Existing models for recruitment, tree growth and survival were used to simulate stand dynamics in alternative management schedules. The amount of established regeneration in a plantation site was predicted with the models of Miina and Saksa (20062008). Their models predict the number of surviving individuals of the plantation species, as well as the amounts of natural regeneration of pine, spruce, birch, and hardwoods other than birch. The prediction depends on site characteristics, site preparation method and the used regeneration method (planting, sowing, or natural regeneration from seed or shelter trees).
In addition to the number of seedlings, the models of Miina and Saksa also predict the mean height of the seedlings three years after planting. Since the residual standard deviations of the height models are also reported, it is possible to generate initial size variation among seedlings. In this study, 15 seedlings of different sizes (15 size classes) were generated to represent the planted species (spruce or pine). In addition, 5 seedlings were generated to represent the other conifer (pine or spruce), 5 seedlings for silver birch (B. pendula), 5 seedlings for pubescent birch (B. pubescent), and 5 seedlings for hardwoods other than birch. As a result, a 3yearold seedling stand corresponding to an average conifer plantation on medium site was obtained.
A tending treatment was simulated at the age of 7 years. It was first assumed that species other than the planted one are completely removed. Then, other optimizations were conducted in which a mixture of pine, spruce and birch was left to continue growing. Hardwoods other than birch were removed completely. Trees were left in all size classes of the plantation species but smaller classes were thinned more than larger ones. Other species were treated with uniform thinning. As a result, the tending treatment reduced the size variation of seedlings only slightly. The tending of the spruce plantation left 330 pines, 1028 spruces, 330 silver birches and 330 pubescent birches per hectare. In the pine plantation, 1525 pines, 300 spruces, 90 silver birches and 90 pubescent birches were kept. The number of birches was lower because of the adverse effect of a dense birch cover on pine development. This is because birches easily overtop pines, which reduces the productivity of the stand. This was also noted in preliminary simulations.
The further development of trees was predicted with the models of Pukkala et al. (2013). Their model set consists of individualtree diameter increment model, individualtree survival model, and models for ingrowth. The ingrowth models are based on stands in which the basalareaweighted mean diameter is at least 10 cm. Accordingly, in the simulations of this study, ingrowth was predicted once the mean tree diameter exceeded 10 cm. Species interactions are included in all models. The diameter increment models predict, among other things, that pine and birch competitors reduce the growth of spruce less than spruce competitors. The ingrowth models predict spruce ingrowth also in pure pine and birch stands, which corresponds to the natural dynamics of boreal forests.
The assortment volumes of removed trees were calculated using the taper models of Laasasenaho (1982). Tree height was required in volume calculations and it was predicted with the models of Pukkala et al. (2009). The top diameters of timber assortments were as follows:

Pine: 15 cm for saw log, 8 cm for pulpwood

Spruce: 16 cm for saw log, 8 cm for pulpwood

Birch: 16 cm for saw log, 9 cm for pulpwood
The crosscutting of each removed tree was simulated, taking into account the minimum piece lengths of different timber assortments. A certain percentage of saw log volume was moved to the pulpwood component to mimic the effect of quality defects. The deduction in saw log volume was 10% for pine, 5% for spruce, 15% for silver birch and 20% for pubescent birch.
Roadside timber prices were used to calculate the income from harvests. The roadside prices were 60 €/m^{3} for pine and spruce saw log, 50 €/m^{3} for birch saw log, and 30 €/m^{3} for pulpwood. To calculate net income, harvesting costs were subtracted from the roadside value of harvested trees. The models of Valsta (1992) were used. According to these models the harvesting cost per removed cubic meter decreases with increasing mean size of harvested trees and increasing volume (m^{3}/ha) of the harvest. Thinnings have a higher harvesting cost per cubic meter than clearfelling if the removed volume and mean size of removed trees are the same. Stand establishment cost in year 0 was 1400 €/ha. The tending cost in year 7 depended on the number and diameter of the removed seedlings, but it was close to 270 €/ha in all cases.
A set of optimizations was done for spruce and pine plantations growing on medium site (mesic site, Myrtillus type). This site type is by far the most common fertility class in the southern part of Finland, covering almost 50% of productive forest land. All the main tree species of Finland grow well in this site, making it possible to manage the forest in many different ways.
The following set of optimizations was as conducted:

1.
All species except the planted one were removed in the tending treatment of the young stand; two thinnings were conducted during the rotation; at most 40% of stand basal area could be removed in thinning; thinnings were conducted as low thinning.

2.
Otherwise the same but thinning type was not restricted to low thinning.

3.
Otherwise similar to alternative 2 except that thinning intensity was not restricted.

4.
Otherwise similar to alternative 3 except that a mixture of pine, spruce, silver birch and pubescent birch was left in the tending treatment of the young stand (at year 7).

5.
Otherwise similar to alternative 4 except that ingrowth was simulated and the number of thinnings was increased from two to three.

6.
Otherwise similar to alternative 5 except that the number of thinnings was increased from three to four.

7.
Otherwise similar to alternative 6 except that the number of thinnings was increased from four to five.
Two thinnings were used in alternatives 1–4 since it has been found that additional thinnings no longer increase the net present value when stand management is optimized without simulating ingrowth (e.g., Pukkala 2006). Alternative 1 corresponds to optimizing the type silviculture that was recommended in Finland for several decades (Anonym 2006). High thinning was forbidden and thinnings could not be too heavy. In the optimization, low thinning was forced by penalizing the solution if the mean tree diameter increased less than 5% as the result of thinning.
Alternative 2 reflects the current situation in which high thinning is permitted but there are regulations that prevent very heavy thinnings. Alternative 3 is a step forward to greater freedom and flexibility, and it may lead to solutions that violate the current forest law of Finland. Henceforth, alternative 1 is referred to as the “lowthinning” alternative and the other alternatives are called as “freethinning” alternatives.
Alternative 4 recognizes the fact that developing mixed stands is often possible even if only one species was planted. Alternatives 5–7 reflect the recent acceptance and increased use of continuous cover management. They allow selective felling and developing the new tree generation from advance regeneration.
The type of thinning was included in the optimization problems by specifying the harvest percentage separately for three different diameter classes. The classes were 10–14 cm, 14–20 cm and > 20 cm for conifers and 10–16 cm, 16–22 cm and > 22 cm for birch. The classification was based on calculations of the absolute and relative value increments of different tree sizes. Trees less than 10 cm in dbh have very high relative value increment during the coming 5–15 years. On the other hand, the road side value of these trees is small and their harvesting is costly. Therefore, it was assumed that trees smaller than 10 cm should never be removed in thinnings. Another diameter class for which the value increment is good is 14–20 cm for conifers and 16–22 cm for birches. This is because trees of this size are approaching the saw log size and their value will therefore increase rapidly. The remaining two diameter classes, 10–14 am (10–16 cm in birch) and > 20 cm (> 22 cm), have much lower relative value increments, which means that removing trees from these classes does not reduce the value increment of the stand as much as cutting trees that are approaching a value threshold.
Based of this rationale, a thinning treatment was specified with three harvest percentages that were optimized separately for pine, spruce, silver birch and pubescent birch. The number of years since planting (first thinning) or previous cutting (other thinnings) defined the timing of the thinning treatment. Therefore, the number of optimized decision variables was 13 (4 × 3 + 1) for each thinning treatment and 1 for the final felling (number of years since the last thinning). A management schedule with 5 thinnings included 5 × 13 + 1 = 66 optimized variables.
The used optimization method was the direct search algorithm proposed by Hooke and Jeeves (1961). In each problem, the direct search was repeated 10 times and the best solution was selected. Every search was started from the best of 100–700 random combinations on decision variables. The number of random searches was increased with increasing number of optimized variables. NPV to infinity (i.e., soil expectation value) with 3% discount rate was maximized in all problems. When calculating the NPV, it was assumed that rotations similar to the simulated one are repeated to infinity.