Mid Sweden University

The price structure of district heating has been no major scientific issue for the last decades in energy related research. However, today trends in district heating pricing tend to move towards a more customer oriented approach with fixed prices under a longer period, leading to a more complex price structure. If a district heating supplier offers district heating with fixed prices in order to compete with similar electricity offers, the financial risk of the fixed price product is significantly higher than the risk of an ordinary variable cost offer. In contrary to an electricity seller, the district heating company can not transfer all of the risk of fixed prices offer to the financial market, instead the company is thrown upon its own ability to handle the risk by, e.g., hedging its own energy purchase. However, all uncertainties can not be coped with in this manner. Thus, there is a need for a methodology that can be used to estimate the financial risk of different price structures and to value different opportunities to reduce the risk. In this article we propose a methodology, implemented in a prototype software, to evaluate the risk associated with new price structures in district heating.

This paper presents a case of interval decision analysis using a tool that takes advantage of interval probabilities, values, and criteria weights, and is capable of handling comparative relations, i.e. interval statements on differences between variables. These statements are represented as constraints to the solution set and evaluated using a number of different evaluation methods, each serving the decision-maker with different insights of the decision problem. We demonstrate the applicability of the tool in a case study regarding three public infrastructure decision problems which had remained unresolved during a number of years.

This article describes the application of computational decision analytic techniques for a national policy decision. It constitutes an example of the increasing use of modern computational decision methods to assist in decision-making in society. An integrated flood catastrophe model is presented as well as some results of a case study made in the Upper Tisza region in north-eastern Hungary, viz. the Palad-Csecsei basin. Background data was provided through the Hungarian Academy of Sciences and complemented by interviews with different stakeholders in the region. Based upon these data, where a large degree of uncertainty is prevailing, we demonstrate how an implementation of a simulation and decision analytical model can provide insights into the effects of imposing different policy options for a flood risk management program in the region. We focus herein primarily on general options for designing a public/private insurance and reinsurance system for Hungary. It should, however, be emphasized that the main purpose of this article is not to provide any definite recommendations, but rather to present a methodology for handling a set of policy packages with the aim of gaining a consensus among stakeholders.

In investment decision-making in organizations, large values can be at stake. The need for a structured process is evident, not least when several people or interests are involved in the process. We advocate that the use of modern computational decision analysis can improve such investment processes by improving visibility and only requiring reasonably precise input data. The applicability of a structured decision analysis to corporate decision-making is demonstrated in a case study at SCA Transforest, a subdivision to SCA. The decision problem consists of whether a new system for logistic control should be implemented or not. The background information was collected through interviews and the structuring and analysis of the problem was performed using the tool DecideIT, designed for handling situations where uncertainties in input data prevail. The result of the analysis points out a reasonable action, but also shows which aspects are crucial to consider for a reliable result.

The nature of much information available to decision makers is vague and imprecise, be it information for human managers in organisations or for process agents in a distributed computer environment. Several models for handling vague and imprecise information in decision situations have been suggested. In particular, various interval methods have prevailed, i.e. methods based on interval estimates of probabilities and, in some cases, interval utility estimates. Even if these approaches in general are well founded, little has been done to take into consideration the evaluation perspective and, in particular, computational aspects and implementation issues. The purpose of this paper is to demonstrate a tool for handling imprecise information in decision situations. The tool is an implementation of our earlier research focussing on finding fast algorithms for solving bilinear systems of equations together with a graphical user interface supporting the interpretation of evaluations of imprecise data.

This paper presents a multi-criteria decision tool built on theories of uncertainty representation and evaluation. The tool supports interval probabilities, interval values (utili¬ties), interval criteria weights, as well as com¬para¬tive statements, not requiring input on single variables, but rather allowing interval statements on differences between variables. The user input is represented as constraints to the solution set of the variables representing the decision problem. The problem is then evaluated using several available evaluation methods each giving a different perspective on the decision problem modeled. Instead of applying separate sensitivity analyses on top of the evalua¬tion, it tries to incorporate the sensitivity analyses into the repre¬sentation, making uncertainty a first-class citizen in the model. The support of interval and comparative state¬ments, in addition to embedded sensitivity analyses and optionally using separate probabilistic event trees for each criterion, makes the tool, to our knowledge, the first of its kind.

The research efforts of the DECIDE Research Group have resulted in a decision tool capable of handling imprecise information in complex decision situations. Some of the research has been directed towards developing decision analytical algorithms and applying these algorithms in a graphical user interface. The decision tool takes intervals as well as comparative relations as input constraint, and is incorporating sensitivity analyses into the repre¬sentation, instead of applying separate sensitivity analyses on top of the evalua¬tion procedure. However, besides the built-in sensitivity analysis, a second form of sensitivity analysis could be useful in order to point out the most critical probabilities, values, or weights to the decision at hand. This paper deals with the problems and the implementation of interval tornado diagrams in a decision tool supporting interval probabilities, values, criteria weights, as well as com¬para¬tive relations.

In imprecise domains the preference order of the alternatives is not straightforward to establish, due to possible overlapping of expected values among the alternatives. Nevertheless, such rankings are useful in decision analysis applications, as obtaining a ranking of alternatives is a way to gain an overview of the situation. The rankings presented in this paper represent overviews of a preference order of the alternatives based on their respective expected utility. The ranking can be either ordinal, focusing only on the ordering, or cardinal, also taking the differences in expected utility into account. The first set of procedures discussed is a cardinal ranking, which provides the user with expected utility intervals of the evaluated alternatives. This yields a more extensive overview with more detailed information. The second set of procedures discussed ordinal rankings of the alternatives based on three different approaches; 1) contraction based ranking, 2) intersection based ranking, and 3) focal point based ranking with indifference level. Finally, we show that regardless of ranking method their respective maximal elements all conform to the maximal element of the ordinal ranking. Hence, if the intention is to find a maximal element, it is sufficient to use either pointwise cardinal ranking or ordinal ranking with zero as indifference level.

Over the years numerous decision analytical models based on interval estimates of probabilities and utilities have been developed, and a few of these models have also been implemented into software. However, only one software, the Delta approach, are capable of handling probabilities, values and weights simultaneously, and also allow for omparative relations, which are very useful where the information quantity is limited. A major disadvantage with this method is that it only allows for single-level decision trees and cannot non-trivially be extended to handle multi-level decision trees. This paper generalizes the Delta approach into a method for handling multi-level decision trees. The straight-forward way of doing this is by using a multi-linear solver; however, this is very demanding from a computational point of view. The proposed solutions are instead to either recursively collapse the multi-level decision tree into a single-level tree or, preferably, use backward induction, thus mapping it to a bilinear problem. This can be solved by LP-based algorithms, which facilitate reasonable computational effort.

We present a decision tree evaluation method for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled in convex sets of utility and probability measures restricted by closed intervals. Evaluation is done relative to a set of rules, generalizing the concept of admissibility, computationally handled through optimization of aggregated utility functions. Pros and cons of two approaches, and tradeoffs in selecting a utility function, are discussed.