Abstract
This chapter presents the concept of stochastic multiple criteria decision making (MCDM) method to solve complex ranking decision problems. This approach is composed of three main areas of research, i.e. classical MCDM, probability theory and classification method. The most important steps of the idea are characterized and specific features of the applied methods are briefly presented. The application of Electre III combined with probability theory, and Promethee II combined with Bayes classifier are described in details. Two case studies of stochastic multiple criteria decision making are presented. The first one shows the distribution system of electrotechnical products, composed of 24 distribution centers (DC), while the core business of the second one is the production and warehousing of pharmaceutical products. Based on the application of presented stochastic MCDM method, different ways of improvements of these complex systems are proposed and the final i.e. the best paths of changes are recommended.
TopIntroduction
Nowadays, an integral part of any organization is the application of practical tools and techniques that make changes to products, processes and services resulting in an introduction of something new in a market. Improving continuously operations is essential for a better performance of the organizations. Due to the growing impact of globalization, migration, technological and knowledge revolutions, it brings added value to customers and helps organizations to remain competitive. Many of them are forced to make changes in various areas, such as: technology, infrastructure, human resources etc. Moreover, to meet customers’ expectations and needs, companies should also consider organization’s manager interests, as well as the supplier’s opinions, customers’ point of view and the other stakeholders’ preferences. It makes the decision situation very complex and the application of decision aiding methods seems crucial.
According to Vincke (1992) multiple criteria decision making (MCDM) is a field which aims at giving the decision maker (DM) some tools in order to enable him/her to solve a complex decision problem where several points of view must be taken into account. This methodology concentrates on suggesting “compromise solution”, taking into consideration the trade-offs between criteria and the DM’s preferences. The above mentioned compromise solution is selected from the family of variants. They are constructed in different ways. In some situations, it is assumed that the variants are exclusive and at least two of them cannot be implemented together. There are also real-world situations where two or more alternatives can be introduced conjointly.
The variants are evaluated by the set of criteria, which should be characterized by the following aspects (Roy, 1985):
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Completeness due to the decision-making aspects of the considered problem.
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Appropriate formation, taking into account the global preferences of the decision maker.
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Non-redundancy, i.e. a situation in which semantic ranges of criteria are not repeated.
Thanks to the criteria it is possible to compare variants, especially when the performances are expressed as deterministic values. However, in some cases the alternatives are modeled e.g. in a simulation tool and their performances are presented as stochastic values. In such circumstances the comparison process becomes complex. It is usually supported by stochastic MCDM methods, but most of them concentrate on decision maker’s stochastic preferences. Based on the author’s experience the methods dedicated to solve complex decision problems with stochastic criteria values are not efficient enough.
The procedure presented in this chapter shows that the combination of a classical group of MCDM methods aiming at ranking of variants, e.g. Electre III, Promethee II, with probability formula or a classical method of artificial intelligence aiming at classification of objects, e.g. Bayes classifier, could solve these complex problems.
Key Terms in this Chapter
Decision Maker: A person, who expresses his/her preferences, evaluates the decision situation and the results of the computational experiments. This person makes the final decision regarding the considered problem, e.g. selects the best redesign scenario.
MADM: An abbreviation of Multiple Attribute Decision Making. It is one of the Multiple Criteria Decision Making approaches referring to the situation of finite set of alternatives evaluated by the set of attributes leading to the selection of the best solution.
Stochastic Information: Information represented by a random number, usually by a random probability distribution. It is connected with uncertainty about the values of parameters, expected input or output information. In the real-world systems the stochastic information is the result of unexpected disturbances, demand fluctuations etc.
Decision Problem: A situation where the decision maker has to face the problem of selecting one of at least two alternatives. The decision problem is composed of the description of the decision situation, definition of constraints and evaluation criteria, identification of the decision maker and his/her role in the decision process and definition of stakeholders, as well.
MCDM: An abbreviation of Multiple Criteria Decision Making. It is composed of two approaches, i.e. MADM (Multiple Attribute Decision Making) and MODM (Multiple Objective Decision Making). In MADM problems the number of alternatives is finite and the evaluation attributes are usually conflicting, while in MODM problems the set of alternatives is infinite and the evaluation criteria are described by continuous function.
Classification Theory: The research field of artificial intelligence concentrated on categorization of objects to predefined classes. It is assumed that these objects are characterized by quantitative information.
Ranking Methods: A group of MCDM methods concentrated on finding the final hierarchy of alternatives, i.e. the rank. Generally, ranking methods are divided into two sets referring to different methodological backgrounds. The first one originates from European school and it is based on outranking relation, e.g. Electre III, Promethee II methods. The second one, belongs to American school and it is based on multiattribute utility theory, e.g. AHP, UTA methods.