Strategic Supply Chain Management WS 0809... · Facility Location and Strategic Supply Chain Management Prof. Dr. Stefan Nickel Page 2 Strategic Supply Chain Management Scope of the

Facility Location and Strategic Supply Chain Management

Prof. Dr. Stefan Nickel

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Strategic Supply Chain Management

Chapter 8 – Strategic Supply Chain Management

Contents

• Topic

• Sales Forecasting

• Cost Factors & Data Aggregation

• Strategic Supply Chain Model from Practice



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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.



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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.



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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.



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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



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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



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Contents

• Topic

• Sales Forecasting- Forecasting Methods- Time Series Analysis- Quality of Forecasts





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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%



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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



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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



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



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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



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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



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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



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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



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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



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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



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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

55

56

57

58

59

60

61

62

1 2 3 4 5 6 7 8 9 10 11 12 13

Demand Moving Average

Underestimation⇒ increase

Overestimation⇒ decrease

Moving Average



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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



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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



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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



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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

55

56

57

58

59

60

61

62

1 2 3 4 5 6 7 8 9 10 11 12 13

Demand Exp. Smoothing Moving Avg.




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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




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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



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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



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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



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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



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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

50

55

60

65

70

75

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Demand Regression

Linear Regression



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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



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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



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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



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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

50

55

60

65

70

75

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Demand Holt Regression

Method of Holt – Double Exponential Smoothing



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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



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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



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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



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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



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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



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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



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Content

• Topic






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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.



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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



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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.



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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.



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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.



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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.



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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.



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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



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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).



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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



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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



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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



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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), …



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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



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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



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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



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Contents

• Topic






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Strategic Supply Chain Model from PracticeConsider a model with

• capacities• several periods• several products• several highly general, non-hierarchic levels



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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.



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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.



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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.



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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



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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.



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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.



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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.



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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.



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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



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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



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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, …



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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.



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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.



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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)



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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.



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Mixed integer linear programObjective function

procurement and production

distribution

resource extension

unsatisfied demand

location decisions

inventory costs



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Constraints

Flow conservation

incoming transports

procurement production

inventorylast period

outgoingtransports unsatisfied

demand

consumptionto production inventory

this period

demand

incoming goods

outgoing goods



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Strategic Supply Chain Model from PracticeResources

Production

Handling

Feasibility of extension

Incoming goods and goods issue, respectively,by transports

goods issueby procurement



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Strategic Supply Chain Model from PracticeLocation decisions

Selectable facilities can be opened and closed, respectively, only once

Define

Activities at selectable facilitiesProcurement

and



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Strategic Supply Chain Model from PracticeProduction

Storage

Outgoing distribution

Incoming distribution



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Strategic Supply Chain Model from PracticeInteger and non-negativity constraints

Documents

Strategic Supply Chain Management WS 0809... · Facility Location and Strategic Supply Chain Management Prof. Dr. Stefan Nickel Page 2 Strategic Supply Chain Management Scope of the