2 Spatial decision making Multiple criteria and GIS The concept of non-inferiority Basic multiple criteria solution techniques Goal programming Weighting method
GIS as Decision Support Tool3 Spatial decision making Spatial decision making is a process in decision making based on spatial relationships and phenomena. Spatial decision making requires comprehensive analysis on spatial and attribute data. There are great uncertainties involved in spatial decision making since we do not fully understand the earth environment that we are living on, so that the geographical theory that we rely on can be challenged.
GIS as Decision Support Tool4 Examples of spatial decision making Identify shortest path that connects a specified set of points e.g. for power line route, vehicle scheduling Identify optimal location of a facility to maximise accessibility e.g. retail store, school, health facility Identify parcel of land for commercial development which maximises economic efficiency
GIS as Decision Support Tool5 The traditional approach Identify the issue Collect the necessary data Define the problem rigorously by stating objectives, assumptions and constraints. If there is more than one objective, then define the relationship between objectives by quantifying them in commensurate term, i.e. express each objective in the same units. Find appropriate solution procedure Solve the problem by finding the optimum solution.
GIS as Decision Support Tool6 Assumptions involved The objectives can be expressed in commensurate terms. The problem can be collapsed and simplified into a single objective for analysis. Decision makers agree on the relative importance of the commensurable objects. However, these assumptions do not necessarily hold.
GIS as Decision Support Tool7 Problem: to locate a new fire station in a city Objectives: maximise coverage of population maximise coverage of real estate Conflict: Most valued real estate is not necessarily located where most people reside. Therefore, objectives are in spatial conflict. Solution: Collapse two objectives into one by defining a relationship between the value of real estate and value of life. However: the two objectives are non- commensurate since one cannot place a monetary value on a human life. Case 1: The fire station location problem
GIS as Decision Support Tool8 Problem: suitability evaluation of a number of sites for commercial development Objectives Maximise economic efficiency Minimise environmental impact Conflict: Express environmental quality in terms of economic efficiency (monetary values), while different interest groups will value environment differently. Solution: Identify and map the different landuse, land assessments and environmental impacts on separate layers. The construct several combinations of overlays based on various priorities. Derive suitability surfaces for the different combinations or priorities and let politicians make the ultimate choice. Case 2: Land suitability assessment
GIS as Decision Support Tool9 In the real world, decision making problems rarely collapse into a net single objective. Real world problems are inherently multi- objective in nature and consensus rarely exists concerning the relationships between the various objectives. General observations No. of decision-makers 1>1 No. of criteria 1fewsome >1somemost
GIS as Decision Support Tool10 It is more appropriate to identify and maintain the multiple criteria nature of real world problems for analysis and decision making. Decision makers are frequently interested in the trade off relationship between the various criteria. This allow them to make the final decisions in a political environment. e.g. in Case 1, trading total population covered for total value of real estate covered. In summary …
GIS as Decision Support Tool11 A GIS is an ideal tool to use to analyse and solve multiple criteria problems GIS data bases combine spatial and non-spatial information. A GIS generally has ideal data viewing capabilities. A GIS generally allows users to interactively modify solutions to perform sensitivity analysis. A GIS should also contain spatial query and analytical capabilities such as measurement of area and distance, overlay capability and corridor analysis. Multiple criteria and GIS
GIS as Decision Support Tool12 Non-inferiority Objective 1: Real estate coverage Objective 2: Population coverage P1P1 P2P2 P3P3 P4P4 Feasible region of the objective space (0, 0) Non-inferior solution set The objective space P 1 : Optimum solution when covering for population P 2 : Optimum solution when covering for real estate only
GIS as Decision Support Tool13 The concept of non-inferiority Two objectives: real estate and population P 1 represents the solution which optimise coverage of population alone. P 2 represents the solution which optimise coverage of real estate. A site is non-inferior if there exists no alternative site where a gain could be obtained in one objective without enforcing a loss in the other. P 3 represents a feasible solution which is not non- inferior. P 4 is a non-inferior solution since to improve P 4 for one objective requires a loss on the other.
GIS as Decision Support Tool14 The concept of non-inferiority (cont.) The curved line represents the set of non-inferior solutions. The set of non-inferior solutions is the set of best compromise solutions or the “trade-off curve” in welfare economics. A point on the “trade-off curve” represents a point of Pareto optimality which indicates a solution point where no one objective can be improved upon without a sacrifice in another.
GIS as Decision Support Tool15 Basic multiple criteria solution techniques Preference oriented approaches derive a unique solution by specifying goals or preferences; assumes the set of possible solutions is known and small; an example is goal programming. Non-inferior solution set generating techniques derive the entire set of non-inferior solutions and leave the choice to the decision-maker; are used when a very large number of options exist; an example is the weighting method.
GIS as Decision Support Tool16 Goal programming Case 2: Land suitability assessment Given a set of parcels of land, identify which best suits a set of development or search criteria. The overall aim is to meet all the criteria or goals to the greatest extent possible, to choose the most desirable plan from a set of possible options. Procedure Choose criteria and assign weights Build a concordance matrix Compare the index of preferability. The larger the index, the more preferred the option.
GIS as Decision Support Tool17 Preference table Alternative sites CriteriaABCDWeights environment43210.1 transport34120.1 school43120.1 location12430.2 price44220.2 amenity14320.1 population43210.1 safety34210.1 1 = most preferred, 4 = least preferred 1.0
GIS as Decision Support Tool18 ABCDRow A-0.60.3 1.2 B0.4-0.2 0.8 C0.70.8-0.31.8 D0.70.80.7-2.2 Concordance matrix Calculation example: pair AB X = Concordance set with weight (where A beats B) = 0.5 Y = Discordance set with weight (where B beats A) = 0.3 Z = Tie set with weight (where preference are equal) = 0.2 Concordance for pair AB = X + Z/2 = 0.5 + 0.2/2 = 0.6 Concordance for pair BA = Y + Z/2 = 0.3 + 0.2/2 = 0.4
GIS as Decision Support Tool19 Weighting method Strategy Combine the criteria using a range of different weightings for each criterion, ranging from 100% on only one criterion to 100% on the other. Find the best solutions for each combination. Due to the number of combinations that must be evaluated, this is not generally practical for more than 2 criteria. The weighting method does not guarantee that all solutions in the non-inferior set will be found. The number found depends on how many combinations of weights are used.
GIS as Decision Support Tool20 Soil depthSoil SeriesDEM Water availability Oxygen availability Nutrient availability Erosion hazard Slope classes Suitability classes Characteristics Qualities Evaluation A land suitability model
GIS as Decision Support Tool21 C = CROSS operation (Combine) R = RECODE operation (Reclassify) D = DIFFERENTIATE operation (Slope) MAX = MAXIMISE operation (Max) Darker tones on all maps except ‘SOIL’ indicate ‘more’ or ‘better’ (from Burrough, 1986) A land suitability model (cont.)
GIS as Decision Support Tool22 A soil erosion prediction model Soil seriesSoil depthSlopeSoil lengthRockiness EROSION MODEL New depthRate of erosion Nutrient availability Oxygen availability Water availability Soil conditions for maize Suitability classes 1° characteristics 2° characteristics Qualities Evaluation Flow chart of the operations used to estimate the suitability of the area for maize 40 years hence (from Burrough, 1986).
GIS as Decision Support Tool23 A soil erosion prediction model (cont.) SLEMSA USLE Estimating erosion under maize in Kisii, Kenya (from Burrough, 1986).
GIS as Decision Support Tool24 Soil map DEM Suitability for coffee Proximity zones Coffee price Transport costs Profit zones Flow chart of the operations used to estimate the profitability of growing coffee (after Burrough, 1986). Reclassify CostDistance Subtract (-) A profit prediction model
GIS as Decision Support Tool25 a) Expected returns from coffee based on physical suitability b) Transport cost zones c) Proximity to roads as a function of distance and altitude d) Expected profits for coffee as a function of physical suitability and proximity to transport A profit prediction model (cont.)
GIS as Decision Support Tool26 Summary Spatial decision making is based on spatial relationships and phenomena. In the real world, decision making problems rarely collapse into a net single objective. Decision makers are frequently interested in the trade off relationship between the various criteria. Two approaches to derive multi-criteria solutions: Preference-oriented approach: derive a unique solution by specifying goals or preferences Non-inferior solution set: derive the entire set of non- inferior solutions and leave the choice to the decision-maker GIS is an ideal tool for multi-criteria decision-making