Design and testing of stand-specific bucking instructions for use on modern cut-to-length harvesters

This study addresses three important issues in tree bucking optimization in the context of cut-to-length harvesting. (1) Would the fit between the log demand and log output distributions be better if the price and/or demand matrices controlling the bucking decisions on modern cut-to-length harvesters were adjusted to the unique conditions of each individual stand? (2) In what ways can we generate stand and product specific price and demand matrices? (3) What alternatives do we have to measure the fit between the log demand and log output distributions, and what would be an ideal goodness-of-fit measure? Three iterative search systems were developed for seeking stand-specific price and demand matrix sets: (1) A fuzzy logic control system for calibrating the price matrix of one log product for one stand at a time (the stand-level one-product approach); (2) a genetic algorithm system for adjusting the price matrices of one log product in parallel for several stands (the forest-level one-product approach); and (3) a genetic algorithm system for dividing the overall demand matrix of each of the several log products into stand-specific sub-demands simultaneously for several stands and products (the forest-level multi-product approach). The stem material used for testing the performance of the stand-specific price and demand matrices against that of the reference matrices was comprised of 9 155 Norway spruce (Picea abies (L.) Karst.) sawlog stems gathered by harvesters from 15 mature spruce-dominated stands in southern Finland. The reference price and demand matrices were either direct copies or slightly modified versions of those used by two Finnish sawmilling companies. Two types of stand-specific bucking matrices were compiled for each log product. One was from the harvester-collected stem profiles and the other was from the pre-harvest inventory data. Four goodness-of-fit measures were analyzed for their appropriateness in determining the similarity between the log demand and log output distributions: (1) the apportionment degree (index), (2) the chi-square statistic, (3) Laspeyres quantity index, and (4) the price-weighted apportionment degree. The study confirmed that any improvement in the fit between the log demand and log output distributions can only be realized at the expense of log volumes produced. Stand-level pre-control of price matrices was found to be advantageous, provided the control is done with perfect stem data. Forest-level pre-control of price matrices resulted in no improvement in the cumulative apportionment degree. Cutting stands under the control of stand-specific demand matrices yielded a better total fit between the demand and output matrices at the forest level than was obtained by cutting each stand with non-stand-specific reference matrices. The theoretical and experimental analyses suggest that none of the three alternative goodness-of-fit measures clearly outperforms the traditional apportionment degree measure. Keywords: harvesting, tree bucking optimization, simulation, fuzzy control, genetic algorithms, goodness-of-fit

Simulating and Forecasting the Demand for New Consumer Durables

A diffusion/replacement model for new consumer durables designed to be used as a long-term forecasting tool is developed. The model simulates new demand as well as replacement demand over time. The model is called DEMSIM and is built upon a counteractive adoption model specifying the basic forces affecting the adoption behaviour of individual consumers. These forces are the promoting forces and the resisting forces. The promoting forces are further divided into internal and external influences. These influences are operationalized within a multi-segmental diffusion model generating the adoption behaviour of the consumers in each segment as an expected value. This diffusion model is combined with a replacement model built upon the same segmental structure as the diffusion model. This model generates, in turn, the expected replacement behaviour in each segment. To be able to use DEMSIM as a forecasting tool in early stages of a diffusion process estimates of the model parameters are needed as soon as possible after product launch. However, traditional statistical techniques are not very helpful in estimating such parameters in early stages of a diffusion process. To enable early parameter calibration an optimization algorithm is developed by which the main parameters of the diffusion model can be estimated on the basis of very few sales observations. The optimization is carried out in iterative simulation runs. Empirical validations using the optimization algorithm reveal that the diffusion model performs well in early long-term sales forecasts, especially as it comes to the timing of future sales peaks.

Kalman Filter Algorithm for Rating and Prediction in Basketball

The Thesis presents a state-space model for a basketball league and a Kalman filter algorithm for the estimation of the state of the league. In the state-space model, each of the basketball teams is associated with a rating that represents its strength compared to the other teams. The ratings are assumed to evolve in time following a stochastic process with independent Gaussian increments. The estimation of the team ratings is based on the observed game scores that are assumed to depend linearly on the true strengths of the teams and independent Gaussian noise. The team ratings are estimated using a recursive Kalman filter algorithm that produces least squares optimal estimates for the team strengths and predictions for the scores of the future games. Additionally, if the Gaussianity assumption holds, the predictions given by the Kalman filter maximize the likelihood of the observed scores. The team ratings allow probabilistic inference about the ranking of the teams and their relative strengths as well as about the teams’ winning probabilities in future games. The predictions about the winners of the games are correct 65-70% of the time. The team ratings explain 16% of the random variation observed in the game scores. Furthermore, the winning probabilities given by the model are concurrent with the observed scores. The state-space model includes four independent parameters that involve the variances of noise terms and the home court advantage observed in the scores. The Thesis presents the estimation of these parameters using the maximum likelihood method as well as using other techniques. The Thesis also gives various example analyses related to the American professional basketball league, i.e., National Basketball Association (NBA), and regular seasons played in year 2005 through 2010. Additionally, the season 2009-2010 is discussed in full detail, including the playoffs.

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds. We apply our results to give a distributed (2 + ε)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

An optimal local approximation algorithm for max-min linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.