concerned with techniques through which the decision‐makers would be able to evaluate the feasible alternatives in a mathematical sense (Bell et al. 1988; Kleindorfer et al. 1993). Note that traditional normative analysis is based on the assumption of rationalism through the evolved entities of the decision‐making problem, which, loosely speaking, is a term that refers to decision‐makers pursuing what was described through the previous stages, as their interests and goals. Naturally, making a decision irrationally is beyond the scope of this book, though methods are introduced throughout this book that would enable decision‐makers to cope with different types of criteria, including intangible criteria.
The final stage of the decision‐making process is called prescriptive analysis. In this stage, decision‐makers go beyond predicting future outcomes to determine which alternatives would be the most advantageous or desirable solutions to the problem at hand (Saad 2001). In other words, prescriptive analytics combine the information gathered through studying the behavioral patterns of the stockholders (descriptive analysis), the likelihood of random events inherent to the decision‐making problems (predictive analysis), which would be expressed in mathematical‐oriented frameworks (normative analysis), to obtain the best course of actions for the decision‐makers. Furthermore, through the realms of prescriptive analysis, decision‐makers can explore the possible options on how to take advantage of future opportunities or coping with future risks, and, eventually, evaluate the implication of each feasible decision option based on the nature the decision‐making problem at hand (Bell et al. 1988; Kleindorfer et al. 1993; Tzeng and Huang 2011).
Having defined decision‐making, we consider what is a good choice or alternative in a decision‐making problem. Indeed, the notion of a “good alternative” may differ among decision‐makers’ viewpoints due to their different personal desires, experiences, and backgrounds. In other words, one’s idea of a “good choice” may not necessarily represent every decision‐makers’ ideal choice. Furthermore, the selection procedure of decision‐makers may differ from one another, when facing the same decision‐making problem. Nevertheless, the decision‐makers’ selection procedure is founded on a basic and similar principle, which is that decision‐makers would have to choose a set of solutions that would outperform other feasible alternatives based on a set of evaluation criteria defined either explicitly or implicitly by the decision‐makers for the specific problem at hand. In fact, this decision paradigm underlies multicriteria decision‐making (MCDM) in general. In practice, almost everyone may face an MCDM problem on a daily bases, which most cope with by aggregating the criteria through an intuition‐oriented weighting mechanism. Nevertheless implementing a systematic MCDM approach is essential to making informed and logical decision.
In technical terms, MCDM is a procedure by which the decision‐maker explicitly evaluates a set of alternatives with regard to multiple, usually conflicting, criteria. Decision makers apply MCDMs to restructure and redefine the decision‐making problem to make an informed decision. Although developing and implementing MCDM methods are not novel ideas, there have been undeniable advances in this field since the blooming era of computational intelligence (CI) during the early 1960 and 1970s, especially in the form of mathematically oriented methods that recapture and redefine MCDM. MCDM has been an active area of research that has played a crucial role in an array of disciplines, ranging from politics and business to the environment and energy (Zolghadr‐Asli et al. 2018a).
Hwang and Yoon (1981) proposed clustering MCDM problems based on the nature of solutions that are available for the problem in hand into two main categories, namely, multiobjective decision‐making (MODM), and multiattribute decision‐making (MADM). Essentially, the aforementioned classification is based on whether the solutions are explicitly or implicitly defined (Mendoza and Martins 2006; Tzeng and Huang 2011; Velasquez and Hester 2013).
MODM problems describe a situation in which decision‐makers are searching for a set of solutions that would satisfy the constraints imposed on the given problem and obtain results that constitute an optimal set of solutions based on the decision‐makers objectives (Hwang and Yoon 1981). In essence, MODM is suitable for tackling design and planning problems, in which the decision‐makers aim to achieve states objectives or goals by considering the various interactions within the given constraints. The decision space of MODM problems can be described as a multidimensional Cartesian space, with each (conflicting) objective acting as an axis, defined by a set of constraints that separate the feasible and infeasible solutions. MODM can solve problems with continuous or discrete decision spaces. MODM solution methods are usually associated with mathematical programming methods (Tzeng and Huang 2011).
In general, MODM involve trade‐off and scale problems (Tzeng and Huang 2011; Zolghadr‐Asli et al. 2018a). MODM involves more than one objective, therefore, the optimal solutions to a MODM problem must be posed in terms of Pareto fronts or production possibility frontier (after the Italian economist Vilfredo Pareto 1848–1923), which are sets of points representing combinations of the values of the objective functions with the best tradeoffs among objectives that are achievable for the problem being solved. In classic MODM techniques, an optimal solution is commonly obtained with mathematical programming. This means multiple objectives are merged into a single‐objective problem through a weighting of the various objectives. The process of obtaining a proper weighting scheme for the objectives is a trade‐off problem. If such trade‐off information is unavailable, Pareto solutions must be derived. Pareto solutions to MODM problems are expressed as a set of nondominated solutions. A nondominated solution has the property that it is not possible to improve the solution’s utility or degree of preference without degrading at least one objective (Zolghadr‐Asli et al. 2017, 2018a). The MODM’s scaling problem, on the other hand, is a computational challenge surrounding most real‐world, practical, decision‐making problems, whereby the stakeholders must consider several conflicting objectives. As the number of objectives increases the decision makers face the curse of dimensionality, whereby the computational costs of solving a MODM problem become burdensome in the extreme, and sometimes computationally unassailable (Bozorg‐Haddad et al. 2017; Zolghadr‐Asli et al. 2017, 2018a). In an attempt to surmount this challenge, meta‐heuristic algorithms have arisen to search within the decision‐space and identify potential solutions to a MODM problem (Bozorg‐Haddad et al. 2017, Zolghadr‐Asli et al. 2018b, c, d).
MADM problems describe a situation in which the decision‐makers evaluate a finite number of predefined alternatives. The alternatives are known at the beginning of the solution process. The decision‐makers attempt to systematically assess each alternative via a discrete preference rating mechanism. The rating mechanism used by decision‐makers to evaluate and compare the performance of each of the alternatives under consideration is defined either explicitly or implicitly (Hwang and Yoon 1981). Table 1.1 compares the main characteristic of MCDM approaches, namely, MODM and MADM (Malczewski 1999; Mendoza and Martins 2006; Tzeng and Huang 2011; Velasquez and Hester 2013).
Table 1.1 Comparison of MODM and MADM approaches.
| Criteria for comparison | MODM | MADM |
|---|---|---|
| Criteria defined | Objectives | Attributes |
| Objective defined | Explicitly | Implicitly |
| Attributes defined | Implicitly | Explicitly |
| Constraints defined | Explicitly | Implicitly |
| Alternatives defined | Implicitly | Explicitly |
| Number of alternatives |