugs cost $1.00, sell for $5.00
• Question– How many, when to order?
EOQ: A View of Inventory*
Time
Inventory
OrderSize
Note:• No Stockouts• Order when no inventory• Order Size determines policy
Avg. Inven
EOQ: Calculating Total Cost*
• Purchase Cost Constant• Holding Cost: (Avg. Inven) * (Holding
Cost)• Ordering (Setup Cost):
Number of Orders * Order Cost• Goal: Find the Order Quantity that
Minimizes These Costs:
EOQ:Total Cost*
0
20
40
60
80
100
120
140
160
0 500 1000 1500
Order Quantity
Cos
t
Total Cost
Order Cost
Holding Cost
EOQ: Optimal Order Quantity*
• Optimal Quantity =
(2*Demand*Setup Cost)/holding cost
• So for our problem, the optimal quantity is 316
EOQ: 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
Order Quantity 50% 80% 90% 100% 110% 120% 150% 200%
Cost Increase 125% 103% 101% 100% 101% 102% 108% 125%
The 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
Demand Forecast
• 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
SnowTime Sporting Goods
• Fashion items have short life cycles, high variety of competitors
• SnowTime Sporting Goods – 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.
Supply Chain Time Lines
Jan 00 Jan 01 Jan 02
Feb 00 Sep 00 Sep 01
Design Production Retailing
Feb 01Production
SnowTime Demand Scenarios
Demand Scenarios
0%5%
10%15%20%25%30%
Sales
Pro
babil
ity
SnowTime 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
SnowTime 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
SnowTime Best Solution
• Find order quantity that maximizes weighted average profit.
• Question: Will this quantity be less than, equal to, or greater than average demand?
What to Make?
• Question: Will this quantity be less than, equal to, or greater than average demand?
• Average demand is 13,100• Look at 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
SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Prof
it
SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Prof
it
SnowTime: Important 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?
SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Prof
it
Probability of Outcomes
0%
20%
40%
60%
80%
100%
Revenue
Pro
babi
lity
Q=9000
Q=16000
Key Insights from this Model
• 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
SnowTime Costs: Initial Inventory
• 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
SnowTime Expected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Prof
it
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 SnowTime do? What should they do if there are 10,000 remaining?
Initial Inventory and Profit
0100000200000300000400000500000
Production Quantity
Prof
it
Initial Inventory and Profit
0100000200000300000400000500000
Production Quantity
Prof
it
Initial Inventory and Profit
0100000200000300000400000500000
Production Quantity
Prof
it
Initial Inventory and Profit
0100000200000300000400000500000
5000
6000
7000
8000
9000
1000
0
1100
0
1200
0
1300
0
1400
0
1500
0
1600
0
Production Quantity
Prof
it
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Contracts
Demand Scenarios
Demand Scenarios
0%5%
10%15%20%25%30%
Sales
Pro
babi
lity
Distributor Expected Profit
Expected Profit
0
100000
200000
300000
400000
500000
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity
Distributor Expected Profit
Expected Profit
0
100000
200000
300000
400000
500000
6000 8000 10000 12000 14000 16000 18000 20000
Order Quantity
Supply Contracts (cont.)
• Distributor optimal order quantity is 12,000 units
• Distributor expected profit is $470,000• Manufacturer profit is $440,000• Supply Chain Profit is $910,000
–Is there anything that the distributor and manufacturer can do to increase the profit of both?
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Contracts
Retailer Profit (Buy Back=$55)
0
100,000
200,000
300,000
400,000
500,000
600,000
Order Quantity
Reta
iler P
rofit
Retailer Profit (Buy Back=$55)
0
100,000
200,000
300,000
400,000
500,000
600,000
Order Quantity
Reta
iler P
rofit
$513,800
Manufacturer Profit (Buy Back=$55)
0
100,000
200,000
300,000
400,000
500,000
600,000
Production Quantity
Man
ufac
ture
r Pro
fit
Manufacturer Profit (Buy Back=$55)
0
100,000
200,000
300,000
400,000
500,000
600,000
Production Quantity
Man
ufac
ture
r Pro
fit $471,900
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$??
Supply Contracts
Retailer Profit (Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
Order Quantity
Reta
iler P
rofit
Retailer Profit (Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
Order Quantity
Reta
iler P
rofit
$504,325
Manufacturer Profit (Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
Production Quantity
Man
ufac
ture
r Pro
fit
Manufacturer Profit (Wholesale Price $70, RS 15%)
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
Production Quantity
Man
ufac
ture
r Pro
fit $481,375
Supply Contracts
Strategy Retailer Manufacturer TotalSequential Optimization 470,700 440,000 910,700 Buyback 513,800 471,900 985,700 Revenue Sharing 504,325 481,375 985,700
Manufacturer Manufacturer DC Retail DC
Stores
Fixed Production Cost =$100,000
Variable Production Cost=$35
Selling Price=$125
Salvage Value=$20
Wholesale Price =$80
Supply Contracts
Supply Chain Profit
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
Production Quantity
Supp
ly C
hain
Pro
fit
Supply Chain Profit
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
Production Quantity
Supp
ly C
hain
Pro
fit $1,014,500
Supply Contracts
Strategy Retailer Manufacturer TotalSequential Optimization 470,700 440,000 910,700 Buyback 513,800 471,900 985,700 Revenue Sharing 504,325 481,375 985,700 Global Optimization 1,014,500
Supply Contracts: Key Insights
• Effective supply contracts allow supply chain partners to replace sequential optimization by global optimization
• Buy Back and Revenue Sharing contracts achieve this objective through risk sharing
Contracts and Supply Chain Performance
• Contracts for Product Availability and Supply Chain Profits– Buyback Contracts– Revenue-Sharing Contracts– Quantity Flexibility Contracts
• Contracts to Coordinate Supply Chain Costs• Contracts to Increase Agent Effort• Contracts to Induce Performance Improvement
Contracts for Product Availability and Supply Chain Profits
• Many shortcomings in supply chain performance occur because the buyer and supplier are separate organizations and each tries to optimize its own profit
• Total supply chain profits might therefore be lower than if the supply chain coordinated actions to have a common objective of maximizing total supply chain profits
• Double marginalization results in suboptimal order quantity
• An approach to dealing with this problem is to design a contract that encourages a buyer to purchase more and increase the level of product availability
• The supplier must share in some of the buyer’s demand uncertainty, however
Contracts for Product Availability and Supply Chain Profits: Buyback Contracts• Allows a retailer to return unsold inventory up to a
specified amount at an agreed upon price• Increases the optimal order quantity for the retailer,
resulting in higher product availability and higher profits for both the retailer and the supplier
• Most effective for products with low variable cost, such as music, software, books, magazines, and newspapers
• Downside is that buyback contract results in surplus inventory that must be disposed of, which increases supply chain costs
• Can also increase information distortion through the supply chain because the supply chain reacts to retail orders, not actual customer demand
Contracts for Product Availability and Supply Chain Profits: Revenue Sharing Contracts
• The buyer pays a minimal amount for each unit purchased from the supplier but shares a fraction of the revenue for each unit sold
• Decreases the cost per unit charged to the retailer, which effectively decreases the cost of overstocking
• Can result in supply chain information distortion, however, just as in the case of buyback contracts
Contracts for Product Availability and Supply Chain Profits: Quantity Flexibility
Contracts• Allows the buyer to modify the order (within
limits) as demand visibility increases closer to the point of sale
• Better matching of supply and demand• Increased overall supply chain profits if the
supplier has flexible capacity• Lower levels of information distortion than either
buyback contracts or revenue sharing contracts
Contracts to CoordinateSupply Chain Costs
• Differences in costs at the buyer and supplier can lead to decisions that increase total supply chain costs
• Example: Replenishment order size placed by the buyer. The buyer’s EOQ does not take into account the supplier’s costs.
• A quantity discount contract may encourage the buyer to purchase a larger quantity (which would be lower costs for the supplier), which would result in lower total supply chain costs
• Quantity discounts lead to information distortion because of order batching
Contracts to Increase Agent Effort
• There are many instances in a supply chain where an agent acts on the behalf of a principal and the agent’s actions affect the reward for the principal
• Example: A car dealer who sells the cars of a manufacturer, as well as those of other manufacturers
• Examples of contracts to increase agent effort include two-part tariffs and threshold contracts
• Threshold contracts increase information distortion, however
Contracts to InducePerformance Improvement
• A buyer may want performance improvement from a supplier who otherwise would have little incentive to do so
• A shared savings contract provides the supplier with a fraction of the savings that result from the performance improvement
• Particularly effective where the benefit from improvement accrues primarily to the buyer, but where the effort for the improvement comes primarily from the supplier
Supply Contracts: Case Study• Example: Demand for a movie newly released
video cassette typically starts high and decreases rapidly– Peak demand last about 10 weeks
• Blockbuster purchases a copy from a studio for $65 and rent for $3– Hence, retailer must rent the tape at least 22 times
before earning profit• Retailers cannot justify purchasing enough to
cover the peak demand– In 1998, 20% of surveyed customers reported that
they could not rent the movie they wanted
Supply Contracts: Case Study• Starting in 1998 Blockbuster entered a revenue
sharing agreement with the major studios– Studio charges $8 per copy– Blockbuster pays 30-45% of its rental income
• Even if Blockbuster keeps only half of the rental income, the breakeven point is 6 rental per copy
• The impact of revenue sharing on Blockbuster was dramatic– Rentals increased by 75% in test markets– Market share increased from 25% to 31% (The 2nd
largest retailer, Hollywood Entertainment Corp has 5% market share)
(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
A Multi-Period Inventory Model
• Often, there are multiple 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
Reminder: The Normal Distribution
0 10 20 30 40 50 60
Average = 30
Standard Deviation = 5
Standard Deviation = 10
The DC holds inventory to:
• Satisfy demand during lead time
• Protect against demand uncertainty
• Balance fixed costs and holding costs
The Multi-Period Continuous
Review 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, how will this effect our policy?
A View of (s, S) Policy
Time
Inve
ntor
y Le
vel
S
s
0
LeadTimeLeadTime
Inventory Position
The (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
Notation• AVG = average daily demand• STD = standard deviation of daily demand• LT = replenishment lead time in days• h = holding cost of one unit for one day• K = fixed cost• SL = service level (for example, 95%). This implies that
the probability of stocking out is 100%-SL (for example, 5%)
• Also, the Inventory Position at any time is the actual inventory plus items already ordered, but not yet delivered.
Analysis• The reorder point (s) has two components:
– To account for average demand during lead time:LTAVG
– To account for deviations from average (we call this safety stock)z STD LT
where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is 100%-SL.
• Since there is a fixed cost, we order more than up to the reorder point:
Q=(2 K AVG)/h• The total order-up-to level is:
S=Q+s
Example• 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 = (175/44.6) weeks of supply at warehouse and in the pipeline
Example, Cont.
• Weekly inventory holding cost: 0.87= (0.18x250/52)– Therefore, Q=679
• Order-up-to level thus equals:– Reorder Point + Q = 176+679 = 855
Periodic Review
• Suppose the distributor places orders every month
• What policy should the distributor use?
• What about the fixed cost?
Base-Stock PolicyIn
vent
ory
Leve
l
Time
Base-stock Level
0
Inventory Position
r r
L L L
Periodic Review Policy
• Each review echelon, inventory position is raised to the base-stock level.
• The base-stock level includes two components:– Average demand during r+L days (the time
until the next order arrives):(r+L)*AVG
– Safety stock during that time:z*STD* r+L
Market Two
Risk Pooling
• Consider these two systems:
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier WarehouseMarket One
Market Two
Risk 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?
Risk Pooling Example
• Compare the two systems:– 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
Risk Pooling Example
Week 1 2 3 4 5 6 7 8
Prod A,Market 1
33 45 37 38 55 30 18 58
Prod A,Market 2
46 35 41 40 26 48 18 55
Prod B,Market 1
0 2 3 0 0 1 3 0
Product B,Market 2
2 4 0 0 3 1 0 0
Risk Pooling Example
Warehouse Product AVG STD CV
Market 1 A 39.3 13.2 .34
Market 2 A 38.6 12.0 .31
Market 1 B 1.125 1.36 1.21
Market 2 B 1.25 1.58 1.26
Risk Pooling Example
Warehouse Product AVG STD CV s S Avg. Inven.
% Dec.
Market 1 A 39.3 13.2 .34 65 197 91
Market 2 A 38.6 12.0 .31 62 193 88
Market 1 B 1.125 1.36 1.21 4 29 14 Market 2 B 1.25 1.58 1.26 5 29 15 Cent. A 77.9 20.7 .27 118 304 132 36% Cent B 2.375 1.9 .81 6 39 20 43%
Risk Pooling:Important 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 increases
required safety stock.– Negatively correlated demand. Why?
• What other kinds of risk pooling will we see?
To Centralize or not to Centralize
• What is the effect on:– Safety stock?– Service level?– Overhead?– Lead time?– Transportation Costs?
• Centralized Decision
Supplier
Warehouse
Retailers
Centralized Systems*
Centralized Distribution Systems*
• Question: How much inventory should management keep at each location?
• A good strategy:– The retailer raises inventory to level Sr each period– The supplier raises the sum of inventory in the
retailer and supplier warehouses and in transit to Ss
– 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.
Inventory Management: Best Practice
• Periodic inventory reviews• Tight management of usage rates, lead
times and safety stock• ABC approach• Reduced safety stock levels • Shift more inventory, or inventory
ownership, to suppliers • Quantitative approaches
Changes In Inventory Turnover
• Inventory turnover ratio = annual sales/avg. inventory level
• Inventory turns increased by 30% from 1995 to 1998
• Inventory turns increased by 27% from 1998 to 2000
• Overall the increase is from 8.0 turns per year to over 13 per year over a five year period ending in year 2000.
Industry Upper Quartile
Median Lower Quartile
Dairy Products 34.4 19.3 9.2 Electronic Component 9.8 5.7 3.7 Electronic Computers 9.4 5.3 3.5
Books: publishing 9.8 2.4 1.3
Household audio & video equipment
6.2 3.4 2.3
Household electrical appliances
8.0 5.0 3.8
Industrial chemical 10.3 6.6 4.4
Inventory Turnover Ratio
Factors that Drive Reduction in Inventory
• Top management emphasis on inventory reduction (19%)
• Reduce the Number of SKUs in the warehouse (10%)
• Improved forecasting (7%)• Use of sophisticated inventory management
software (6%)• Coordination among supply chain members (6%)• Others
Factors that Drive Inventory Turns Increase
• Better software for inventory management (16.2%)
• Reduced lead time (15%)• Improved forecasting (10.7%)• Application of SCM principals (9.6%)• More attention to inventory management (6.6%)• Reduction in SKU (5.1%)• Others
Forecasting
• Recall the three rules• Nevertheless, forecast is critical• General Overview:
– Judgment methods– Market research methods– Time Series methods– Causal methods
Judgment Methods
• Assemble the opinion of experts• Sales-force composite combines
salespeople’s estimates• Panels of experts – internal, external, both• Delphi method
– Each member surveyed– Opinions are compiled– Each member is given the opportunity to
change his opinion
Market Research Methods
• Particularly valuable for developing forecasts of newly introduced products
• Market testing– Focus groups assembled.– Responses tested.– Extrapolations to rest of market made.
• Market surveys– Data gathered from potential customers– Interviews, phone-surveys, written surveys, etc.
Time Series Methods• Past data is used to estimate future data• Examples include
– Moving averages – average of some previous demand points.– Exponential Smoothing – more recent points receive more
weight– Methods for data with trends:
• Regression analysis – fits line to data• Holt’s method – combines exponential smoothing concepts with the
ability to follow a trend– Methods for data with seasonality
• Seasonal decomposition methods (seasonal patterns removed)• Winter’s method: advanced approach based on exponential
smoothing– Complex methods (not clear that these work better)
Causal Methods
• Forecasts are generated based on data other than the data being predicted
• Examples include:– Inflation rates– GNP– Unemployment rates– Weather– Sales of other products
Selecting the Appropriate Approach:
• What is the purpose of the forecast?– Gross or detailed estimates?
• What are the dynamics of the system being forecast?– Is it sensitive to economic data?– Is it seasonal? Trending?
• How important is the past in estimating the future?• Different approaches may be appropriate for different
stages of the product lifecycle:– Testing and intro: market research methods, judgment methods– Rapid growth: time series methods– Mature: time series, causal methods (particularly for long-range
planning)• It is typically effective to combine approaches.