facility location and strategic supply chain management ws 0809... · • the transportation costs...

Facility Location and Strategic

Supply Chain Management

Winter Term 2008/2009

Professor Dr. Stefan Nickel

Chair of Business AdministrationOperations Research and Logistics

Facility Location and Strategic Supply Chain Management

Prof. Dr. Stefan Nickel


Structure

I. Location ConceptsChapter 1 – IntroductionChapter 2 – Economic and Descriptive Facility Location

Models

II. Location Theory

III. Strategic Supply Chain Management



Location Concepts

Chapter 1 – Introduction

Contents

• Examples for Facility Location Problems in Practice

• Why Facility Location Planning?

• Subareas of Facility Location Planning

• Terms and Definitions

• Location Factors




Examples for Location Problems in Practice

Example 1: Airport

Two cities, A and B, would like to use an airport together and therefore look for a logistically suitable location.

ObjectiveLocate the airport such that the sum of the travel costs between this airport and the inhabitants of the cities A and B that use the airport is minimized.

In other wordsWhere to locate the airport in orderto minimize the average travelcosts per passenger?

AB



Examples for Location Problems in PracticeAssumptions

• The expected passenger volume of the two cities is:D(A) = 1 000 and D(B) = 1 500

• Travel costs TC = 0.50 € per passenger and km

• Euclidean distance d(A, B) = 100 km between A and B.

• The new airport X can be situated anywhere on the plane.

• d(A, X) or d(B, X) indicates the distance from X to city A or B.

Find a location X for the airport so that the total travel costs are minimized.

Because of the triangle inequality for the distance, a cost minimal location will beon the line connecting the two cities.



Example 1: AirportPossible alternatives

• in the middle between the two cities:cost: 50 · 0.5 · 1 000 + 50 · 0.5 · 1 500 = 62 500 €

• closer to city B, e.g. 20 km outside B:cost: 80 · 0.5 · 1 000 + 20 · 0.5 · 1 500 = 55 000 €

• directly at city B:cost: 100 · 0.5 · 1 000 + 0 · 0.5 · 1 500 = 50 000 €

Locate the airport directly at city B !

AB

AB

AB



Example 1: AirportNew situation

We expect that the passenger volume of city A increases disproportionately compared to city B during the next years. So for example, in 5 years the expectedpassenger volumes for A and B will be:

D(A) = 2 000 and D(B) = 2 000

QuestionWould one make a different decision regarding the new situation?

A new analysis results in the following costs:

• In the middle: 50 · 0.5 · 2 000 + 50 · 0.5 · 2 000 = 100 000 €• 20 km outside B: 80 · 0.5 · 2 000 + 20 · 0.5 · 2 000 = 100 000 €• directly at city B: 100 · 0.5 · 2 000 + 0 · 0.5 · 2 000 = 100 000 €

Locate the airport anywhere between city A and B!



Example 1: AirportProblem

It is not desirable to locate the airport directly at city B because of the noise pollution.

Alternative 1Define an area around city B where the placement of the airport is not allowed, e.g. within a radius of 10 km around B.

A

Locate the airport 10 km outside Bcosts: 90 · 0.5 · 1 000 + 10 · 0.5 · 1 500 = 52 500 €



Example 1: AirportAlternative 2

Look for a location where the average travel costs AND the nuisance is as small as possible.

The resulting problem can be formulated as a 2-criteria facility location problem

where DB denotes the noise pollution depending on the distance.

ProblemThe two criteria “pull” the location into opposite directions. The cost minimalairport is located directly at B whereas the most quiet location is in the middle between the two cities.

Find a good compromise




Example 2: WarehousesA company decides to reorganize its distribution system and does not want to send its products directly from the plant to the shops any more, but via two warehouses (DCs).

ObjectiveFind among a given set of potential locations for warehouses those that minimize the opening costs for the warehouses and the transportation costs of shipping the goods from the warehouses to the shops.

Shops

Potential locations

B

X

Y

Z

E

A

B

C

D



Example 2: WarehousesGiven

• A set of shops Shops = {A, B, C, D, E}and their corresponding demand sets D for a product.

• A set of potential locations Cand = {X, Y, Z} for the new warehouses and their building costs (fixed costs) F.

• The transportation costs TC per unit between warehouse locations and shops.

AssumptionA shop is always supplied by the warehouse with the smallest transportation costs.

A B C D EX 40 20 30 20 40Y 20 20 60 30 40Z 40 30 20 80 50

A B C D ED 400 200 300 200 500

X Y ZF 18 000 15 000 17 000



Example 2: WarehousesFind the two locations S1 and S2 among the set of the candidate locations Candthat minimize the total costs = transportation costs + building costs

Possible combinations

Locations Transportation costs

Fixed costs

Sum Utiliza-tion

X and Y 20 · 400 + 20 · 200 + 30 · 300 + 20 · 200 + 40 · 500

18 000 + 15 000

78 000 € 1 000 600

X and Z 40 · 400 + 20 · 200 + 20 · 300 + 20 · 200 + 40 · 500

18 000 +17 000

85 000 € 900700

Y and Z 20 · 400 + 20 · 200 + 20 · 300 + 30 · 200 + 40 · 500

15 000 +17 000

76 000 € 1 300 300

Build two warehouses at the locations Y and Z, respectively !

X

Y

Z

E

A

B

C

D



Example 2: WarehousesProblemEach warehouse only has a restricted capacity of 1 000 units.

the previous solution is not feasible any more since the utilization of location Yexceeds the capacity. Find a new solution.

Build two warehouses at locations X and Y, respectively !

Location Transportation costs

Fixed costs

Sum Utiliza-tion

X and Y 20 · 400 + 20 · 200 + 30 · 300 + 20 · 200 + 40 · 500

18 000 +15 000

78 000 € 1 000 600

X and Z 40 · 400 + 20 · 200 + 20 · 300 + 20 · 200 + 40 · 500

18 000 +17 000

85 000 € 900700

Y and Z 20 · 400 + 20 · 200 + 20 · 300 + 30 · 200 + 40 · 200 + 50 · 300

15 000 +17 000

79 000 € 1 000 600

X

Y

Z

E

A

B

C

D

Modification compared to the previous solution



Example 2: WarehousesProblem

Since the railway company decides to close the station near location Y within the next year, the transportation costs increase to 50.

New solution computed for the next two years

Build two warehouses at location X and Z, respectively !

Locations Transportation costs Fixed costs

SumFirst year Second year

X and Y 45 000 € 61 000 € 33 000 € 139 000 €

X and Z 50 000 € 50 000 € 35 000 € 135 000 €

Y and Z 47 000 € 58 000 € 32 000 € 137 000 €

X

Y

Z

E

A

B

C

D




Example 3: AmbulanceA city would like to reorganize its emergency system in such a way that any point of the city can be reached within 8 minutes.

ObjectiveLocate a minimal number of ambulances in the urban area so that an area-wide„8 - minutes“ coverage is guaranteed.

ProblemBecause the costs are too high a complete coverage is not possible.

Find a compromise between lowcosts and high coverage.



Example 3: AmbulanceAlternative 1

Locate a fixed number of ambulances in the urban area such that the number of inhabitants who can be reached within 8 minutes is maximal.

Analyze the trade-off for different numbers of ambulances (exemplary)

# Ambulances 1 2 3 4 5 6 7 8 9

% Coverage 20 40 60 75 85 90 95 98 100

Observation: The coverage barely changes from 7 ambulances on



Example 3: AmbulanceAlternative 2

Given a fixed number of ambulances, locate these ambulances in such a way that the maximum time that an ambulance needs to get to an emergency („response time“) within the urban area is minimized.

Analyze the response times for several numbers of ambulances (exemplary)

# Ambulance 1 2 3 4 5 6 7 8 9

Response Time 25 20 16 14 13 10 8.8 8.5 8

Observation: The response time barely changes any more from 7 ambulances on



Example 3: AmbulanceAnother problem

What happens if two emergencies occur in the same urban area in a short sequence and the responsible ambulance is not „back“ yet?

The next closest ambulance has to help. Thereby the Response Time may rise dramatically.

Way outDon‘t consider occurring emergencies as static events, but as random events distributed over time.

Now locate the ambulances such thatareas with high to very highemergency rates are covered multiple times by ambulances so that the expected Response Time becomes minimal.



Location Concepts


Contents









Why facility location planning ?

The competitiveness and the economic success of a company depends on the locations of its factories and the internal locations.

The location of an company is very important for its survivability and there is only low flexibility for changing locations quickly.Therefore, a future-orientated planning that includes facility location considerations in the strategic business planning is crucial.

The disadvantage of an inappropriate facility location asks for special efforts to compensate competitive advantages of the competitors with respect to locations and endanger the profitability of the enterprise.



Why Location Planning ?Triggers for location planning

• Start-up companies

• Increased capacity requirement or surplus,e.g. as a result of fusions

• Intracorporate or extracorporate deficiencies concerning locations,e.g. changed production scheme or changed sales markets, answers to new economic areas

• Inefficiencies of historically grown structures



Location Concepts


Contents









Subareas of facility location planning

The scientific approaches to location planning can be classified into 3 parts:

• Economic location theories• Location planning in a logistics network• In-house location planning (Layout planning)

Furthermore within location planning and layout planning there is a difference between• descriptive and• prescriptive (normative)

approaches.



Subareas of Facility Location Planning

Economic location theoriesThese approaches try to explain or optimize the placement of enterprisesand factories of economic sectors in the plane (within an economic area).

v. Thünen (1826)v. Thünen investigated the composition of agricultural manufacturing sectors in an isolated state with one market under the consideration of the land value, the distance to the market, and the production costs.

He wanted to find out why the agricultural land around a city was conducted to acertain use and why the different activities like agriculture farming, pasture farming, timber industry, and dairy farming are always ordered in a certain sequence around the city.




Circle 1 6

Deterioration fast slow

Relation Weight/ Value

high low

Cultivation intensive extensive

1 2 3 4 5 6

Circle 1 2 3 4 5 6 7

Cultivation Intensive Agriculture

Forestry Crop alternation

Rotation of enclosed

fields

Three field

rotation

Grazing Chase

He came to the conclusion that the way of agrarian land utilization is not only determined by the natural, irreversible soil conditions but essentiallydepends on economic facts, namely the distance from the production location to the location of consumption that is, the transportation costs.

„The Thünen circles“ Features concerning land utilization




Industrial location planning

These approaches deal with questions of site selection for enterprises with spatially divided facilities, e.g. plants, central or distribution warehouses. The choice of location for public facilities like schools, hospitals, etc. is also a part of industrial location planning.

Launhardt (1882)Discussed especially the theoretic case of facility location problems in triangles by exploring the location at minimum transport cost between two raw material deposits and a market.

Weber (1909): „Theory of the Location of Industries“Generalisation of Launhardt‘s quantitative approach.



Industrial Location PlanningBoth papers deal with the choice of locations for manufacturing plantsconsidering transportation, labor, and material costs.

Assumptions• the transportation costs increase proportionally to quantity and distance• the means of transport are available in the whole plane• the places and quantities are known for the materials and the products• labor and material costs are given• every point of the plane is a potential location for one or more plants.

Weber identified locations with minimaltransportation costs as well as level curvesthat contain locations with equal transportationcosts.

Optimum




In-house location planning: Layout planning

These approaches describe the planning of the areal disposition of organizational entities („resources“) within the limits of factory premises. The result is a plan, called layout, that gives the physical disposition of the organizational entities.

Examples are the dispositions of- the manufacturing, stockage and management areas at the premises- work shops or machines in halls- work stations or kinds of goods in warehouses

First papers: Hundhausen (1925)He formulated a set of principles and aims that should be considered and followed for in-house location planning.



Subareas of Facility Location PlanningKoopmanns and Beckmann (1957)

Formulation of the Layout Problem as a Quadratic Assignment Problem.

Patients / Staff

Room 1 Room 3

Room 2

9,3' / 1,9' 9,5' / 8,4'

5,2' / 7,0'0,5' / 6,1' 6,8' / 1,9' 5,7' / 1,1'

OP Lab

X-ray

52 / 47 75 / 70

23 / 6063 / 51 2 / 17 5 / 14

Assuming that all organizational entities (OE) that have to be disposed require the same space, we look for a disposition of the OEson the equal sized places that minimizes the transportation costs.




Descriptive approaches

Descriptive location planning has to perform among other things the development of conceptual instruments in order to generally describe the premises and sequences of decision processes concerning the planning oflocations.

Prescriptive approaches

Prescriptive location theory deals with the development of objectively (inter-subjectively) verifiable criteria (models, solution procedures) which help to make a location decision in a concrete planning situation.



Location Concepts


Contents








Chapter 1 - Introduction

Terms and Definitions

Customershave requirements / demand for

• products• services

Various characteristics of demand:- one or several products/services- deterministic- probabilistic- time-dependent- depending on the nearest service or supply location




FacilitiesOne differentiates

• Facilities that offer a service.Either:

- active: pizza service, ambulance depots, fire departments, …- passive: swimming pools, libraries, …

These usually are public facilities.

• Industrial facilities:- Department stores, factories, suppliers

Differ in:- quality- equipment and service offer- size and capacity- technology




LocationsNormally have a spatial reference, e.g. places on maps, places within a building.

Vary among each other in different location characteristics and site-related factors, e.g. space on offer, position, infrastructure, rent.

Potential locations for new facilities can• be all points of a homogeneous space, e.g. anywhere on the map• only be placed along certain networks, e.g. freeway or railway network• only be selected from a given set of points.

e.g. from a set of candidate locations which meet the requirements.




Distances

As seen, transportation costs represent an essential location factor. Assuming that the transportation costs are proportional to the covered distance (and transported quantity), the distance between locations remains an essential factor concerning the choice of a location.

Typical distance measures

• (squared) Euclidean distance, air-line- Global, supraregional

• Road distance- Regional, within cities

• Manhattan distance- Within cities or buildings

B

A

BA

B

A




Cost categoriesFixed costs

Setup costs for a facility that occur independently from operational costs.

Examples• Land, development and building costs• Disposition and loan interest, rent, insurance and taxes• Depreciations on buildings and machines• (personnel) costs independent from the utilization, e.g. night-watchmen

More detailedAbsolutely fixed costs: constant over the whole planning horizonStep-wise costs : dependent on the expected utilization, e.g.

stage of expansion of the warehouse, number of production lines



Terms and DefinitionsVariable costs

are dependent on the number of pieces or on the activity level and are modeled using cost functions.

Examples• material, raw material and production costs• transportation costs• personnel costs, unit costs



Cost functions


• Constant • Step function

• Proportional to the amount, linear • Cost degression

• Proportional to the amount plusfixed costs,affin linear

• Piecewise linear



Location Concepts


Contents








Chapter 1 - Introduction

Location FactorsOn the one hand every enterprise makes certain requirements on a potential location and on the other hand it deals with certain conditions.

Requirements on locationsAll demands an enterprise makes on locations to be able to perform the service process.

Conditions regarding locationsAll facts of a location that can be used by the enterprises to perform their tasks. The attention turns to these conditions regarding locations which are different from place to place.

Location factorsWhile conditions regarding locations generally denote the facts of a place, site-related factors are just the special conditions that are used by a certain enterprise.



Location Factors

Classification of location factors

Already in 1909 , Weber dealt with the classification of location factors for the choice of locations for manufacturing plants. However, according to the environment he restricted these to economic advantages like e.g. cost advantages.

He distinguished the location factors• by the amount of their importance in general (e.g. procurement prices, labor

costs) and particular (e.g. climatic and geologic conditions) location factors• by their spatial effect in regional, agglomeration and deglomeration factors as

wells as• by the way of their composition in natural-technical (e.g. clime, quality of the

labour) and social-cultural (e.g. regional interest levels) factors.

Regional factors lead to the fact, that a geographical place is more attractive forcertain sectors of industry than another one. Agglomeration factors enhance industrial urban agglomerations while deglomeration factors cause a decentralisation of locations (e.g. subsidation of the borderland).



Location FactorsWeber‘s economically orientated classification was enhanced over the years to detailed, extensive catalogues of location factors.

Focus of many researches about the relevance of industrial location factorsis the question:

„Which factors determine the industrial choice of location?“

It is not about individual location factors and their importance within the choice of location, but the description of all possible location in fact the interest applies to all location factors.

A catalogue of possible location factors (which however makes no claim to be complete) follows.



Location FactorsLocationSituation and sizePossibilities of expansionExploitationBuilding directions

Traffic and TransportRoad and railway networkInland waterway transportation

ProductionClimatical conditionsReplacements for machines

Investment and FinancingConstruction companyProducer of capital goodsFinancial institutes

General InfrastructureLiving spaceEducational institutionsCultural institutionsHealth care level

LaboursPotential (number)Education level

Procurement and DisposalRaw and auxiliary materialsEnergyWaterWaste disposal

Public authoritiesSubsidesTax allowances

DistributionPotential of populationConsumer buying habitsSpending capacityCompetitorsDistribution supporting institutions

Personal PreferencesAddress Possibilities of recreation and vacation

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