Decision support system case study with solution
The expected value cost of action a2 is the lowest, based on the probability likelihood of occurrence assigned for each outcome, pij and this course of action can be followed [ 9 ]. In lexicographic analysis of problems, a chronological elimination process is continued until either a single solution is found or all the problems are solved. In this method criteria are first rank-ordered in terms of importance. The alternative with the best performance score on the most important criterion is selected. If there are ties related to this attribute, the performance of the joined option on the next most important factor will be compared until the unique alternative is chosen [ 31 ].
The concept of cost—benefit analysis CBA originated in the United States in the s where it was used to find a solution to problems of water provision. This method is used to estimate all the costs and benefits associated with a particular project which is usually defined in money terms, in order to weigh up whether a project will bring a net benefit to the public and to be able to compare the possible options for limited resources. It is one of the most comprehensive and at the same time the most difficult technique for decision-making [ 32 ]. According to Kuik et al. Second, certain costs and benefits which are in the social and environmental domains might be difficult to quantify in monetary terms.
MAUT is based upon the use of utility functions. Utility functions are employed to quantify the preference of the decision-maker by allocating a numerical index to different degrees of satisfaction as the attribute under consideration takes values between the most and least defined limits [ 34 ].
They are considered a compliant tool of representing how much an attribute or a measure satisfies the decision-maker objectives to transform the raw performance values of the alternatives against diverse criteria, both factual quantitative and judgmental qualitative , to a general dimensionless scale [ 35 ]. They represent a means to translate attributes units into utility units. Utility functions can be specified in terms of a graph, table or mathematical expression. Mathematical expressions of utility functions include: straight-line, logarithmic, or exponential functions [ 34 ].
The utility values are estimated by normalizing the output of the simulation tests.
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Normalization of performance measures is conducted utilizing the minimum and maximum limits that are obtained from the simulation. Moreover, they are commonly checked against the outputs and replaced if there are values beyond the limits. This method was initially developed by Edwards [ 50 ] and is based on direct numerical ratings that are aggregated additively. In a basic format of SMART, there is a rank-ordering of action items for each criterion setting the worst to zero and the best to and interpolating between [ 27 ].
By filtering the performance values with associated weights for all criteria a utility value for each option is estimated [ 36 ]. The advantage of this approach is that the assessments are not relative; hence shifting the number of options will not change the final outcomes.
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If new alternatives are likely to be added, and the action items are compliant to a rating model, then SMART can be a better option [ 37 ]. One of the limitations of this technique is that it disregards the interrelationships between parameters. However, SMART is a valuable technique since it is uncomplicated, easy and quick which is quite important for decision makers.
In SMART, changing the number of alternatives will not change the decision scores of the original alternatives and this is useful when new alternatives are added [ 37 ]. He also argued that using SMART in performance measures can be a better alternative than other methods. The AHP was suggested by Saaty and uses an objective function to aggregate various features of a decision where the main goal is to select the decision alternative that has the maximum value of the objective function [ 38 ].
The AHP is based on four clearly defined axioms Saaty [ 39 ]. The process of AHP includes three phases: decomposition, comparative judgments, and synthesis of priority. Through the AHP process, problems are decomposed into a hierarchical structure, and both quantitative and qualitative information can be used to develop ratio scales between the decision elements at each level using pair wise comparisons. The top level of hierarchy corresponds to overall objectives and the lower levels criteria, sub-criteria, and alternatives.
Users are asked to set up a comparison matrix with comparative judgments by comparing pairs of criteria or sub-criteria. A scale of quantities -ranging from 1 indifference to 9 extreme preference is used to identify the users priorities. Eventually, each matrix is then solved by an eigenvector technique for measuring the performance [ 41 ]. Preferences are then calculated from the comparison matrix by normalising the matrix, to develop the priority vector, by A.
A threshold value of 0. Table 2 shows the average consistencies of RI. Random inconsistency index, adapted from Ishizaka [ 44 ]. The advantages of the AHP method are that it demonstrates a systematic approach through a hierarchy and it has an objectivity and reliability for estimating weighting factors for criteria [ 45 ].
It can also provide a well-tested method which allows analysts to embrace multiple, conflicting, non-monetary attributes into their decision-making. Moreover if a new alternative is added after finishing an evaluation calculation, it is very troublesome because all the calculation processes have to be restarted again [ 46 ]. The limitations of AHP are of a more theoretical nature, and have been the subject of some debate in the technical literature. Many analysts have pointed out that, the attribute weighting questions must be answered with respect to the average performance levels of the alternatives.
Others have noted the possibility for ranking reversal among remaining alternatives after one is deleted from consideration.
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The most important outranking methods assume data availability roughly similar to what required for the MAUT methods. Fundamental problems with most MAUT and MAUT-related methods are handling uncertain or fuzzy information and dealing with information stated in other than ratio or interval scale. In some conditions, instead of quantitative measures descriptive expressions are frequently faced [ 48 ]. The outranking method acts as one alternative for approaching complex choice problems with multiple criteria and multiple participants.
Outranking shows the degree of domination of one alternative over another and facilitates the employment of incomplete value information and, for example, judgments on ordinal measurement scale. They provide the partial preference ranking of the alternatives, not a principal measure of the preference relation [ 48 ].
The main aim of the ELECTRE method is to choose alternative that unites two conditions from the preference concordance on many evaluations with the competitor and preference discordance was supervised by many options of the comparison. The starting point is the data of the decision matrix assuming the sum of the weights equals to 1 [ 49 ]. As shown in Eq.
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The calculation of the discordance index djk is more complex. If Aj performs better than Ak on all criteria, the discordance index will be zero. Otherwise, as per Eq. The maximum of these ratios must be between 0 and 1 is the discordance index [ 27 ]. This method determines a partial raking on the alternatives. The set of all options that outrank at least one other alternative and are themselves not outranked. This method was introduced by Brans and Vincke [ 47 ], Brans et al. The scores of the decision table need not necessarily be normalized or transformed into a dimensionless scale.
Higher score value indicates a better performance. It is also assumed that a preference function is associated to each attribute. For this aim, a preference function PFi Aj, Ak is defined showing the degree of the preference of option A j over A k for criterion C i :.
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The main benefit of these preferences functions is the simplicity since there are no more than two parameters in each case. The value of this index is between 0 and 1, and characterises the global intensity of preference between the couples of choices [ 27 ]. For ranking the alternatives, the following outranking flows Eq. The positive outranking describes how much each option is outranking the other items.
The negative outranking flow shows the power of A j its outranking character. The negative outranking flow shows how much each alternative is outranked by the others. The basic concept of TOPSIS is that the selected option should have the shortest distance from the positive ideal solution and the farthest distance from the negative-ideal solution in a geometrical sense. Then the method selects a solution with the maximum similarity to the positive-ideal solution.
The default assumption is that the larger the outcome, the greater the preference for benefit attributes and the less the preference for cost attributes [ 51 ].