Decision Support Systems

K.Fedra ‘97

Decision Support SystemsDecision Support SystemsDecision Support SystemsDecision Support Systems

an introduction to DSS with an introduction to DSS with environmental application environmental application

examplesexamples

an introduction to DSS with an introduction to DSS with environmental application environmental application

examplesexamples

K.Fedra ‘97

What is a DSS ?What is a DSS ?What is a DSS ?What is a DSS ?

• Attempts at definitionAttempts at definition

• Decision making processesDecision making processes

• A general DSS architectureA general DSS architecture

• Decision Support ParadigmsDecision Support Paradigms

• Application examplesApplication examples






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K.Fedra ‘97

DSS DefinitionDSS DefinitionDSS DefinitionDSS Definition

A DSS is a computer based A DSS is a computer based

problem solving system that problem solving system that

assists assists choicechoice between between

alternativesalternatives in complex and in complex and

controversial domains.controversial domains.

A DSS is a computer based A DSS is a computer based

problem solving system that problem solving system that

assists assists choicechoice between between

alternativesalternatives in complex and in complex and

controversial domains.controversial domains.

K.Fedra ‘97

DSS DefinitionDSS DefinitionDSS DefinitionDSS Definition

A DSS provides A DSS provides • structured presentation structured presentation • problem context, problem context, • and tools for theand tools for the

– design, – evaluation,– selection

of alternativesof alternatives

A DSS provides A DSS provides • structured presentation structured presentation • problem context, problem context, • and tools for theand tools for the

– design, – evaluation,– selection

of alternativesof alternatives

K.Fedra ‘97



• Decision making processesDecision making processes• A general DSS architectureA general DSS architecture




• Decision making processesDecision making processes• A general DSS architectureA general DSS architecture



K.Fedra ‘97

Decision making processesDecision making processesDecision making processesDecision making processes

Handbook of ORHandbook of OR (B.E.Gillet, 1976):(B.E.Gillet, 1976):

• Formulation of the problemFormulation of the problem• Construction of a mathematical modelConstruction of a mathematical model• Derive solution from modelDerive solution from model• Testing model and solutionTesting model and solution• Establish control over the solutionEstablish control over the solution• Put it to work (implementation)Put it to work (implementation)

Handbook of ORHandbook of OR (B.E.Gillet, 1976):(B.E.Gillet, 1976):

• Formulation of the problemFormulation of the problem• Construction of a mathematical modelConstruction of a mathematical model• Derive solution from modelDerive solution from model• Testing model and solutionTesting model and solution• Establish control over the solutionEstablish control over the solution• Put it to work (implementation)Put it to work (implementation)

K.Fedra ‘97


HeuristicsHeuristics (How to solve it, G.Polya)(How to solve it, G.Polya)

• understand the problemunderstand the problem

• make a plan (algorithm)make a plan (algorithm)

• implement step by stepimplement step by step

• check each stepcheck each step

• check the solution (looking back)check the solution (looking back)

HeuristicsHeuristics (How to solve it, G.Polya)(How to solve it, G.Polya)

• understand the problemunderstand the problem

• make a plan (algorithm)make a plan (algorithm)

• implement step by stepimplement step by step

• check each stepcheck each step

• check the solution (looking back)check the solution (looking back)

K.Fedra ‘97


(in the real world)(in the real world) are characterized by: are characterized by:

• multiple actorsmultiple actors

• conflicting objectivesconflicting objectives

• multiple criteriamultiple criteria

• plural rationalitiesplural rationalities

• hidden agendahidden agenda

(in the real world)(in the real world) are characterized by: are characterized by:






K.Fedra ‘97


are characterized by:are characterized by:












K.Fedra ‘97


multiple actors:multiple actors:multiple actors:multiple actors:• researchers and analystsresearchers and analysts• planners and managersplanners and managers• policy and decision makerspolicy and decision makers• general public:general public:

• consumers (market)consumers (market)• concerned citizen (voters)concerned citizen (voters)

• researchers and analystsresearchers and analysts• planners and managersplanners and managers• policy and decision makerspolicy and decision makers• general public:general public:

• consumers (market)consumers (market)• concerned citizen (voters)concerned citizen (voters)

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K.Fedra ‘97


conflicting objectives:conflicting objectives:• maximize economic benefits maximize economic benefits • minimize environmental costsminimize environmental costs• maximize environmental benefitsmaximize environmental benefits• minimize economic costsminimize economic costs• maintain equitymaintain equity::

• between social groupsbetween social groups• between regions and countriesbetween regions and countries• between generationsbetween generations

• maximize economic benefits maximize economic benefits • minimize environmental costsminimize environmental costs• maximize environmental benefitsmaximize environmental benefits• minimize economic costsminimize economic costs• maintain equitymaintain equity::

• between social groupsbetween social groups• between regions and countriesbetween regions and countries• between generationsbetween generations

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K.Fedra ‘97


multiple criteria:multiple criteria:• economic criteria economic criteria (costs)(costs)

• environmental criteriaenvironmental criteria• standards standards (measurements)(measurements)

• perceptions perceptions (believes, fears)(believes, fears)

• political criteria political criteria (equity)(equity)

• regulatory criteria regulatory criteria (constraints)(constraints)

• technological criteria technological criteria (constraints)(constraints)

• economic criteria economic criteria (costs)(costs)

• environmental criteriaenvironmental criteria• standards standards (measurements)(measurements)

• perceptions perceptions (believes, fears)(believes, fears)

• political criteria political criteria (equity)(equity)

• regulatory criteria regulatory criteria (constraints)(constraints)

• technological criteria technological criteria (constraints)(constraints)

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K.Fedra ‘97


plural rationalitiesplural rationalities

rationalrational: relating to, based on, : relating to, based on, agreeable to agreeable to reasonreason. .

reason: the power of inferring, reason: the power of inferring, comprehending, or thinking in an comprehending, or thinking in an orderly, orderly, rational rational way.way.


rationalrational: relating to, based on, : relating to, based on, agreeable to agreeable to reasonreason. .

reason: the power of inferring, reason: the power of inferring, comprehending, or thinking in an comprehending, or thinking in an orderly, orderly, rational rational way.way.

K.Fedra ‘97



rationalrational: L. : L. ratio (reor, reri, ratus)ratio (reor, reri, ratus)

computation, advantage, interest,computation, advantage, interest,

behavior, procedure, ways and means, behavior, procedure, ways and means, motivation, argument, proof, opinion, motivation, argument, proof, opinion, (scientific) theory.(scientific) theory.


rationalrational: L. : L. ratio (reor, reri, ratus)ratio (reor, reri, ratus)

computation, advantage, interest,computation, advantage, interest,

behavior, procedure, ways and means, behavior, procedure, ways and means, motivation, argument, proof, opinion, motivation, argument, proof, opinion, (scientific) theory.(scientific) theory.

K.Fedra ‘97



reaching different (contradictory) reaching different (contradictory) conclusions from the same set of conclusions from the same set of premises in an internally consistent premises in an internally consistent logical way.logical way.


reaching different (contradictory) reaching different (contradictory) conclusions from the same set of conclusions from the same set of premises in an internally consistent premises in an internally consistent logical way.logical way.

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K.Fedra ‘97




• A general DSS architectureA general DSS architecture• Decision Support ParadigmsDecision Support Paradigms




• A general DSS architectureA general DSS architecture• Decision Support ParadigmsDecision Support Paradigms


K.Fedra ‘97

A general DSS architectureA general DSS architectureA general DSS architectureA general DSS architecture

• Information resourcesInformation resources

• The analytical engineThe analytical engine

• The user interfaceThe user interface




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data acquisition layerdata acquisition layer

graphical user interfacegraphical user interface

analyticalanalyticalengineengine

modelsmodelsexpert expert systemsystem

DBMSDBMSGISGIS

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K.Fedra ‘97

Information ResourcesInformation ResourcesInformation ResourcesInformation Resources

• information on the information on the status-quo status-quo (monitoring)(monitoring)

• background for the background for the identification or designidentification or design of decision alternativesof decision alternatives

• information on the information on the status-quo status-quo (monitoring)(monitoring)

• background for the background for the identification or designidentification or design of decision alternativesof decision alternatives

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The analytical engineThe analytical engineThe analytical engineThe analytical engine

• Data base management systemData base management system

• Geographic Information SystemGeographic Information System

• Simulation and optimization modelsSimulation and optimization models

• Expert systems (rules)Expert systems (rules)

• Decision Support tools Decision Support tools properproper

• Data base management systemData base management system

• Geographic Information SystemGeographic Information System

• Simulation and optimization modelsSimulation and optimization models

• Expert systems (rules)Expert systems (rules)

• Decision Support tools Decision Support tools properproper

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K.Fedra ‘97

User interface characteristicsUser interface characteristicsUser interface characteristicsUser interface characteristics

• IntegrationIntegration

• InteractionInteraction

• VisualizationVisualization

• IntelligenceIntelligence

• CustomizationCustomization

• IntegrationIntegration

• InteractionInteraction

• VisualizationVisualization

• IntelligenceIntelligence

• CustomizationCustomization

K.Fedra ‘97

The User InterfaceThe User InterfaceThe User InterfaceThe User Interface

• provides integration of functionsprovides integration of functions• interactive, dialogue oriented, interactive, dialogue oriented,

menu drivenmenu driven• intuitive, graphical, symbolicintuitive, graphical, symbolic• consistent syntax and semantics, consistent syntax and semantics,

layout and symbolismlayout and symbolism• intelligent, context awareintelligent, context aware• customizedcustomized

• provides integration of functionsprovides integration of functions• interactive, dialogue oriented, interactive, dialogue oriented,

menu drivenmenu driven• intuitive, graphical, symbolicintuitive, graphical, symbolic• consistent syntax and semantics, consistent syntax and semantics,

layout and symbolismlayout and symbolism• intelligent, context awareintelligent, context aware• customizedcustomized

K.Fedra ‘97


• provides integration of functionsprovides integration of functionsshould provide access to should provide access to ALLALL

systems functions and resources.:systems functions and resources.: seamless integration.seamless integration.

For the non-technical user, the user For the non-technical user, the user interface interface ISIS the system. the system.

• provides integration of functionsprovides integration of functionsshould provide access to should provide access to ALLALL

systems functions and resources.:systems functions and resources.: seamless integration.seamless integration.

For the non-technical user, the user For the non-technical user, the user interface interface ISIS the system. the system.

K.Fedra ‘97


• interactive dialogue, menu driveninteractive dialogue, menu drivenmodeled after the dialogue with a modeled after the dialogue with a

human experthuman expertimmediate responseimmediate responseincremental problem definitionsincremental problem definitionsincremental detail of answersincremental detail of answersparaphrasing, explanation,paraphrasing, explanation,analogiesanalogies

• interactive dialogue, menu driveninteractive dialogue, menu drivenmodeled after the dialogue with a modeled after the dialogue with a

human experthuman expertimmediate responseimmediate responseincremental problem definitionsincremental problem definitionsincremental detail of answersincremental detail of answersparaphrasing, explanation,paraphrasing, explanation,analogiesanalogies

K.Fedra ‘97


• intuitive, graphical, symbolicintuitive, graphical, symbolic

intuitively understandable formatsintuitively understandable formatsgraphical representation of complex graphical representation of complex

and large data volumesand large data volumessymbolic representation of abstract symbolic representation of abstract

concepts concepts

• intuitive, graphical, symbolicintuitive, graphical, symbolic

intuitively understandable formatsintuitively understandable formatsgraphical representation of complex graphical representation of complex

and large data volumesand large data volumessymbolic representation of abstract symbolic representation of abstract

concepts concepts

K.Fedra ‘97


• consistent syntax and semantics, consistent syntax and semantics, layout and symbolismlayout and symbolism

ease-of-use through familiarityease-of-use through familiarityeasy orientationeasy orientationfast learningfast learning

• consistent syntax and semantics, consistent syntax and semantics, layout and symbolismlayout and symbolism

ease-of-use through familiarityease-of-use through familiarityeasy orientationeasy orientationfast learningfast learning

K.Fedra ‘97


• intelligent, context awareintelligent, context aware

built-in information about the built-in information about the application domainapplication domain

information about data availabilityinformation about data availabilityinformation about the userinformation about the useradaptive behaviour, learningadaptive behaviour, learning

• intelligent, context awareintelligent, context aware

built-in information about the built-in information about the application domainapplication domain

information about data availabilityinformation about data availabilityinformation about the userinformation about the useradaptive behaviour, learningadaptive behaviour, learning

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• customizedcustomized

uses the language, jargon, style, etc. uses the language, jargon, style, etc. of the end userof the end user

simulates familiar structures and simulates familiar structures and formats of informationformats of information

It is easier to change software than It is easier to change software than institutions and habits.institutions and habits.

• customizedcustomized

uses the language, jargon, style, etc. uses the language, jargon, style, etc. of the end userof the end user

simulates familiar structures and simulates familiar structures and formats of informationformats of information

It is easier to change software than It is easier to change software than institutions and habits.institutions and habits.

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K.Fedra ‘97

Decision support paradigmsDecision support paradigmsDecision support paradigmsDecision support paradigms

• Information systemsInformation systems

• Scenario analysisScenario analysis

WHAT IFWHAT IF

• Rational maximizationRational maximization

HOW TOHOW TO

• Multiple attributesMultiple attributes



WHAT IFWHAT IF


HOW TOHOW TO


K.Fedra ‘97




WHAT IFWHAT IF


HOW TOHOW TO




WHAT IFWHAT IF


HOW TOHOW TO


K.Fedra ‘97

Information systemsInformation systemsInformation systemsInformation systems

• provide problem contextprovide problem context

• describe available alternativesdescribe available alternatives

• offer a common language and offer a common language and shared information basis for the shared information basis for the participants in the decision making participants in the decision making processprocess

• provide problem contextprovide problem context

• describe available alternativesdescribe available alternatives

• offer a common language and offer a common language and shared information basis for the shared information basis for the participants in the decision making participants in the decision making processprocess

K.Fedra ‘97

Information systemsInformation systemsInformation systemsInformation systems

typical application example:typical application example:

State-of-the-Environment ReportingState-of-the-Environment Reporting

decision process usually diffuse, decision process usually diffuse, multi-stage and lengthy without multi-stage and lengthy without clear technical objectives.clear technical objectives.

Public information, awareness Public information, awareness building, assists argumentation.building, assists argumentation.


State-of-the-Environment ReportingState-of-the-Environment Reporting

decision process usually diffuse, decision process usually diffuse, multi-stage and lengthy without multi-stage and lengthy without clear technical objectives.clear technical objectives.

Public information, awareness Public information, awareness building, assists argumentation.building, assists argumentation.

K.Fedra ‘97




WHAT IFWHAT IF


HOW TOHOW TO




WHAT IFWHAT IF


HOW TOHOW TO


K.Fedra ‘97


Scenario analysisScenario analysisexplores the reaction of a system to explores the reaction of a system to

changes in the controlchanges in the control or decision or decision variables on the performance variables on the performance variables (criteria) in terms of the variables (criteria) in terms of the objectives and constraints of the objectives and constraints of the decision problem.decision problem.

Scenario analysisScenario analysisexplores the reaction of a system to explores the reaction of a system to

changes in the controlchanges in the control or decision or decision variables on the performance variables on the performance variables (criteria) in terms of the variables (criteria) in terms of the objectives and constraints of the objectives and constraints of the decision problem.decision problem.

K.Fedra ‘97


Scenario Scenario from L. from L. scaenarium, scaenarium, the stagethe stage

an account or synopsis of a projected an account or synopsis of a projected

course of action or events;course of action or events;

a set of assumptions.a set of assumptions.

Scenario Scenario from L. from L. scaenarium, scaenarium, the stagethe stage

an account or synopsis of a projected an account or synopsis of a projected

course of action or events;course of action or events;

a set of assumptions.a set of assumptions.

K.Fedra ‘97



Environmental Impact Environmental Impact AssessmentAssessment, that evaluates and , that evaluates and compares project alternatives.compares project alternatives.

Exploratory (policy) assessment, Exploratory (policy) assessment, design of alternatives.design of alternatives.


Environmental Impact Environmental Impact AssessmentAssessment, that evaluates and , that evaluates and compares project alternatives.compares project alternatives.

Exploratory (policy) assessment, Exploratory (policy) assessment, design of alternatives.design of alternatives.

K.Fedra ‘97




WHAT IFWHAT IF


HOW TOHOW TO




WHAT IFWHAT IF


HOW TOHOW TO


K.Fedra ‘97

Rational maximizationRational maximizationRational maximizationRational maximization

The individual as rational maximizerThe individual as rational maximizer

chooses a commodity bundle chooses a commodity bundle

c = (cc = (c11,...,c,...,cii,...,c,...,cn n ))

that maximizes the utilitythat maximizes the utility

u(c)u(c)

The individual as rational maximizerThe individual as rational maximizer

chooses a commodity bundle chooses a commodity bundle

c = (cc = (c11,...,c,...,cii,...,c,...,cn n ))

that maximizes the utilitythat maximizes the utility

u(c)u(c)

K.Fedra ‘97


maximize the utility maximize the utility u(c)u(c)– over different groups over different groups ( i )( i )– over space over space (x,y,z)(x,y,z)– over time over time ( t )( t )

maximize the utility maximize the utility u(c)u(c)– over different groups over different groups ( i )( i )– over space over space (x,y,z)(x,y,z)– over time over time ( t )( t )

K.Fedra ‘97


The social welfare functionThe social welfare function

u*(c) = f [uu*(c) = f [u11(c),u(c),u22(c),...,u(c),...,unn(c) ](c) ]

as the sum as the sum

iiuuii(c)(c)

of individual or group of individual or group

utility functions uutility functions uii(c)(c)

The social welfare functionThe social welfare function

u*(c) = f [uu*(c) = f [u11(c),u(c),u22(c),...,u(c),...,unn(c) ](c) ]

as the sum as the sum

iiuuii(c)(c)

of individual or group of individual or group

utility functions uutility functions uii(c)(c)

K.Fedra ‘97

Rational choiceRational choiceRational choiceRational choice

context dependence and bias:context dependence and bias:

certainty versus probabilitycertainty versus probability

gain versus lossgain versus loss

absolute versus relative changeabsolute versus relative change

context dependence and bias:context dependence and bias:

certainty versus probabilitycertainty versus probability

gain versus lossgain versus loss

absolute versus relative changeabsolute versus relative change

K.Fedra ‘97

Decision makingDecision makingDecision makingDecision making

Minimax and Bayesian approaches:Minimax and Bayesian approaches:

Decision maker has:Decision maker has:

• a finite number of possible decision a finite number of possible decision alternativesalternatives

• a finite number of a finite number of outcomesoutcomes (state of nature) (state of nature)

which may have a known probability of outcomewhich may have a known probability of outcome

• a a cost or benefitcost or benefit for each decision - state-of- for each decision - state-of-

nature combinationnature combination

Minimax and Bayesian approaches:Minimax and Bayesian approaches:

Decision maker has:Decision maker has:

• a finite number of possible decision a finite number of possible decision alternativesalternatives

• a finite number of a finite number of outcomesoutcomes (state of nature) (state of nature)

which may have a known probability of outcomewhich may have a known probability of outcome

• a a cost or benefitcost or benefit for each decision - state-of- for each decision - state-of-

nature combinationnature combination

K.Fedra ‘97


Decision Table:Decision Table:

State of NatureState of Nature

DecisionDecision rain no-rainrain no-rain

take a raincoattake a raincoat 0 0 3 3

no raincoatno raincoat 6 6 0 0(0, 3, 6, are the associated costs)(0, 3, 6, are the associated costs)

What do you do ?What do you do ?




take a raincoattake a raincoat 0 0 3 3

no raincoatno raincoat 6 6 0 0(0, 3, 6, are the associated costs)(0, 3, 6, are the associated costs)

What do you do ?What do you do ?

K.Fedra ‘97





take a raincoattake a raincoat 0 0 3 3 ((33))

no raincoatno raincoat 6 6 0 0 (6)(6)

Minimax Solution (conservative):Minimax Solution (conservative):

take a raincoat !take a raincoat !




take a raincoattake a raincoat 0 0 3 3 ((33))

no raincoatno raincoat 6 6 0 0 (6)(6)

Minimax Solution (conservative):Minimax Solution (conservative):

take a raincoat !take a raincoat !

K.Fedra ‘97


Decision Table: Decision Table: (with added probabilities)(with added probabilities)


DecisionDecision rain rain (0.1)(0.1) no-rain no-rain (0.9)(0.9)

take a raincoattake a raincoat 0 (0) 0 (0) 3 3 (2.7)(2.7) (2.7)(2.7)

no raincoatno raincoat 6 (0.6) 6 (0.6) 0 0 (0) (0) ((0.60.6))

Bayesian Solution:Bayesian Solution:

don’t take a raincoat !don’t take a raincoat !

Decision Table: Decision Table: (with added probabilities)(with added probabilities)


DecisionDecision rain rain (0.1)(0.1) no-rain no-rain (0.9)(0.9)

take a raincoattake a raincoat 0 (0) 0 (0) 3 3 (2.7)(2.7) (2.7)(2.7)

no raincoatno raincoat 6 (0.6) 6 (0.6) 0 0 (0) (0) ((0.60.6))

Bayesian Solution:Bayesian Solution:

don’t take a raincoat !don’t take a raincoat !

K.Fedra ‘97



States of NatureStates of Nature

DecisionDecision rain rain (0.1)(0.1) little little (0.5)(0.5) none none (0.4)(0.4)

take a raincoattake a raincoat 0 (0) 0 (0) 0 (0) 3 (1.2) 0 (0) 3 (1.2)

no raincoatno raincoat 6 (0.6) 1 (0.5) 0 (0) 6 (0.6) 1 (0.5) 0 (0)

And now ?And now ?




take a raincoattake a raincoat 0 (0) 0 (0) 0 (0) 3 (1.2) 0 (0) 3 (1.2)

no raincoatno raincoat 6 (0.6) 1 (0.5) 0 (0) 6 (0.6) 1 (0.5) 0 (0)

And now ?And now ?

K.Fedra ‘97





take a raincoattake a raincoat 0 (0) 0 (0) 0 (0) 0 (0) 33 (1.2) (1.2) 1.21.2

no raincoatno raincoat 66 (0.6) 1 (0.5) 0 (0) (0.6) 1 (0.5) 0 (0) 1.11.1

MiniMaxMiniMax: : take a raincoat take a raincoat

BayesianBayesian:: take no raincoat take no raincoat




take a raincoattake a raincoat 0 (0) 0 (0) 0 (0) 0 (0) 33 (1.2) (1.2) 1.21.2

no raincoatno raincoat 66 (0.6) 1 (0.5) 0 (0) (0.6) 1 (0.5) 0 (0) 1.11.1

MiniMaxMiniMax: : take a raincoat take a raincoat

BayesianBayesian:: take no raincoat take no raincoat

K.Fedra ‘97




WHAT IFWHAT IF


HOW TOHOW TO




WHAT IFWHAT IF


HOW TOHOW TO


K.Fedra ‘97


Multiple attributesMultiple attributes

multiple objectivesmultiple objectives

multiple criteriamultiple criteria

trade-off, compromise, trade-off, compromise,

satisfaction, acceptancesatisfaction, acceptance

Multiple attributesMultiple attributes

multiple objectivesmultiple objectives

multiple criteriamultiple criteria

trade-off, compromise, trade-off, compromise,

satisfaction, acceptancesatisfaction, acceptance

K.Fedra ‘97

Decision making processDecision making processDecision making processDecision making process

• Problem descriptionProblem description

• Set of criteriaSet of criteria– objectives– constraints

• Set of feasible alternativesSet of feasible alternatives

• Evaluation of alternativesEvaluation of alternatives

• Decision rulesDecision rules

• Problem descriptionProblem description

• Set of criteriaSet of criteria– objectives– constraints

• Set of feasible alternativesSet of feasible alternatives

• Evaluation of alternativesEvaluation of alternatives

• Decision rulesDecision rules

K.Fedra ‘97

Decision making processDecision making processDecision making processDecision making process

SpatialSpatial decisions: decisions:

• Set of Set of criteriacriteria– objectives

– constraints

areare functions of spacefunctions of space

SpatialSpatial decisions: decisions:

• Set of Set of criteriacriteria– objectives

– constraints

areare functions of spacefunctions of space

K.Fedra ‘97

Spatial decisionsSpatial decisionsSpatial decisionsSpatial decisions

Environmental decision are also Environmental decision are also spatial decisionsspatial decisions::

• site selection, locationsite selection, location

• pollution controlpollution control

• natural resources managementnatural resources management

• environmental impact assessmentenvironmental impact assessment

• risk analysis and managementrisk analysis and management

Environmental decision are also Environmental decision are also spatial decisionsspatial decisions::

• site selection, locationsite selection, location

• pollution controlpollution control

• natural resources managementnatural resources management

• environmental impact assessmentenvironmental impact assessment

• risk analysis and managementrisk analysis and management

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Decision Support Systems

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