Decision problem

More specifically, the basic notions of a Turing Machine, of computable functions and of undecidable properties are needed for Chapter VI (Decision Problems) the definitions of recursive, primitive recursive and partial recursive functions are helpful for Section F of Chapter IV and two of the proofs in Chapter VI. The basic facts regarding regular sets, context-free languages and pushdown store automata are helpful in Chapter VIII (Monadic Recursion Schemes) and in the proof of Theorem 3.14. For Chapter V (Correctness and Program Verification) it is useful to know the basic notation and ideas of the first order predicate calculus a highly abbreviated version of this material appears as Appendix A. 

In principal the generation of the quant network is done by decomposing the overall decision problem into smaller sub-problems by looping around nested recursive functions that are used to divide the search tree into the parts that are useful to... 

The concept of successive planning is to decompose the overall decision problem into smaller subproblems and to tackle each of these with a suitable solution methodology. This decomposition often follows the principals of hierarchical planning, as most practical problems can be structured hierarchically. In the area of supply chain management, the so-called supply chain planning matrix is an... 

With variables Kjt properly defined, additional constraints can be identified to cope with the different restrictions posed to the decision problem by the production environment. As outlined in Section 11.3.1, minimal lot sizes, maximal lot sizes and lot sizes which are multiples of an integer batch size are relevant restrictions to be considered here. 

In a decision problem it is desired to minimize the expected risk defined as follows ... 

Given this political history of hydropower in Switzerland, a standard for sustainable hydropower operation was likely to provoke major political reactions. However, expectations associated with market liberalization also partly motivated actors to reconsider their original interest positions. However, solutions could not be found because the interlocked nature of the decision problem represented a classical social dilemma [11]. A social dilemma is present if decisions of two actors depend on each other and if both actors are forced to select a sub-optimal strategy of conduct to minimize their potential losses. An optimal solution would only be realized if each party could tmst the other. 

Once a person knows that he is likely to react in a certain way to specific circumstances, that knowledge becomes part of his decision problem. To use a metaphor—which should not be taken too seriously—his future selves may then appear as constraints on the decision of his current self. He cannot lay plans for later periods and blithely assume that his future selves will implement them. Instead, if he would like to take two drinks at the party but knows that if he does he is likely to take five, he might decide to limit himself to one drink if that will leave his rate of time discounting unaffected. This example supports the commonsense idea that sophistication about one s own undesirable tendencies can... 

As discussed in Chapter 2.2.2 a broad range of criteria have to be considered if an in-depth assessment of individual sites is required. In practice matters are further complicated by the fact that the majority of sites host plants from multiple value chains. In this chapter a uniform decision support tool is developed to ensure consistent evaluations in all instances requiring site assessments. To this end Chapter 4.1 introduces the field of Multiple Criteria Decision Analysis (MCDA). Two different families of tools that could be applied to the decision problem at hand are discussed in greater detail in Chapters 4.2 and 4.3 respectively. As the use of Data Envelopment Analysis (DEA) for multiple criteria decision problems has been proposed in literature, too, the method is introduced in Chapter 4.4. An evaluation model for specialty chemicals production sites developed in cooperation with the industrial partner is presented in Chapter 4.5 and insights from application case studies are reported. 

However, only a subset of the methods available is useful for the decision problem at hand. It is common to differentiate between two types of multiple criteria decision situations (cf. Hwang and Yoon 1981, pp. 2-4 Mustafa and Goh 1996, pp. 169-170) ... 

Structuring a decision problem is an iterative process that ideally involves all major stakeholders and might lead to considerable revisions of the original problem formulation (cf. Roy 1999, pp. 1-6). In practice, the process in itself often is at least as valuable as the recommendation arrived at by later use of a decision analysis model (cf. Belton and Hodgkin 1999, p. 248 Goodwin and Wright 1998, p. 397 Phillips 1986, p. 189). 

Clearly, not all (sub-) objectives of a decision problem are equally important. Consequently, most MADA tools require that the decision maker defines weights for each objective. Common weight elicitation methods with varying degrees of sophistication are introduced below and pitfalls in weight elicitation discussed. 

Using software tools such as VISA (Visual Interactive Sensitivity Analysis, cf. Belton and Vickers 1989) does not only make it more comfortable to analyze large-scale decision problems but especially allows the decision maker to conduct interactive visual sensitivity analyses. Bana e Costa et al. (1999) describe a case example that illustrates the interaction of the MACBETH approach with the VISA software. 

The first step in using the AHP to analyze a decision problem is to hierarchically break down the decision problem (objective) into its constituent components and identify the alternatives to be evaluated. The resulting hierarchy consists of the overall objective (goal) and one or more levels of sub-objectives. The alternatives to be evaluated are added at the lowest level of the hierarchy. According to Saaty (1980, pp. 79-83) a cluster should not contain more than 7 elements because results from psychological tests show that 1+1-2 are the maximum number of elements a person can effectively compare simultaneously. 

In a second phase, alternative sites to locate the consolidated site were evaluated. Four sites were considered with one of the alternatives involving a co-location at an existing site and the others requiring the construction of a new site. To reflect the nature of the decision problem the objective hierarchy described above was modified to include the net present value of the alternatives in addition to the qualitative criteria. On this basis trade-offs between qualitative and quantitative objectives were analyzed. In the case example it turned out that co-locating the plant at the existing site is both the most attractive option financially (mainly because no property rent or acquisition was required) and from a qualitative perspective (mainly due to proximity of the existing site to major customers). It should be noted that no major utilities infrastructure was required for the value chain considered and hence constructing a new site could not be ruled out up front for financial reasons. 

The decision problem is represented by the decision tree in Figure 5, in which open circles represent chance nodes, squares represent decision nodes, and the black circle is a value node. The first decision node is the selection of the sample size n used in the experiment, and c represents the cost per observation. The experiment will generate random data values y that have to be analyzed by an inference method a. The difference between the true state of nature, represented by the fold changes 6 = 9, 9g), and the inference will determine a loss L(-) that is a function of the two decisions n and a, the data, and the experimental costs. There are two choices in this decision problem the optimal sample size and the optimal inference. 

Another interesting interaction problem arises when decisions are to be made at decentralized locations in a system, as at local plants in a large company. Such decentralized decision problems can be solved by the Dantzig-Wolfe decomposition principle (Dl). Although this problem certainly involves interaction, it involves feasibility as well, and so we defer its discussion to the very end of the monograph. 

The unsolvable decision problems are of two types. The first type of the problem is solvable but not with the objects and decision-counting methods we have at our disposal. The example is the unsolvability of the binomical equations in the real axis. But with the Complex Numbers Theory they are solvable describing the physical reality. The help is that the imaginary axis (the new dimension) has been introduced. The another example is the Great Fermat Theorem and its solution (Andrew Wiles 1993 and Ann. Math. 1995). 

Post, E. L. (1943). Formal reductions of the general combinatorial decision problem. American Journal of Mathematics, 65, 197-215. 

A company typically has several projects competing for funds to be invested. The projects are ranked based on their NPV and risk. This is an economic decision problem. However, each project is an optimization problem by itself For a valid comparison among projects, the optimum design is required for each project to have the maximum NPV. 

Moreover, if the groups are not cyclic, one can partition the discrete-logarithm problem into a decision problem whether a discrete logarithm exists and the computation. 

In this contribution, we use the term decision model for both a representation of design rationale [856], i.e., the decisions taken by a designer during a design process that led to a particular artifact, and for a representation of some rules or methods which can guide a designer confronted with a decision problem or which can even solve a decision problem algorithmically. 

The Decision Representation Language (DRL, [808, 809]) is a notation for decision rationale. Its top-level element is the Decision Problem, equivalent to the Question in QOC. Alternatives and Goals in DRL correspond to Options and Criteria, respectively. The outstanding characteristic of DRL is that Claims, i.e., statements which may be judged or evaluated, can be linked in a way that enables to represent complex argumentations in a straightforward... 

Alternatives are options meant to solve a decision problem. For instance, batch and continuous mode as well as their combinations would be Alternatives for the DecisionProblem to choose a mode of operation. Alternatives can be linked to Decision Problems by two different relations. The first one, isAnAlternativePor, does not express any evaluation or even preference of the Alternatives. It is an auxiliary to capture any Alternatives which possibly solve the DecisionProblem, before a suitable Alternative for the problem is eventually evaluated by means of the second relation, IsAGoodAlternativeFor. 

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