### 2015-12

by Bronnikov, S.; Dolgui, A., Lazarev, A.; Morozov, N.; Petrov, A.; Sadykov, R.; Sologub, A.; Werner, F.; Yadrentsev, D.; Musatova, E.; Khusnullin, N..

**Series:** 2015-12, Preprints

- MSC:
- 90C27 Combinatorial optimization
- 90C10 Integer programming
- 90B35 Scheduling theory, deterministic

**Abstract:**

We consider the problem of planning the ISS cosmonaut training with different objectives. A pre-defined set of minimum qualification levels should be distributed between the crew members with minimum training time differences, training expenses or a maximum of the training level with a limitation of the budget.

First, a description of the cosmonaut training process is given. Then four models are considered for the volume planning problem. The objective of the first model is to minimize the differences between the total time of the preparation of all crew members, the objective of the second one is to minimize the training expenses with a limitation of the training level, and the objective of the third one is to maximize the training level with a limited budget. The fourth model considers the problem as an n-partition problem.

Then two models are considered for the calendar planning problem.

For the volume planning problem, two algorithms are presented. The first one is a heuristic with a complexity of O(n) operations. The second one consists of a heuristic and exact parts, and it is based on the n-partition problem approach.

**Keywords:**

Planning, Scheduling, Integer programming, Heuristic algorithms, Cosmonaut training