A shift-based sequencing method for twin-shuttle automated storage and retrieval systems

Figures & data

Fig. 1 The 15 retrieval locations and retrieval pairings by three methods.

Table 1 An example problem with 15 retrievals

	x-coordinate	y-coordinate
1	0.749 29	0.237 26
2	0.545 95	0.737 50
3	0.803 17	0.951 08
4	0.314 16	0.096 72
5	0.112 62	0.865 70
6	0.431 87	0.418 52
7	0.959 01	0.151 22
8	0.197 77	0.987 17
9	0.965 15	0.259 69
10	0.984 85	0.358 16
11	0.140 94	0.720 50
12	0.420 41	0.817 62
13	0.748 93	0.267 58
14	0.278 07	0.535 66
15	0.557 41	0.428 08

Fig. 2 Travel-between time by different methods when b = 0.6.

Table 5 Comparison of Optimum, NN and FCFS with 15 individual problems when b = 0.2 and n = 10

Optimum		NN		FCFS
0.0992 98	0.8602 60	0.1106 68	0.8716 30	0.1185 50	0.8795 12
0.1242 04	1.1761 90	0.1242 04	1.1761 90	0.1960 26	1.2480 10
0.1137 82	0.8781 84	0.1171 82	0.8815 84	0.3739 70	1.1383 70
0.0952 28	1.2269 80	0.1252 32	1.2569 80	0.3896 12	1.5213 60
0.1056 88	1.2827 20	0.1564 22	1.3334 50	0.4157 70	1.5928 00
0.0899 80	0.9238 30	0.1030 70	0.9369 20	0.2352 90	1.0691 40
0.1341 90	1.3677 50	0.2526 54	1.4862 10	0.3214 22	1.5549 80
0.1466 64	1.4029 30	0.1744 20	1.4306 80	0.2925 66	1.5488 30
0.1173 28	1.1668 70	0.1247 56	1.1743 00	0.5100 56	1.5596 00
0.1176 46	1.0477 90	0.1176 46	1.0477 90	0.4983 78	1.4285 20
0.1026 50	1.1909 90	0.1563 76	1.2447 10	0.3989 88	1.4873 20
0.1261 26	1.6762 30	0.1313 34	1.6814 40	0.2494 82	1.7995 80
0.0994 14	1.0662 60	0.0994 14	1.0662 60	0.3581 04	1.3249 50
0.0994 74	1.2611 30	0.0994 74	1.2611 30	0.3303 38	1.4919 90
0.1153 58	1.0392 60	0.2439 08	1.1678 10	0.4080 68	1.3319 70

Table 2 Comparison of Optimum, NN and FCFS when b = 1 (square rack)

	Optimum		NN		FCFS
Number of retrievals
4	0.347 59	1.742 20	0.386 42	1.781 04	0.539 62	1.934 23
6	0.294 16	1.683 42	0.350 52	1.739 78	0.490 22	1.879 48
8	0.231 92	1.627 65	0.270 13	1.665 86	0.495 01	1.890 74
10	0.211 56	1.611 49	0.254 74	1.654 66	0.486 13	1.886 05
20	0.143 26	1.463 54	0.186 80	1.507 08	0.432 52	1.752 80
40	0.099 03	1.417 10	0.130 51	1.448 58	0.430 85	1.748 92
80	0.065 94	1.376 12	0.087 82	1.398 00	0.451 66	1.761 85
160	0.046 90	1.369 28	0.061 13	1.383 51	0.455 76	1.778 14
320	0.032 35	1.361 15	0.043 39	1.372 19	0.462 58	1.791 39

Table 3 Comparison of Optimum, NN and FCFS when b = 0.6

	Optimum		NN		FCFS
Number of retrievals
4	0.299 66	1.361 33	0.362 51	1.424 18	0.403 56	1.465 23
6	0.245 05	1.273 24	0.299 17	1.327 36	0.387 05	1.415 23
8	0.192 75	1.249 23	0.213 15	1.269 63	0.382 00	1.438 48
10	0.165 21	1.259 72	0.199 78	1.294 30	0.392 48	1.486 99
20	0.119 40	1.222 47	0.153 42	1.256 49	0.413 12	1.516 19
40	0.075 61	1.186 50	0.109 09	1.219 98	0.387 95	1.498 85
80	0.051 88	1.143 83	0.075 81	1.167 77	0.388 46	1.480 42
160	0.035 22	1.146 65	0.049 22	1.160 64	0.393 24	1.504 67
320	0.024 56	1.136 67	0.032 77	1.144 88	0.393 31	1.505 41

Table 4 Comparison of Optimum, NN and FCFS when b = 0.2

	Optimum		NN		FCFS
Number of retrievals
4	0.228 55	1.286 08	0.233 85	1.291 38	0.362 18	1.419 71
6	0.149 77	1.224 00	0.159 62	1.233 85	0.330 08	1.404 32
8	0.132 23	1.198 05	0.150 81	1.216 64	0.339 48	1.405 30
10	0.112 47	1.171 16	0.142 45	1.201 14	0.339 77	1.398 46
20	0.067 60	1.110 37	0.088 26	1.131 03	0.353 82	1.396 59
40	0.044 81	1.064 26	0.059 02	1.078 47	0.353 70	1.373 15
80	0.030 42	1.044 29	0.040 22	1.054 10	0.353 97	1.367 84
160	0.020 98	1.034 68	0.026 77	1.040 47	0.352 69	1.366 39
320	0.014 54	1.022 32	0.019 02	1.026 80	0.344 09	1.351 88

Fig. 3 Travel-between time by different methods when b = 1.0.

Table 6 Percentage difference between NN T and predicted E(TB _2n ^NN)

	b
Number of retrievals	1	0.6
4	3.77	19.86
6	9.64	16.20
8	−5.15	−6.59
10	6.17	4.53
20	−2.29	0.68
40	−5.76	−0.37

Table 7 Percentage difference between optimal T and lower bound E(TB _2n ^LB)

	b
Number of retrievals	1	0.6
4	24.99	36.96
6	37.26	46.30
8	28.77	37.29
10	48.57	49.10
20	33.77	43.51
40	34.19	31.95