1

Fig. 1. Material and process flow in log yard.

2

Fig. 2. Original shaped log yard.

3

Fig. 3. Rearranged log yard.

Table 1. Minimal and maximal values of volume, number of moves and capacity in the new and original problem with 28 and 42 storage boxes.
  Minimum Maximum
Va 5.46 12.20
Na 21 68
C28 4.1 12.3
C42 4.0 10.6
Table 2. Comparable solutions of the log yard and box assignment problem.
Assortment Number
of trips 		Original Excel
double-stage 		Xpress
double-stage 		Xpress
partition 		Xpress
partition
1 - 1/- 1/- 1/- 1/- 1/-
2 - 2/- 2/- 2/- 2/- 2/-
3 - 3/- 3/- 3/- 3/- 3/-
4 68 12/12 a 17/16 c 18/18 a 18/18 a 18/18 a, 18c
5 54 8/8 a 11/18 c 14/18 c 17/17 b, 18 c 17/17 b, 18d
6 44 2/2 a 9/17 b 17/17 b 15/17 a 15/17 a
7 56 16/16 a 18/18 a 16/16 a 16/16 a 16/16 a, 18 b
8 44 10/10 a 10/14 c 12/16 c 11/13 a 12/14 b, 16 c
9 37 4/4 a 8/12 c 10/14 c 12/16 c 13/6 c, 15 a
10 46 17/17 a, b 16/16 a 11/14 a 14/14 a 14/14 a, 16 b
11 36 9/10 c 7/10 a 8/12 c 10/14 c 9/12 a, 16 d
12 30 6/6 a 6/10 c 6/10 c 6/10 c 11/8 c, 13 a
13 46 13/13 a 13/15 a 13/15 a 13/15 a 10/12 b, 14 c, d
14 36 18/18 a 14/14 a 9/12 a 9/12 a 7/10 a, 10 b
15 30 11/12 c 5/8 a 7/10 a 8/12 c 8/12 c, 12 d
16 32 15/15 a 15/13 a 15/13 a 7/5 a, 10 a 6/8 b, 10 c
17 25 14/14 a 12/12 a 5/8 a 5/8 a 5/5 a, 8 a
18 21 7/8 c 4/8 c 4/8 c 4/6 a 4/6 a, 6 b
# storage boxes   42 28 28 28 42
Transportation time (min) - 342.8 326.3 301.5 288.1 293.6
Computational time - - - 0.0 sec 106.3 sec approx. 6 days
Saving - - 4.8 % 12.1 % 16.0 % 14.4 %
Table 3. Best bound and gap on the best solution of 293.979 minutes, which is found after 20 minutes, of the partition model with 42 storage boxes.
  Best bound Gap
30 min 291.311 0.91%
60 min 291.537 0.83%
90 min 291.658 0.79%
120 min 291.744 0.76%
180 min 291.855 0.72%
240 min 291.932 0.70%