Solutions to group work problems

All necessary files have been collected in a ZIP-file called NOVA_DYN.ZIP , which may be downloaded and unzipped in an appropriate directory. It contains the demonstration program (HIERARKI.EXE) as well as all specified models and Excell files used in the group work session.

1. A stage in the main process begins right after weaning of a first parity ewe and runs during the entire life time of the present sheep, includes the replacement and ends right after weaning of the first litter of the replacement ewe. A state is defined as the genetic merit of the sheep in question.
2. Definition of subprocesses:
   • Stage: Stage n of a subprocess begins right after weaning at parity n and ends right after weaning at parity n+1 if the sheep is kept. If the sheep is replaced, stage length is zero.
   • State variables: The general pattern is that a state at stage n is defined by the value of two state variables: a. Litter size (0, 1 or 2) at weaning, parity n and b. Litter size (0, 1 or 2) at weaning, parity n-1. Thus, initially 9 states are defined at each stage. In addition, we shall define an artificial 10th state representing a situation where the present sheep has been replaced. According to these principles the states of a subprocess are defined as follows:
     • Stage 1:
       1. No lambs weaned, present parity.
       2. 1 lamb weaned, present parity
       3. 2 lambs weaned, present parity
     • Stages 2-9:
       1. 0 lamb weaned, previous parity - 0 lamb weaned, present parity
       2. 0 lamb weaned, previous parity - 1 lamb weaned, present parity
       3. 0 lamb weaned, previous parity - 2 lamb weaned, present parity
       4. 1 lamb weaned, previous parity - 0 lamb weaned, present parity
       5. 1 lamb weaned, previous parity - 1 lamb weaned, present parity
       6. 1 lamb weaned, previous parity - 2 lamb weaned, present parity
       7. 2 lamb weaned, previous parity - 0 lamb weaned, present parity
       8. 2 lamb weaned, previous parity - 1 lamb weaned, present parity
       9. 2 lamb weaned, previous parity - 2 lamb weaned, present parity
       10. Artificial state: Ewe has been replaced.
     • Stage 10:
       1. Artificial state: Ewe has been replaced.
   • Actions: 2 alternative actions are defined: 1 = "Keep" and 2 = "Replace". If the ewe is kept, the stage length is 1 year, and the reward is the expected net returns during the stage. In case of replacement, the stage length is zero. The reward is then the carcass value of the ewe, and the process transfers directly to state 10 (the artificial state). In state 10, the stage lenths are zero, and the rewards are zero too. No decisions are defined in state 10 (i.e. both decisions have exactly the same consequences).
3. Since the genetic merit of the next ewe is independent of the present ewe, the transition probabilities of the main process are all equal to 1/3.
4. The Excell spreadsheet is used. The file 'SHEEP1.XLS' contains the spreadsheet used. The final solution is shown in the file 'SHEEP2.XLS' (both files are included in the ZIP-file 'NOVA_DYN.ZIP'.
5. See Problem 4.
6. If the ewe is kept, the stage length is 1 year. In case of replacement, the stage length is zero. In state 10, the stage lenths are zero.
7. Use the demonstration program to load the file SHEEP (item "Get hierarchic design from disk"). All parameter values for the subprocesses 2 and 3 have been entered in advance. Enter the values for subprocess no. 1 (low genetic merit). The result is shown in the files SHEEP-D (discounting criterion) and SHEEP-A (average criterion). All files are included in the ZIP-file 'NOVA_DYN.ZIP'.

8. Optimal sheep replacement policy under the discounting criterion

9. Optimal sheep replacement policy under the average criterion and calculated ratios

10. See Problem 9.
11. See Problem 9.
12. See Problem 9.
13. See Problem 9.

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