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Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 1
Strategic Supply Chain Management
Chapter 8 – Strategic Supply Chain Management
Contents
• Topic
• Sales Forecasting
• Cost Factors & Data Aggregation
• Strategic Supply Chain Model from Practice
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 2
Strategic Supply Chain Management
Scope of the Strategic SCMStrategic level of the SCM
Comprises the strategic planning of locations for companies as well as basic logistics nodes in the field of procurement, production or distribution.
Concerns the identification of long-term sourcing, procurement, production and distribution strategies.
In many cases planning software considers flows of quantities as well as logistics costs to support the strategic level decisions.
Sometimes location decisions are on a tactical level, too.Example: Renting storage space or production capacities.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Topic of the Strategic SCM
Characteristics of strategic planning
• high data aggregation
• high imprecision of the forecasted data or even no data available
• long-term decisions
• involve high investments
• decisions involve the higher management level
Strategic decisions heavily influence the
• efficiency and cost-effectiveness of a supply chain
• customer satisfaction.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 4
Topic of the Strategic SCM
Involved decisions
Procurement Choice of suppliers and determination of the demand on raw materials.
Production Which products should be produced where and in what amount.
Location planning Number, location and capacity of new facilities.
Distribution Choice of transportation routes for the distribution of products between facilities and customers.
Market area Allocation between facilities and customers.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Topic of the Strategic SCM
Make decisions in such a way that the total costs for satisfying customer demands are minimized with regard to different service levels.
Balance between service level (close to customers) and
• Procurement and production costs• Inventory costs• Setup costs (storage, labor, administration, …)• Transportation costs
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Topic of the Strategic SCM
Trade-off using the example of warehousesA higher number of distribution centers results in
• an increasing service level due to shorter transportation times to the customers
• increasing inventory costs due to higher safety stocks in all distribution centers
• higher administration and organization efforts and higher fixed costs
• reduced costs for outgoing transports from the warehouses to the customers
• increasing costs for incoming deliveries from the suppliers / factoriesto the distribution centers
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Strategic Supply Chain Management
Strategic Supply Chain Management
Contents
• Topic
• Sales Forecasting- Forecasting Methods- Time Series Analysis- Quality of Forecasts
• Cost Factors & Data Aggregation
• Strategic Supply Chain Model from Practice
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 8
Strategic Supply Chain Management
Sales Forecasting
• A sales forecasting estimates the future trendof the demand
• Almost every planning decision baseson sales forecasting
• Sales forecasting is a structuredprocessThere are several different methodsto forecast future demand, dependingon the application and aims of the forecast
Your demand will decrease about 50%
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Sales Forecasting
Long-term forecasts are often wrong
“… 640K ought to be enough for anybody …”Bill Gates, 1981
When the phone was first demonstrated to President Rutherford Hayes, he is reportedto have said: “That’s an amazing invention, but who would ever want to use one of them?” President Rutherford B. Hayes, 1876
“A phonograph is just a mere toy, which had no commercial value .”Thomas A. Edison, 1880
“I think there is a world market for maybe five computers.”Thomas J. Watson, 1948
“There is no reason for any individual to have a computer in their home.”Ken Olsen, 1977
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Sales Forecasting
Forecasting methodsJudgmental methods The opinions of several persons
are combined to one forecast.Qualitative criteria.
Demand for flights in 20 years
Causal methods A function is estimated, which represents the influence of known underlying factors on the demand.
Demand for service personnel for the next year
Time series These methods use historicaldemand as the basis of estimating.
Demand for detergent for the next month
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Forecasting Methods
Examples
Question Forecasting method (typical)
1. Which energy sources will be used in 20 years?
Judgmental method
2. How will the UMTS sales develop in the next five years?
Judgmental method
3. How much service personnel is needed to maintain the telephone network?
Causal method
4. How will the GSM sales develop within the next 12 months?
Time series
5. How many salesmen will be needed within the next week?
Time series
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Forecasting Methods
Judgmental Methods
Application• Are used if no foretime data is available or the data is not appropriate for
forecasts. Example: Demand forecasting for a new technology
• Are used to fit causal and time series methods.Example: Observance of a unique promotion by time series
Methods• Manager’s opinion• Sales estimate • Customer market survey• Expert opinion• Delphi method• Scenario techniques
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Causal Methods
Application• Can be used, if the demand for a product or service can be forecasted on the
basis of a known parameter.Example: Demand for cabs subject to the population of a city
• In general, a regression analysis estimates the parameter of a function so as to give a "best fit" of the data.Example: Demand for cabs = population/1000
Methods• Linear regression • Non-linear regression
Forecasting Methods
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Time series
Application• Construction of a forecast on the basis of observed demand over time.• The operator estimates or supposes the behavior of the demand (constant level,
trend, ...).• Different forecasting methods for different demand behaviors.
Methods• (Simple) Moving average• Simple exponential smoothing• Linear regression• Method of Holt – double exponential smoothing• Method of Winters – triple exponential smoothing
Forecasting Methods
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Time Series
Notation
t time period, t = 1, 2, …
dt historical data (demand values), t = 1, …, T
yt forecast of the values, t = 2, 3, …
et forecasting error: et = dt - yt , t = 2, …, T
MSEt Mean Square Error:
also Mean Squared Average
Sales Forecasting
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Time Series
Typical Time Series Patterns and Forecasting Models
Constant Level• (Simple) moving average• Simple exponential smoothing
Linear Trend• Linear regression• Holts Method – double exponential smoothing
Seasonal Effects• Winters Method – triple exponential smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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(Simple) Moving Averages (MA)
The forecast value yt+1 for period t+1 corresponds to the average of the previous r observations (demand values)
Formula
If t < r, set r = t.
Remarks• One of the most simple forecasting methods• The forecast is easy to update from period to period• The last r demands all have the same weight 1/r• Special case: r = 1
„Trivial forecast“:
Constant Level
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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ExampleDemand for portable televisions per week. Choose r = 4
MSE12 = 2.34
t dt yt et
1 602 59 60.0 -1.03 61 59.5 1.54 58 60.0 -2.05 57 59.3 -2.36 59 58.7 0.37 58 58.0 0.08 59 58.0 1.09 61 58.7 2.3
10 60 59.3 0.711 58 60.0 -2.012 60 59.7 0.313 59.3
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1 2 3 4 5 6 7 8 9 10 11 12 13
Demand Moving Average
Underestimation⇒ increase
Overestimation⇒ decrease
Moving Average
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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It is difficult to choose the right r.
Small r (Extreme case r = 1) • Forecasts respond to changes in demand very fast• Large parts of the information about the demand in the past gets lost
Large r (Extreme case r = hole demand history)• Forecasts respond to changes in the demand very slowly• Even very old data have the same weight as very recent ones
Experimental determination of a good value for r
Forecast for period t +τ: yt+τ = yt+1 , τ = 1, 2, …
r 1 2 3 4 5MSE12 3.09 2.68 2.16 2.34 2.38
Moving Average
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Exponential Smoothing (ES), also called Exponential Moving Average
Consider all historical demands, but weight recent observations more than older ones.
Forecasting formula
α = smoothing factor, 0 < α < 1y2 = d1
InterpretationRecursive initiation of yt into the formula above yields to
⇒ Demands are multiplied with exponentially decreasing weights
Constant Level
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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In additionyt+1 is a convex combination of d1, …, dt
Equivalent formulation
InterpretationThe new forecast is a weighted sum of the preceding forecast and the most recent observation.
0
0,05
0,1
0,15
0,2
0 1 2 3 4 5 6 7 8
α = 0.2 α
α(1-α)
α(1-α)2
Exponential Smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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ExampleDemand for portable televisions per week. Choose α = 0.3
MSE12 = 2.09
t dt yt et
1 602 59 60.0 -1.03 61 59.7 1.34 58 60.1 -2.15 57 59.5 -2.56 59 58.7 0.37 58 58.8 -0.88 59 58.6 0.49 61 58.7 2.3
10 60 59.4 0.611 58 59.6 -1.612 60 59.1 0.913 59.4
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1 2 3 4 5 6 7 8 9 10 11 12 13
Demand Exp. Smoothing Moving Avg.
Exponential Smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Typical values for α are between 0.01 and 0.3
Small α• Forecast responds to changes in demand slowly• Also older data relatively strong weighted (though never as much as more recent
ones)
Big α• Forecast responds to changes in demand fast• Information of historical data gets lost very fast
Experimental determination of a good α - valueα 0.05 0.1 0.2 0.3
MSE12 2.14 2.05 2.04 2.09
Exponential Smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 24
Typical Time Series Patterns and Forecasting Models
Constant Level• Moving average• Single exponential smoothing
Linear Trend • Linear regression• Holts method – double exponential smoothing
Seasonal Effects• Winters method – triple exponential smoothing
Time Series
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Linear TrendAssumption
The demand forecasting yt,t+τ in period t for period t +τ ,τ > 1 isyt+τ = at + bt τ
The y-intercept at is an estimator for the constant level and the slope bt for the trend. Estimation of the values via forecasting method.
Forecasting methods for theconstant level systematicallyunderestimate the demand.
ExampleMA and ES for r = 4and α = 0.2.
⇒ structural forecast error52
56
60
64
68
72
76
1 2 3 4 5 6 7 8 9 10 11 12
Demand Moving Avg. Exp. Smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Linear Regression LR
Basic ideaDetermine a line L with y-intercept aand slope b, which minimizes the mean square error
over all observations.
MSE(a,b) is a convex, continuousdifferentiable function in a and b⇒ Differentiate with respect to a and b.
Setting the derivative to zero yields the optimal values
Demand
Time
Y-intercept a
Slope b
0
5
10
15
0 2 4 6 8 10
et
Linear Trend
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 27
at and bt are computed based on the regression line, which interpolates ther > 1 latest demands best.
⇒ Result for t ≥ 2
as optimal values for the y-intercept and the slope.
Remark• If 1 < t < r, set r = t. • If t = 1, set y2 = d1
Linear Regression
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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ExampleDemand for portable televisions per week. Choose r = 4
MSE12 = 6.59
t dt yt et
1 592 58 59.0 -1.03 63 57.0 6.04 61 64.0 -3.05 64 63.0 1.06 68 65.5 2.57 67 68.5 -1.58 70 70.5 -0.59 74 71.5 2.5
10 73 75.0 -2.011 76 76.5 -0.512 75 77.5 -2.513 76.014 76.6
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1 2 3 4 5 6 7 8 9 10 11 12 13 14
Demand Regression
Linear Regression
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Problems• Complex formula• All periods are equal weighted• Updating the parameter is cumbersome
Special case: r = 2
Again an experimental determination of a good r-value
r 2 3 4 5 6MSE12 19.18 10.78 6.59 7.34 7.18
Linear Regression
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Holds Method – Double Exponential Smoothing
Similar to simple exponential smoothing, but with a smoothing factor for the y-intercept (α) and one for the slope (β) of the forecasting function.
Parameter
whereas t ≥ 2, 0 < α < 1 and 0 < β < 1.
Interpretationat Combination of the new observation and the preceding forecast (identical to
simple exponential smoothing)
bt Combination of the difference between the new constant level and the previous one and the preceding estimator for the trend
Trend
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Remarks• Initial values:
a1 = d1 and b1 = (dT - d1) / T-1
• For β = 0 one gets the simple exponential smoothing as a special case.
• New estimators are simple to compute
• Consideration of older demands with exponentially decreasing weights
• Experimental determination of good values for α and β.
Method of Holt – Double Exponential Smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 32
ExampleDemand for portable televisions per week. Choose α = 0.3 and β = 0.4.
MSE12 = 3.49
t dt yt et
1 592 58 59.0 -1.03 63 60.9 2.14 61 62.9 -1.95 64 63.5 0.56 68 64.9 3.17 67 67.4 -0.48 70 68.9 1.19 74 70.9 3.1
10 73 73.9 -0.911 76 75.6 0.412 75 77.7 -2.713 78.614 80.3
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1 2 3 4 5 6 7 8 9 10 11 12 13 14
Demand Holt Regression
Method of Holt – Double Exponential Smoothing
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 33
Typical Time Series Patterns and Forecasting Models
Constant Level• Moving average• Single exponential smoothing
Linear Trend• Linear regression• Holts method – double exponential smoothing
Seasonal Effects• Winters method – triple exponential smoothing
Time Series
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 34
Seasonal Effects
If there exist seasonal effects in the run of the demand curve, there is a demand pattern, which repeats every P periods.
General ideaDecouple the seasonal component in the demand curve from the trend component
Time Series
Demand TrendComponent
SeasonalComponent
(at + btτ) ct
at + btτ
s1
s2
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 35
Forecasting formula
st+τ seasonal factorP length of the seasonal period
Computation of at, bt and st+τ
whereas t > P and 0 < α, β, γ < 1.
Seasonal Effects
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 36
For the recursion it is necessary to know the • Initial values a0, b0 and st, t = 1, …, P• Demand values for N ≥ 2 seasonal periods
Then•
•
•
Seasonal Effects
where
average demand in the i-th seasonal period
Non-normalized seasonal factors
average slopeof the trend function
Y-intercept of the trend function
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 37
Quality of forecasts
Various measures for the forecasting error• Mean Squared Error
• Mean Absolute Deviation
• Mean Absolute Percentage Deviation
Sales Forecasting
• Often used• Good theoretical properties
• Intuitively better to interpretthan MSE
• Allows to estimate the quality of the forecasting method:
≤ 10% very good> 10%, ≤ 20% good> 20%, ≤ 30% medium> 30% bad
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 38
Forecasting Control
The tracking signal
shows structural forecasting errors, i.e. permanent over- or underestimation.
Sales Forecasts
1 2 3 4 5 6 7 8 9 10
smax
-smaxcontinuous overestimation⇒Reconsider the choice of
the parameters or theforecasting method
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 39
Strategic Supply Chain Management
Strategic Supply Chain Management
Content
• Topic
• Sales Forecasting
• Cost Factors & Data Aggregation
• Strategic Supply Chain Model from Practice
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 40
Cost Factors & Data Aggregation
Cost Factors
Transportation costsare one of the most important aspects in the planning and optimization of supply chains.Depend on
• Freight rate• Quantity• Distance
Freight rate depends on• Product conditions: size, manageability, vulnerability• Means of transport: truck, tank lorry, rail, airplane• Batch size: full truckloads are cheaper than less than truckloads or package freight
Freight rate can be taken from tables for each product.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 41
Transportation CostsFreight costs per unit generally
• decrease inversely proportionally (possibly with steps) with the quantity• increase (piecewise) linearly with the distance
The considered distance is based on• Street (rail) distance• Euclidean distance
Can be computed with geographical information systems (GIS).
Problem with the Euclidean distanceUnderestimates the real street distances
Multiply distance with correction factor:• Urban areas: 1.14• Europe, general: 1.3
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
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Cost Factors
Inventory Costs
Inventory costs basically consist of three cost components:
Handling costsConsists of labor costs and material costs, which are proportional to the stock turn-over.
Storage costsEncompasses the costs for the inventory, which are proportional to the average positive stock of inventory.
Fixed costsComprise absolute and step-wise costs, which are proportional to the size of the warehouse, but not to the quantity of goods.
Handling costs are easy to determine.However it is a problem to calculate the average positive stock of inventory as well as the size of the warehouses.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 43
Inventory CostsIn the case of strategic planning for several years the data is extrapolated
A result of a strategic planning may be:The estimated stock turn-over of a new warehouse has an amount of 20’000 units per period.
Question• What is the average positive stock of inventory?
• How much capacity is needed in the warehouse, to guarantee the operational business of the inventory at any time?
Should be proportional to the maximum stock/ handling quantity.
One can use the inventory turn-over ratio ITR to compute the average positive stock of inventory .
Inventory turn-over ratio for several product types known.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 44
Inventory CostsReference
Simchi-Levi et al., 2003
Considering the relation
the average positive stock of inventory per period can be determined as
and therewith the inventory costs.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 45
Inventory CostsSize of the Warehouse
The required capacity for storage equals approx. twice the average stock of inventory.
Furthermore room for offices, packing, handling goods and so on needed.
Real size of the warehouses equals approx. three times the pure inventory capacity.
Therewith the fixed costs for the inventory can be calculated.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 46
Cost Factors & Data Aggregation
Data AggregationIf one models the complete supply chain, one often has to consider many thousands of customers and products.⇒ high effort to obtain and handle detailed data⇒ aggregate data for planning and optimization
Aggregation also for „smaller“ supply chains useful, since• data not always fully available• forecasts for the trend of demand and costs often imprecise
Keyword: Risk Pooling – EffectSince the data aggregation reduces the variability, the forecasts for demand are more accurate on an aggregated level.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 47
Data AggregationAggregation Error
Planning with aggregated data and original data, respectively, leads to different costs and results.
Consider the trade-off for• less exact results due to the aggregation and• unnecessary high complexity
Two classical alternatives for aggregation• customers (demand)• products
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 48
Data AggregationAggregation of Customers (Demand)
Clustering is based on
Geographical positionAggregate geographically close customers to a customer zone.
All customers within a single cell/cluster are replaced by just a single customerlocated at the center of this cell/cluster.
Aggregation for example based on
- Network GridAggregate all customers within the same grid cell.
- Zip codesAggregate customers according to zip code (e.g. all customers where the first two are the same).
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 49
Aggregation of Customers
Aggregation of American „ZIP-code areas“ (Simchi-Levi et al., 2003)18 000 5-digit zip codes 800 3-digit zip codes
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 50
Aggregation of CustomersSimilar characteristics
Aggregate customers with- similar service requests- the same supply frequency
Efficiency of aggregation depends on• the number of customer zones• distribution of the customers within the zones
Recommended• at least 300 customer zones• similar customer demand in each zone
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 51
Aggregation of Customers
Example (Simchi-Levi et al.)Locating factories. Only transportation costs considered.
⇒ Aggregation error < 0.05%
Total costs: $5 796 000Number of customers: 18 000
Total costs: $5 793 000Number of customers: 800
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 52
Data Aggregation
Aggregation of Products
Clustering is based on
Model similarityAggregate products, which only have marginal differences (e.g. variations of the same model: color, equipment details or type of packaging) .
Distribution SampleAggregate products, which are produced/ loaded in the same facility and delivered to the same customers.
Further alternativesAggregate products with the same weight, same size, same shipping method (unit load, frozen cargo), …
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 53
Aggregation of Products
Example for model similarity (Fraunhofer ITWM)Various intense aggregation of electro-closets
coated,2 doors
not coated,2 doors
not coated,1 door
coated,2 doors
coated, 1 doorcoated, 1 door
coated, 1 door
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 54
Aggregation of Products
Example for logistics characteristics (Simchi-Levi et al.)Aggregate products with similar weight-volume ratio.
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
Volume (pallets per case)
Wei
ght (
lbs
per c
ase)
Rectangle denote clusters
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 55
Aggregation of Products
Example (Simchi-Levi et al.)5 factories, locating warehouses.
⇒ Aggregation error < 0.03%
Total costs: $104 564 000Number of products: 46
Total costs: $104 599 000Number of products: 4
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 56
Strategic Supply Chain Management
Strategic Supply Chain Management
Contents
• Topic
• Sales Forecasting
• Cost Factors & Data Aggregation
• Strategic Supply Chain Model from Practice
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 57
Strategic Supply Chain Management
Strategic Supply Chain Model from PracticeConsider a model with
• capacities• several periods• several products• several highly general, non-hierarchic levels
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 58
Strategic Supply Chain ManagementMake decisions on
• locations• procurement and production• storage and distribution• satisfaction of customer demands
in consideration of costs for• procurement and production• warehousing (inventory, stock turn-over)• opening and closure of facilities• transportation• unsatisfied customer demands
to minimize these costs.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 59
Strategic Supply Chain Model from Practice
Components of the model
FacilitiesVery general term.
May• „be anything“
i.e. customers, Warehouses, factories, production lines, cross-docks etc., and
• „make everything“i.e. produce, store, handle products, consume, etc.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 60
Strategic Supply Chain model from practiceUniquely defined relationship between facilities and locations.There already exist a facility at a location or this location is a candidate for a new facility.
Distinguish facilities in • Selectable ones
Subject of the planning and may change their status, i.e. can be opened or closed.Typically: factories, distribution centers, …
• Not selectable onesFixed.Typically: suppliers, customers, as well as factories, inventories, which should be maintained
In the following we only talk about facilities.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 61
Strategic Supply Chain Model from PracticeThe facilities modeled in the supply chain do not necessarily have to be part of the own organization. E.g. external supplier.
Notation
⇒ S = So ∪ Sc.
= Set of all products= Set of all time periods
L = Set of all facilitiesS = Set of all selectable facilitiesSo = Set of all selectable facilities, which could be opened
Sc = Set of all selectable facilities, which could be closed
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 62
Strategic Supply Chain model from practiceLocation decisions
Open
Close
OCtℓ = Opening Costs for the facility ℓ ∈ So at the beginning of period t and for
its operation for the rest of the planning period.CCt
ℓ = Costs for closure of the facility ℓ ∈ Sc at the end of period t and their operation until then.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 63
Strategic Supply Chain Model from PracticeDemand
Facilities can have demand for products.
Forecast future demands.
If the forecasts are not exact enough, then consider the problem several times for different scenarios of demand trends
- pessimistic (worst-case)- normal (average-case)- optimistic- …
Notation
D tℓ,p = Demand in quantity units for product p at facility ℓ in period t.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 64
Strategic Supply Chain Model from PracticeSatisfaction of customer demands
It may be that the demand can/shall not be (completely) satisfied.
Example:- Costs for the satisfaction of demand is too high (compared to profit)- Supply within the given service time is not possible, or just with very high
efforts- Capacities are not sufficient
Unsatisfied demand incurs penalty costs.However, they are difficult to quantify.
Possibility: lost profits, service level which has to be satisfied
z tℓ,p = Number of quantity units of demand at facility ℓ for product p in
period t, which were not delivered.PDC t
ℓ,p = Penalty costs per quantity unit of product p, which were notdelivered to facility ℓ in period t to satisfy the demand.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 65
Strategic Supply Chain Model from PracticeProcurement
Facilities can buy products from „external“, i.e. from external suppliers.
Example- raw material or semi-finished goods, which can not be produced at the own
facilities- products, that are cheaper to buy than to produce them (Out-Sourcing)
Notation
btℓ,p = Amount of product p, which is procured at facility ℓ in period t.
BCtℓ,p = Costs for procurement of one unit of product p at facility ℓ in period t.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 66
Strategic Supply Chain Model from PracticeProduction
Manufacturing of finished goods from different inputs.Example
- „classical“ manufacturing of finished goods in factories from raw material and intermediate goods
- packaging or picking products in distribution centers. E.g. drill machine from factory A with boring head from factory B packed together.
Manufacturing processes are specified by lists of materials.
ExampleIntermediate product Z1 is manufactured by raw material R1 and R2.The numbers on the arcs indicate the related material consumption factors.The production of one unit of Z1 needs 2 and 1.5units of raw materials Z1 and Z2, respectively
1.52
Z 1
R 2R 1
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 67
Strategic Supply Chain Model from PracticeSimplify multi-stage lists of material to single-stage ones.
Notation
aℓ,p,q = Number of units of product q, needed to manufacture one unit of product p in facility ℓ.
htℓ,p = Amount of product p, produced in facility ℓ in period t.
HCtℓ,p = Costs for manufacturing one unit of product p in facility ℓ in period t.
Includes costs for material, machine utilization, ….
2 3
1.52
P 1
R 1
Z 2Z 1
R 3R 2
14.56
P 1
R 1 R 3R 2
2
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 68
Strategic Supply Chain Model from PracticeStorage
Products (raw material, intermediate products, finished goods) can be stored in facilities from one period to the next.
Notation
invtℓ,p = Amount of product p, stored at facility ℓ in period t.
ICtℓ,p = Costs for storing one unit of product p at facility ℓ in period t.
Include costs for inventory, stock ground, …
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 69
Strategic Supply Chain Model from PracticeDistribution
Transportation link between all facilities possible.
Notation
The transportation costs depend on the distance, but also on the product and the means of transportation.
Include often costs for goods issue (e.g. order picking, shipment) at the starting facility and for incoming goods (warehousing) at the destination facility.
Sometimes costs for storage (within a period) at the starting location, too.
xtℓ,ℓ‘,p = Amount of product p, transported from facility ℓ to ℓ‘ in period t.
TCtℓ,ℓ‘,p = Transportation costs for one unit of product p from facility ℓ to ℓ‘ in
period t.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 70
Strategic Supply Chain Model from PracticeCapacities
Displayed via resources.Example
- machine, stockyard- storage-, order picking system- staff, shift
Resources characterized by• Base capacity (e.g. production capacity of a machine, maximal throughput of the
picking system per period).• Consumption factor states for each product the consumption of resources in
resource units per quantity unit of a product.• Expansible capacity of the resource (e.g. overtime, leasable storage or
production capacity).• Penalty costs per unit, that extend (overload) the base capacity.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 71
Strategic Supply Chain Model from PracticeRelations between facilities and resources
one – to – manyThe same resource can be used on several facilities.Example: executive producer, which is responsible for several production lines
one – to – oneThe same resource is used by all products of one facility.Example: flexible configurable machine
many – to – oneSeveral resources attached in the same facility.Example: facilities correspond to production lines and resources to executive
producers
Consider resources for- production and- incoming goods and goods issue (handling)
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 72
Strategic Supply Chain Model from PracticeNotation
Rp = Set of production resources
Rh = Set of handling resources
μℓ,r,p = Consumption factor of production resource r ∈ Rp per unit of product p at facility ℓ.
λiℓ,r,p,
λoℓ,r,p
= Consumption factor of production resource r ∈ Rh per unit of product p at goods receipt respectively issue at facility ℓ.
vtr = Number of units, the resource r ∈ Rp ∪ Rh has been extended in
period t.RKt
r = Base capacity of resource r ∈ Rp ∪ Rh in period t.
ERKtr = Maximally allowed extension of the capacity of the resource
r ∈ Rp ∪ Rh in period t.RCt
r = Penalty costs per extended resource unit of resource r ∈ Rp ∪ Rh in period t.
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 73
Strategic Supply Chain Model from Practice
Mixed integer linear programObjective function
procurement and production
distribution
resource extension
unsatisfied demand
location decisions
inventory costs
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 74
Strategic Supply Chain Model from Practice
Constraints
Flow conservation
incoming transports
procurement production
inventorylast period
outgoingtransports unsatisfied
demand
consumptionto production inventory
this period
demand
incoming goods
outgoing goods
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 75
Strategic Supply Chain Model from PracticeResources
Production
Handling
Feasibility of extension
Incoming goods and goods issue, respectively,by transports
goods issueby procurement
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 76
Strategic Supply Chain Model from PracticeLocation decisions
Selectable facilities can be opened and closed, respectively, only once
Define
Activities at selectable facilitiesProcurement
and
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 77
Strategic Supply Chain Model from PracticeProduction
Storage
Outgoing distribution
Incoming distribution
Facility Location and Strategic Supply Chain Management
Prof. Dr. Stefan Nickel
Page 78
Strategic Supply Chain Model from PracticeInteger and non-negativity constraints