Recursive partitioning approach
for the Manufacturer's Pallet Loading Problem

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Cover IIIB - Remaining problems

970 problems from Cover IIIB have no certificate of optimality. Then we decided to find the optimal solution of each one of these problems by using an exact model to solve the pallet loading problem and running it in GAMS with CPLEX. The table below shows the problems already run. Until this moment, 287 problems were solved and each one of them has the same solution found by the Recursive Partitioning Algorithm.

Problem	L	W	l	w	Optimal solution
1	100	94	9	7	solving
2	101	52	8	5	solving
3	101	68	15	4	113
4	101	72	15	4	120
5	101	75	10	7	107
6	101	78	11	5	142
7	101	80	9	7	127
8	101	81	12	5	135
9	101	87	13	5	134
10	101	93	10	7	133
11	102	73	9	7	117
12	102	81	9	7	130
13	102	87	12	7	solving
14	102	89	9	7	143
15	103	67	8	7	122
16	103	70	12	5	119
17	103	70	15	4	119
18	103	80	12	5	136
19	103	80	8	7	146
20	103	84	9	7	solving
21	103	98	10	7	143
22	104	100	18	5	114
23	104	53	11	4	124
24	104	62	9	7	101
25	104	84	11	6	131
26	104	85	10	7	125
27	104	88	9	7	solving
28	104	89	10	7	131
29	104	95	11	8	111
30	105	104	18	5	120
31	105	105	12	7	130
32	105	59	12	5	102
33	105	81	12	7	100
34	105	82	12	7	101
35	105	93	12	7	115
36	105	94	12	7	116
37	106	104	11	8	124
38	106	105	11	8	solving
39	106	57	9	5	133
40	106	78	11	5	solving
41	106	81	12	5	142
42	106	83	11	7	113
43	106	90	12	7	112
44	106	93	11	6	148
45	107	54	13	4	110
46	107	64	13	5	104
47	107	67	11	5	129
48	107	74	8	7	solving
49	107	75	8	7	solving
50	107	78	10	7	118
51	107	80	14	5	122
52	107	84	11	6	135
53	107	90	14	5	136
54	107	95	10	7	144
55	107	97	11	9	103
56	108	102	12	7	130
57	108	103	11	8	solving
58	108	107	13	6	147
59	108	58	7	6	148
61	108	81	13	6	111
70	109	58	15	4	104
71	109	65	10	7	100
72	109	75	11	7	105
73	109	78	14	5	solving
76	110	104	19	5	119
78	110	65	10	7	101
79	110	72	10	7	112
80	110	75	11	7	106
83	110	81	13	6	113
84	110	82	11	7	116
89	111	58	15	4	106
93	112	57	9	7	100
95	112	62	9	7	109
96	112	64	13	5	109
97	112	66	9	7	116
98	112	72	14	5	114
101	112	76	9	8	117
103	112	81	11	8	102
108	112	88	13	7	107
109	112	89	13	7	108
110	112	92	11	8	116
114	113	103	11	9	116
115	113	58	15	4	108
117	113	62	9	7	110
122	114	62	9	7	111
123	114	72	10	7	116
127	115	58	15	4	110
128	115	62	9	7	112
129	115	69	10	7	112
130	115	72	10	7	solving
134	116	100	11	9	116
139	116	62	9	7	113
145	117	116	13	10	103
146	117	68	11	7	102
147	117	69	10	7	114
151	117	80	12	7	110
155	118	64	11	6	solving
156	118	64	13	5	115
157	118	69	10	7	115
158	118	72	11	7	109
161	118	86	11	8	114
169	120	69	13	6	105
171	120	86	11	8	116
172	120	93	19	5	116
183	122	89	13	8	103
185	123	120	16	9	101
186	123	62	11	6	114
189	123	76	11	8	105
191	123	81	11	8	112
192	123	84	11	8	solving
193	123	86	11	8	119
194	123	91	19	5	116
200	125	106	17	7	110
201	125	109	13	9	115
204	125	63	11	6	118
206	125	93	11	9	116
208	125	96	13	9	101
213	126	117	13	10	112
216	126	68	11	7	110
222	127	69	12	7	103
229	128	73	11	8	105
231	128	86	19	5	114
232	128	87	13	8	106
236	129	66	12	7	100
237	129	70	12	7	106
239	129	86	13	7	120
242	129	96	13	9	solving
243	130	105	19	7	101
244	130	112	19	7	108
246	130	74	19	5	100
249	130	80	17	6	100
252	131	102	16	7	118
255	131	76	11	8	112
256	131	78	11	9	102
262	132	106	17	7	116
267	132	81	19	5	111
268	132	86	19	5	118
270	132	93	17	6	119
275	134	116	13	10	118
276	134	76	12	7	120
283	135	68	11	7	solving
287	135	92	17	6	solving
289	136	111	19	7	112
291	136	68	11	8	104
303	138	69	12	7	112
304	138	74	19	5	106
306	138	76	11	8	118
309	138	84	13	8	110
311	139	105	18	7	114
312	139	111	13	10	solving
315	139	73	11	8	solving
316	139	74	19	5	107
322	140	103	18	7	113
324	140	120	13	11	solving
326	140	121	16	9	116
328	140	70	11	8	110
329	140	70	18	5	107
330	140	78	11	9	109
331	140	79	15	7	104
334	141	108	16	9	104
335	141	122	16	9	solving
338	141	82	13	8	110
339	142	105	16	9	102
349	143	111	19	7	118
350	143	123	19	8	114
351	143	139	20	9	109
352	143	74	19	5	110
355	143	95	14	9	106
362	144	120	23	7	106
364	144	73	13	7	114
367	144	81	16	7	103
368	144	81	17	6	113
370	144	88	16	7	112
374	145	126	20	9	100
375	145	135	20	9	107
381	146	129	26	7	solving
386	146	95	13	10	105
388	147	108	19	7	118
399	148	74	19	5	114
403	149	105	19	7	116
414	150	81	17	6	118
421	151	120	23	7	111
422	151	121	19	8	119
427	151	81	16	7	108
439	152	143	17	12	105
440	152	143	18	11	108
441	152	86	14	9	102
448	153	118	15	11	108
449	153	122	14	11	solving
453	153	140	26	7	116
457	153	88	13	9	114
458	154	102	19	8	102
461	155	143	15	13	112
462	155	149	15	13	117
471	156	86	13	10	102
472	156	96	13	10	114
474	157	108	16	9	solving
480	159	153	20	11	109
485	160	159	20	11	114
487	160	85	15	8	112
491	161	149	25	9	105
493	161	83	17	7	111
494	161	86	14	9	108
495	161	88	18	7	111
496	161	92	19	7	110
501	162	84	13	9	115
502	162	92	14	9	117
507	164	118	15	11	116
514	164	97	14	11	102
516	165	126	20	9	114
521	165	84	15	8	114
523	165	91	19	7	111
524	166	104	17	10	100
527	166	84	13	9	118
532	167	119	21	8	117
534	167	151	19	12	109
536	167	152	17	14	105
537	167	94	19	8	102
545	168	127	20	9	117
546	168	134	15	13	114
551	168	89	23	6	107
552	168	92	19	7	115
556	169	135	16	13	108
559	169	85	13	10	109
564	170	147	19	11	solving
565	170	149	25	9	111
572	171	118	26	7	109
575	171	125	26	7	116
577	171	87	14	9	117
578	171	93	16	9	109
582	173	94	14	11	104
583	174	102	25	7	100
593	174	89	23	6	111
600	175	125	20	9	120
605	175	97	14	11	109
641	180	93	16	9	115
644	181	102	25	7	104
646	181	152	17	14	114
652	183	100	17	10	106
663	184	98	21	8	106
668	185	143	25	9	116
671	186	105	17	11	103
675	186	174	25	11	116
676	187	100	15	11	112
681	187	128	19	11	113
683	187	131	19	12	106
687	188	102	25	7	108
710	195	102	25	7	112
715	195	98	25	7	107
717	196	118	17	12	112
721	197	105	17	11	109
722	197	112	18	11	110
723	197	116	18	11	114
734	200	100	17	10	116
735	200	109	19	11	103
753	206	113	23	9	111
759	207	106	16	13	104
765	208	112	18	11	solving
777	215	112	18	11	120
791	220	111	17	13	109
796	224	132	19	15	102
803	227	122	19	12	120
813	231	164	29	11	117
824	239	132	19	15	109
838	252	148	23	14	solving
842	259	130	22	13	116
858	65	56	9	4	100
859	66	65	7	6	101
860	66	65	9	4	118
861	69	68	9	5	103
862	72	66	7	6	112
863	72	67	9	5	106
864	72	72	9	5	114
865	73	64	7	6	110
867	74	56	9	4	114
868	74	59	8	5	108
869	75	64	11	4	108
870	75	70	11	4	118
877	80	67	13	4	102
880	81	81	9	7	103
881	82	58	7	6	112
882	82	62	11	4	114
883	82	66	9	5	solving
885	82	80	8	7	116
886	83	50	9	4	114
887	84	67	13	4	107
888	84	73	15	4	101
889	84	76	9	7	100
890	85	84	11	6	107
891	85	84	9	7	112
898	86	72	15	4	102
899	86	84	11	6	108
903	87	77	9	7	105
905	88	67	13	4	112
906	88	73	15	4	106
907	88	81	9	7	112
909	89	78	9	7	109
912	90	82	14	5	104
913	91	52	9	5	104
914	91	70	12	5	105
919	92	47	9	4	119
924	92	90	11	7	106
927	93	76	9	7	111
929	93	84	11	6	117
932	94	54	11	4	114
938	95	82	14	5	110
944	96	73	11	6	105
945	96	77	9	7	solving
953	97	50	11	4	109
955	97	69	9	7	105
956	97	72	15	4	115
963	98	78	10	7	108
966	99	59	8	7	103
967	99	70	15	4	114
968	99	75	13	5	113
970	99	91	16	5	111

Recursive partitioning approach for the Manufacturer's Pallet Loading Problem

Cover IIIB - Remaining problems

Recursive partitioning approach
for the Manufacturer's Pallet Loading Problem