Markku Kallio

A class of methods for linear programming

A class of methods is presented for solving standard linear programming problems. Like the simplex method, these methods move from one feasible solution to another at each iteration, improving the objective function as they go. Each such feasible solution is also associated with a basis. However, this feasible solution need not be an extreme point and the basic solution corresponding to the associated basis need not be feasible. Nevertheless, an optimal solution, if one exists, is found in a finite number of iterations (under nondegeneracy). An important example of a method in the class is the reduced gradient method with a slight modification regarding selection of the entering variable.

Estimation methods for choice-based conjoint analysis of consumer preferences

Conjoint analysis, a preference measurement method typical in marketing research, has gradually expanded to other disciplines. Choice-based conjoint analysis (CBC) is currently the most popular type. Very few alternative estimation approaches have been suggested since the introduction of the Hierarchical Bayes (HB) method for estimating CBC utility functions. Studies that compare the performance of more than one of the proposed approaches and the HB are almost non- existing. We compare the performance of four published optimization-based procedures and additionally we introduce a new one called CP. The CP is an estimation approach based on convex penalty minimization. In comparison with HB as the benchmark we use eight field data sets. We base the performance comparisons on holdout validation, i.e. predictive performance. Among the optimization based procedures CP performs best. We run simulations to compare the extent to which CP and HB can recover the true utilities. With the field data on the average, the CP and HB results are equally good. However, depending on the problem characteristics, one may perform better than the other. In terms of average performance, the other four methods were inferior to CP and HB.

Bank branch sales evaluation using extended value efficiency analysis

This article results from our collaborative project with a Finnish bank aiming to evaluate the sales performance of bank branches. The management wishes to evaluate the branches’ ability to generate profit, which rules out the pure technical efficiency considerations. The branches operate in heterogeneous environments. We deal with the heterogeneity by subdividing the branches according to the bank specification into overlapping clusters and analyze each cluster separately. The prices of the branch outputs are hard to assess as the results from the sales efforts can only be observed with long delays. We employ benchmark units similarly as in value efficiency analysis (VEA). However, we extend VEA in two ways. First, in standard VEA the benchmark unit is assumed to yield the maximum profit among the set of feasible technologies; instead, our benchmark technology may or may not be in the feasible set. Second, we consider efficiency tests employing a benchmark with respect to both profit and return. We propose a solution strategy for these extensions. The bank uses the study to support decisions concerning new branches, changes in the operations of inefficient branches, and actions aiming to more flexible deployment of the staff.

Large-Scale Convex Optimization Via Saddle Point Computation

This article proposes large-scale convex optimization problems to be solved via sad dle points of the standard Lagrangian. A recent approach for saddle point computation is specialized, by way of a specific perturbation technique and unique scaling method, to convex optimization problems with differentiable objective and constraint funct ions. In each iteration the update directions for primal and dual variables are determined by gradients of the Lagrangian. These gradients are evaluated at perturbed points that are generated from current points via auxiliary mappings. The resulting algorithm suits massively parallel computing, though in this article we consider only a serial implementation. We test a version of our code embedded within GAMS on 16 nonlinear problems, which are mainly large. These models arise from multistage optimization of economic systems. For larger problems with adequate precision requirements, our implementation appears faster than MINOS.

Real options valuation of forest plantation investments in Brazil

In this paper, we consider investments in eucalyptus plantations in Brazil. For such projects, we discuss real options valuation in the place conventional methods such as IRR or NPV, possibly with CAPM. Traditionally, real options valuation assumes complete markets and neglects market imperfections. Yet, market frictions, such as transaction costs, interest rate spreads, and restricted short positions, can play an important role. We extend real options valuation to allow incomplete and imperfect markets. The value is obtained as a competitive price, given markets of competing investment opportunities, such as real and financial assets. Under perfect and complete markets, such valuation method is consistent with conventional real options theory. Stochastic programming and standard software is used for valuation of eucalyptus plantations. We estimate the underlying interdependent diffusion processes of stock market, interest rates, exchange rates and pulpwood price, and derive novel expressions of stochastic integrals to be employed in scenario generation for discrete time stochastic programming.

Likelihood estimation of consumer preferences in choice-based conjoint analysis

In marketing research the measurement of individual preferences and assessment of utility functions have long traditions. Conjoint analysis, and particularly choice-based conjoint analysis (CBC), is frequently employed for such measurement. The world today appears increasingly customer or user oriented wherefore research intensity in conjoint analysis is rapidly increasing in various fields, OR/MS being no exception. Although several optimization based approaches have been suggested since the introduction of the Hierarchical Bayes (HB) method for estimating CBC utility functions, recent comparisons indicate that challenging HB is hard. Based on likelihood maximization we propose a method called LM and compare its performance with HB using twelve field data sets. Performance comparisons are based on holdout validation, i.e. predictive performance. Average performance of LM indicates an improvement over HB and the difference is statistically significant. We also use simulation based data sets to compare the performance for parameter recovery. In terms of both predictive performance and RMSE a smaller number of questions in CBC appears to favor LM over HB.

Nonparametric Methods for Evaluating Economic Efficiency and Imperfect Competition

This article unifies and extends ideas from nonparametric production analysis and DEA for testing organizational efficiency. We show how the admissible price set can be restricted to account for prior information on prices. These restrictions may relate prices to input and output quantities in order to test noncompetitive behavior of the evaluated decision making unit. While the resulting efficiency tests cannot always be cast into linear programming problems, we discuss various solution strategies for the tests. Thereby we consider the question when does local optimality of the result guarantee global optimality. We also show how the decision makers preferences, for example ranking information, can be adopted into DEA models in a simple manner. Finally, the approach with price restrictions is illustrated with an application to test noncompetitive behavior of the pulp and paper industries in Finland.

Triangular Factorization and Generalized Upper Bounding Techniques

We develop a compact inverse method for linear programming problems having block triangular or sparse constraint matrices. Special cases of the method are, for example, the generalized upper bounding technique and its extensions. For these methods we show how a triangular factorization can be used for the working basis and block bases. In this case and even if the constraint matrix has no special structure our method becomes a variation of the revised simplex method using a single triangular factorization of the basis. However, the updating procedure of the triangular factors differs from existing ones in a way that implies that certain structures are exploited naturally.

Decomposition of arborescent linear programs

We apply what we call sequential projection to reformulate certain linear programs as recursive optimization problems. We then apply the standard idea of approximating the return function at each stage of the recursion by using inner (or outer) linearization, and iteratively refining the approximation until the original linear program has been solved. The contribution of the paper lies in its unification of existing decomposition approaches and in showing that they can be generalized to apply to what we call arborescent linear programs.

Optimal management of naturally regenerating uneven-aged forests

A shift from even-aged forest management to uneven-aged management practices leads to a problem rather different from the existing straightforward practice that follows a rotation cycle of artificial regeneration, thinning of inferior trees and a clearcut. A lack of realistic models and methods suggesting how to manage uneven-aged stands in a way that is economically viable and ecologically sustainable creates difficulties in adopting this new management practice. To tackle this problem, we make a two-fold contribution in this paper. The first contribution is the proposal of an algorithm that is able to handle a realistic uneven-aged stand management model that is otherwise computationally tedious and intractable. The model considered in this paper is an empirically estimated size-structured ecological model for uneven-aged spruce forests. The second contribution is on the sensitivity analysis of the forest model with respect to a number of important parameters. The analysis provides us an insight into the behavior of the uneven-aged forest model.