Risto Lahdelma

Using multicriteria methods in environmental planning and management.

In environmental planning and decision processes several alternatives are analyzed in terms of multiple noncommensurate criteria, and many different stakeholders with conflicting preferences are involved. Based on our experience in real-life applications, we discuss how multicriteria decision aid (MCDA) methods can be used successfully in such processes. MCDA methods support these processes by providing a framework for collecting, storing, and processing all relevant information, thus making the decision process traceable and transparent. It is therefore possible to understand and explain why, under several conflicting preferences, a particular decision was made. The MCDA framework also makes the requirements for new information explicit, thus supporting the allocation of resources for the process.

SMAA - Stochastic multiobjective acceptability analysis

Stochastic multiobjective acceptability analysis (SMAA) is a multicriteria decision support technique for multiple decision makers based on exploring the weight space. Inaccurate or uncertain input data can be represented as probability distributions. In SMAA the decision makers need not express their preferences explicitly or implicitly; instead the technique analyses what kind of valuations would make each alternative the preferred one. The method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative, a central weight vector representing the typical valuations resulting in that decision, and a confidence factor measuring whether the input data is accurate enough for making an informed decision.

Implementing stochastic multicriteria acceptability analysis

Abstract Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision. The computations in SMAA require the evaluation of multidimensional integrals that must in practice be computed numerically. In this paper we present efficient methods for performing the computations through Monte Carlo simulation, analyze the complexity, and assess the accuracy of the presented algorithms. We also test the efficiency of these methods empirically. Based on the tests, the implementation is fast enough to analyze typical-sized discrete problems interactively within seconds. Due to almost linear time complexity, the method is also suitable for analysing very large decision problems, for example, discrete approximations of continuous decision problems.

Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA)

Abstract We suggest a method for providing descriptive information about the acceptability of decision alternatives in discrete co-operative group decision-making problems. The new SMAA-O method is a variant of the stochastic multicriteria acceptability analysis (SMAA). SMAA-O is designed for problems where criteria information for some or all criteria is ordinal; that is, experts (or decision-makers) have ranked the alternatives according to each (ordinal) criterion. Considerable savings can be obtained if rank information for some or all the criteria is sufficient for making decisions without significant loss of quality. The approach is particularly useful for group decision making when the group can agree on the use of an additive decision model but only partial preference information, or none at all, is available.

An efficient linear programming algorithm for combined heat and power production

Abstract Combined heat and power (CHP) production is an increasingly important energy production technology. CHP production is usually applied in back pressure plants, where the heat and power generation follows a joint characteristic. A CHP system may also comprise separate heat and power production facilities. Cost-efficient operation of a CHP system can be planned using an optimisation model based on hourly load forecasts. A long-term optimisation model decomposes into thousands of hourly models, which can be formulated as linear programming (LP) problems. We model the hourly CHP operation as an LP problem with a special structure and present the specialised Power Simplex algorithm that utilises this structure efficiently. The basis can be organised as an identity matrix and a small block of non-zero coefficients. There are only a few different types of non-zero blocks, and extremely fast inversion procedures have been designed for each type. The performance of Power Simplex is compared with realistic models against a non-sparse tabular Simplex algorithm and the LP2 software based on the sparse Revised Simplex algorithm using the product form of inverse. At its best, Power Simplex performs from 21 to 190 times faster than the tabular Simplex. Power Simplex has been implemented as part of the EHTO NEXUS energy optimisation system, which is in commercial use at several Finnish energy companies.

A stochastic method for robustness analysis in sorting problems

ELECTRE TRI is a multiple criteria decision aiding sorting method with a history of successful real-life applications. In ELECTRE TRI, values for certain parameters have to be provided. We propose a new method, SMAA-TRI, that is based on stochastic multicriteria acceptability analysis (SMAA), for analyzing the stability of such parameters. The stability analysis can be used for deriving robust conclusions. SMAA-TRI allows ELECTRE TRI to be used with uncertain, arbitrarily distributed values for weights, the lambda cutting level, and profiles. The method consists of analyzing finite spaces of arbitrarily distributed parameter values. Monte Carlo simulation is applied in this in order to describe for each alternative the share of parameter values that have it assigned to different categories. We show the real-life applicability by re-analyzing a case study in the field of risk assessment.

Data envelopment analysis: Visualizing the results

Abstract Data envelopment analysis (DEA) is a useful technique for assessing the relative efficiency of a set of decision-making units. Although widely known and used by practitioners, its presentation in the managerial community is difficult without suitable visualization techniques. This article examines various two-dimensional charts for illustrating the DEA efficiency results. The presented charts have been drawn using an experimental DEA software tool, AskDEA, developed by the authors.

Fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production

Optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain. The uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product. In this paper, we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product, the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints. Based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution. Simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers. There is a tradeoff between failure risk and material cost. The presented approach applies also for other scrap-based production processes.

A multiple criteria decision model for analyzing and choosing among different development patterns for the Helsinki cargo harbor

Abstract This paper describes a real application of a multicriteria approach to choosing among different options for developing the Helsinki harbor. In addition to the environmental impact assessment procedure, an analysis of the alternatives using the SMAA-method (Stochastic Multiobjective Acceptability Analysis) is carried out. The method applied here has been developed for situations in which the use of decision-makers’ preference information is not possible. Instead, the problem is described by typical weight vectors leading to each solution, taking into account the evident uncertainty embedded in the criteria values.

Determining the implementation order of a general plan by using a multicriteria method

We describe a real-life application of a new multicriteria method in the context of assisting the decision-making for a general plan in the municipality of Kirkkonummi in Uusimaa, Finland. At the time our group started working on the problem, a proposal for an overall plan had already been completed, but the order in which different regional parts of the plan should be implemented needed to be considered based on the environmental impact assessment (EIA) procedure. The EIA procedure generated a large amount of data about the different impacts of the alternatives. For this group decision making problem we developed the SMAA-3 decision support method which does not require any explicit preference information from the decision makers during the procedure. The uncertainty of the basic data is modelled using ELECTRE III-type pseudo-criteria with preference and indifference thresholds.