Planar subgraphs without low-degree nodes

We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k. If G is a unit disk graph, the problem is trivial to solve for k = 1. We show that even the slightest deviation from the trivial case (e.g., quasi unit disk graphs or k = 1) leads to NP-hard problems.

Consumers' attitudes towards food prices

High food prices can be a barrier to healthy eating because some of the food products may be perceived as expensive. Understanding the role of price in food purchase situations is important, but only a few studies document attitudes towards expensiveness or cheapness in foods. In this thesis, the role of food price in food choice and consumers attitudes towards food prices were investigated and the aim was to measure the food price attitudes. Food price attitudes were hypothesized to have an impact on consumers willingness to pay judgements and their willingness to buy premium-priced food products. First, using qualitative data consisting of 40 thematic interviews the experiences of the expensiveness and cheapness in foods were explored by using functional food products as a target product category. Second, a Food Price Attitude Scale was developed using four quantitative surveys representing Finnish consumers (2001 N=1158; 2002 N=1156; 2004a N=1113; 2004b N=1027). Food price attitudes were confirmed to compose a multidimensional construct and consumers may perceive positive and negative attitudes towards both high and low food prices. Finnish consumers were clustered into four groups based on their food price attitudes. In the first group, 29% of respondents were negative towards high food prices and they were willing to seek low food prices, whereas respondents in another group (22%) were positive towards high food prices. Additionally, in the third group consumers (17%) were willing to pay for high quality but still looked for low food prices. In the fourth group, consumers (32%) were willing to look for low food prices, unwilling to pay for high quality, but high-priced food was appreciated if offered to others. It was found in qualitative data that consumers willingness to accept high prices in foods was connected to price fairness and to justifications. Feelings of fairness or unfairness might be a core element of food price attitudes. Using quantitative methods, it was confirmed that positive attitudes towards high food prices in terms of high quality enhanced consumers willingness to buy food products with certain benefits (e.g., a health claim). Additionally, the favourable attitude towards low food prices lowered the willingness to pay estimates. This type of tendency, however, can create a possible bias in small convenient samples. In the food price-related research, it is advisable to take into account food price attitudes as possible background variables. The Food Price Attitude Scale needs further development to increase construct validity even though, in the present study, it was shown to be a reliable measure with good predictive and discriminant validity. The theoretical and managerial implications of the results for a better understanding of the role of price in consumers food purchases are discussed.

Harvesting undelimbed Scots pine (Pinus sylvestris L.) from first thinnings for integrated production of kraft pulp and energy

The present study evaluates the feasibility of undelimbed Scots pine (Pinus sylvestris L.) for integrated production of pulp and energy in a kraft pulp mill from the technical, economic and environmental points of view, focusing on the potential of bundle harvesting. The feasibility of tree sections for pulp production was tested by conducting an industrial wood-handling experiment, laboratory cooking and bleaching trials, using conventional small-diameter Scots pine pulpwood as a reference. These trials showed that undelimbed Scots pine sections can be processed in favourable conditions as a blend with conventional small-diameter pulpwood without reducing the pulp quality. However, fibre losses at various phases of the process may increase when using undelimbed material. In the economic evaluation, both pulp production and wood procurement costs were considered, using the relative wood paying capability of a kraft pulp mill as a determinant. The calculations were made for three Scots pine first-thinning stands with the breast-height diameter of the removal (6 12 cm) as the main distinctive factor. The supply chains included in the comparison were based on cut-to-length harvesting, whole-tree harvesting and bundle harvesting (whole-tree bundling). With the current ratio of pulp and energy prices, the wood paying capability declines with an increase in the proportion of the energy fraction of the raw material. The supply system based on the cut-to-length method was the most efficient option, resulting in the highest residual value at stump in most cases. A decline in the pulp price and an increase in the energy price improved the competitiveness of the whole-tree systems. With short truck transportation distances and low pulp prices, however, the harvesting of loose whole trees can result in higher residual value at stump in small-diameter stands. While savings in transportation costs did not compensate for the high cutting and compaction costs by the second prototype of the bundle harvester, an increase in transportation distances improved its competitiveness. Since harvesting undelimbed assortments increases nutrient export from the site, which can affect soil productivity, the whole-tree alternatives included in the present study cannot be recommended on infertile peatlands and mineral soils. The harvesting of loose whole trees or bundled whole trees implies a reduction in protective logging residues and an increase in site traffic or payloads. These factors increase the risk of soil damage, especially on peat soils with poor bearing capacity. Within the wood procurement parameters which were examined, the CO2 emissions of the supply systems varied from 13 27 kg m3. Compaction of whole trees into bundles reduced emissions from transportation by 30 39%, but these reductions were insufficient to compensate for the increased emissions from cutting and compaction.