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This paper describes an algorithm for a ship scheduling problem, obtained from a Swedish shipowning company. The algorithm uses the Dantzig-Wolfe decomposition method for linear programming. The subprograms are simple network flow problems that are solved by dynamic programming. The master program in the decomposition algorithm is an LP problem with only zero-one elements in the matrix and the right-hand side. Integer solutions are not guaranteed, but generation and solution of a large number of problems indicates that the frequency of fractional solutions is as small as 1–2 per cent. Problems with about 40 ships and 50 cargoes are solved in about 2.5 minutes on an IBM 7090. In order to resolve the fractional cases, some integer programming experiments have been made. The results will be reported in a forthcoming paper.

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In a previous paper, Appelgren (Appelgren, L. 1969. A column generation algorithm for a ship scheduling problem. Trans. Sci. 3 53–68.), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and-bound algorithm, where the branching is performed on one of the “essential” fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the Dantzig-Wolfe decomposition, since the constraints generated in the master program have to be taken into account in the solution of the subprograms. The success in this case is due to the simple structure of the master LP problem.

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In Sweden ca. 20 000 ha forestland is fertilised each year. By using red-listed and 'signal' bryophytes and lichens as indicators, we investigated whether forest stands planned for fertilisation have a biodiversity value, and thus if restrictions due to conservation aspects are motivated. Species occurrences were registered in detailed line-transect analysis, with a record size of 10 × 10 m, in 74 coniferous forest stands with a mean age of 57 years in East-Central Sweden. On the 230 ha totally surveyed, 10 red-listed and 37 signal species were found. The mean number of records ha -1 of red-listed bryophytes and lichens was 0.26 ha -1 , which is considerably less than previously found in mature production stands and woodland key habitats. Red-listed species were found in 31% of the stands and signal species in 95%. More than 70% of all records of red-listed species and 30% of the records of the signal species were found in moist micro-sites. If rare bryophytes and lichens are to be preserved in fertilisation stands, improved instructions regarding avoidance of important micro-sites are needed.

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