Recursive partitioning approach
for the Distributor's Pallet Loading Problem

Introduction - Problem instances - Solutions

Results

Here we present some results we have obtained for several instances. For each instance, we show the value of the solution we have found as well as its graphical representation, which is available in PNG format, and a text file containing a description of the solution. The solution file has the following format. The first line contains two integers: the length L and the width W of the plate. Each one of the following lines contains four integers representing the position of a particular piece. The first two integers indicate the lower left corner of the piece and the last two integers indicate the upper right corner of the piece in the plate. For further details about our experiments, please refer to our paper.

Moderate size instances

Results for the moderate size instances presented in Birgin, Lobato and Morabito (2012).

Results for the moderate size instances presented in Birgin, Lobato and Morabito (2012).
Instance	Two-stage cuts		Guillotine cuts		First-order non-guillotine cuts		L-shaped cuts
Instance	Optimal value	Optimal solution	Optimal value	Optimal solution	Optimal value	Optimal solution	Optimal value	Optimal solution
H	12132	Picture	12348	Picture	12348	Picture	12348	Picture
H	12132	Description	12348	Description	12348	Description	12348	Description
HZ1	5226	Picture	5226	Picture	5226	Picture	5226	Picture
HZ1	5226	Description	5226	Description	5226	Description	5226	Description
HZ2	8046	Picture	8226	Picture	8443	Picture	8443	Picture
HZ2	8046	Description	8226	Description	8443	Description	8443	Description
GCUT1	56460	Picture	56460	Picture	58480	Picture	58480	Picture
GCUT1	56460	Description	56460	Description	58480	Description	58480	Description
GCUT2	60076	Picture	60536	Picture	61146	Picture	61146	Picture
GCUT2	60076	Description	60536	Description	61146	Description	61146	Description
GCUT3	60133	Picture	61036	Picture	61275	Picture	61275	Picture
GCUT3	60133	Description	61036	Description	61275	Description	61275	Description
GCUT4	61698	Picture	61698	Picture	61918	Picture	61918	Picture
GCUT4	61698	Description	61698	Description	61918	Description	61918	Description
GCUT5	246000	Picture	246000	Picture	246000	Picture	246000	Picture
GCUT5	246000	Description	246000	Description	246000	Description	246000	Description
GCUT6	238998	Picture	238998	Picture	243598	Picture	243598	Picture
GCUT6	238998	Description	238998	Description	243598	Description	243598	Description
GCUT7	242567	Picture	242567	Picture	244306	Picture	244306	Picture
GCUT7	242567	Description	242567	Description	244306	Description	244306	Description
GCUT8	245758	Picture	246633	Picture	247815	Picture	247815	Picture
GCUT8	245758	Description	246633	Description	247815	Description	247815	Description
GCUT9	971100	Picture	971100	Picture	971100	Picture	971100	Picture
GCUT9	971100	Description	971100	Description	971100	Description	971100	Description
GCUT10	982025	Picture	982025	Picture	982025	Picture	982025	Picture
GCUT10	982025	Description	982025	Description	982025	Description	982025	Description
GCUT11	980096	Picture	980096	Picture	980096	Picture	980096	Picture
GCUT11	980096	Description	980096	Description	980096	Description	980096	Description
GCUT12	978776	Picture	979986	Picture	979986	Picture	979986	Picture
GCUT12	978776	Description	979986	Description	979986	Description	979986	Description
M1	15024	Picture	15024	Picture	15054	Picture	15073	Picture
M1	15024	Description	15024	Description	15054	Description	15073	Description
M2	72172	Picture	73176	Picture	73255	Picture	73255	Picture
M2	72172	Description	73176	Description	73255	Description	73255	Description
M3	141810	Picture	142817	Picture	147386	Picture	147386	Picture
M3	141810	Description	142817	Description	147386	Description	147386	Description
M4	265768	Picture	265768	Picture	266233	Picture	266233	Picture
M4	265768	Description	265768	Description	266233	Description	266233	Description
M5	577882	Picture	577882	Picture	579883	Picture	579883	Picture
M5	577882	Description	577882	Description	579883	Description	579883	Description
MW1	3882	Picture	3882	Picture	3882	Picture	3882	Picture
MW1	3882	Description	3882	Description	3882	Description	3882	Description
MW2	24950	Picture	24950	Picture	24950	Picture	24950	Picture
MW2	24950	Description	24950	Description	24950	Description	24950	Description
MW3	37068	Picture	37068	Picture	37068	Picture	37068	Picture
MW3	37068	Description	37068	Description	37068	Description	37068	Description
MW4	59364	Picture	59576	Picture	59576	Picture	59576	Picture
MW4	59364	Description	59576	Description	59576	Description	59576	Description
MW5	189924	Picture	189924	Picture	189924	Picture	189924	Picture
MW5	189924	Description	189924	Description	189924	Description	189924	Description
W2	34520	Picture	35159	Picture	35822	Picture	35822	Picture
W2	34520	Description	35159	Description	35822	Description	35822	Description
UU1	240346	Picture	242919	Picture	245205	Picture	245205	Picture
UU1	240346	Description	242919	Description	245205	Description	245205	Description
UU2	595288	Picture	595288	Picture	595288	Picture	595288	Picture
UU2	595288	Description	595288	Description	595288	Description	595288	Description
UU3	1065051	Picture	1072764	Picture	1088154	Picture	1088154	Picture
UU3	1065051	Description	1072764	Description	1088154	Description	1088154	Description
UU4	1177371	Picture	1179050	Picture	1191071	Picture	1191071	Picture
UU4	1177371	Description	1179050	Description	1191071	Description	1191071	Description
UU5	1868985	Picture	1868999	Picture	1870038	Picture	1870038	Picture
UU5	1868985	Description	1868999	Description	1870038	Description	1870038	Description
UU6	2950760	Picture	2950760	Picture	2950760	Picture	2950760	Picture
UU6	2950760	Description	2950760	Description	2950760	Description	2950760	Description
UU7	2925362	Picture	2930654	Picture	2943852	Picture	2943852	Picture
UU7	2925362	Description	2930654	Description	2943852	Description	2943852	Description
UU8	3959352	Picture	3959352	Picture	3969784	Picture	3970877	Picture
UU8	3959352	Description	3959352	Description	3969784	Description	3970877	Description
UU9	6100692	Picture	6100692	Picture	6100692	Picture	6100692	Picture
UU9	6100692	Description	6100692	Description	6100692	Description	6100692	Description
UU10	11929561	Picture	11955852	Picture	11995637	Picture	12001291	Picture
UU10	11929561	Description	11955852	Description	11995637	Description	12001291	Description
UW1	6036	Picture	6036	Picture	6036	Picture	6036	Picture
UW1	6036	Description	6036	Description	6036	Description	6036	Description
UW2	8468	Picture	8468	Picture	8720	Picture	8720	Picture
UW2	8468	Description	8468	Description	8720	Description	8720	Description
UW3	5888	Picture	6302	Picture	6652	Picture	6652	Picture
UW3	5888	Description	6302	Description	6652	Description	6652	Description
UW4	7748	Picture	8326	Picture	8326	Picture	8326	Picture
UW4	7748	Description	8326	Description	8326	Description	8326	Description
UW5	7780	Picture	7780	Picture	7780	Picture	7780	Picture
UW5	7780	Description	7780	Description	7780	Description	7780	Description
UW6	6548	Picture	6615	Picture	6803	Picture	6803	Picture
UW6	6548	Description	6615	Description	6803	Description	6803	Description
UW7	10464	Picture	10464	Picture	10464	Picture	10464	Picture
UW7	10464	Description	10464	Description	10464	Description	10464	Description
UW8	7692	Picture	7692	Picture	7692	Picture	7692	Picture
UW8	7692	Description	7692	Description	7692	Description	7692	Description
UW9	7038	Picture	7038	Picture	7128	Picture	7128	Picture
UW9	7038	Description	7038	Description	7128	Description	7128	Description
UW10	7461	Picture	7507	Picture	7507	Picture	7507	Picture
UW10	7461	Description	7507	Description	7507	Description	7507	Description
UW11	15747	Picture	15747	Picture	16400	Picture	16400	Picture
UW11	15747	Description	15747	Description	16400	Description	16400	Description

Large instances

Results for the large size instances presented in Birgin, Lobato and Morabito (2012).

Results for the large size instances presented in Birgin, Lobato and Morabito (2012).
Instance	Two-stage cuts		Guillotine cuts		First-order non-guillotine cuts		L-shaped cuts
Instance	Optimal value	Optimal solution	Optimal value	Optimal solution	Solution value	Solution	Solution value	Solution
GCUT13	8997780	Picture	8997780	Picture	8997780	Picture	8997780	Picture
GCUT13	8997780	Description	8997780	Description	8997780	Description	8997780	Description
GCUT14	12236280	Picture	12245410	Picture	12245410	Picture	12245410	Picture
GCUT14	12236280	Description	12245410	Description	12245410	Description	12245410	Description
GCUT15	12239904	Picture	12246032	Picture	12246032	Picture	12246032	Picture
GCUT15	12239904	Description	12246032	Description	12246032	Description	12246032	Description
GCUT16	12243100	Picture	12248836	Picture	12248836	Picture	12248836	Picture
GCUT16	12243100	Description	12248836	Description	12248836	Description	12248836	Description
GCUT17	12242998	Picture	12248892	Picture	12248892	Picture	12248892	Picture
GCUT17	12242998	Description	12248892	Description	12248892	Description	12248892	Description
U1	22167051	Picture	22370130	Picture	22370130	Picture	22370130	Picture
U1	22167051	Description	22370130	Description	22370130	Description	22370130	Description
U2	20031845	Picture	20232223	Picture	20232223	Picture	20232223	Picture
U2	20031845	Description	20232223	Description	20232223	Description	20232223	Description
U3	47912942	Picture	48142836	Picture	48142836	Picture	48142836	Picture
U3	47912942	Description	48142836	Description	48142836	Description	48142836	Description
U4	48227224	Picture	48304289	Picture	48304289	Picture	48304289	Picture
U4	48227224	Description	48304289	Description	48304289	Description	48304289	Description
W1	161424	Picture	162867	Picture	162867	Picture	162867	Picture
W1	161424	Description	162867	Description	162867	Description	162867	Description
W2	34520	Picture	35159	Picture	35165	Picture	35165	Picture
W2	34520	Description	35159	Description	35165	Description	35165	Description
W3	234108	Picture	234108	Picture	234108	Picture	234108	Picture
W3	234108	Description	234108	Description	234108	Description	234108	Description
W4	377910	Picture	377910	Picture	377910	Picture	377910	Picture
W4	377910	Description	377910	Description	377910	Description	377910	Description
UU9	6100692	Picture	6100692	Picture	6100692	Picture	6100692	Picture
UU9	6100692	Description	6100692	Description	6100692	Description	6100692	Description
UU10	11929561	Picture	11955852	Picture	11955852	Picture	11955852	Picture
UU10	11929561	Description	11955852	Description	11955852	Description	11955852	Description
UU11	13066737	Picture	13157811	Picture	13157811	Picture	13157811	Picture
UU11	13066737	Description	13157811	Description	13157811	Description	13157811	Description
APT10	3585612	Picture	3589703	Picture	3589703	Picture	3589703	Picture
APT10	3585612	Description	3589703	Description	3589703	Description	3589703	Description
APT11	4175414	Picture	4188915	Picture	4188915	Picture	4188915	Picture
APT11	4175414	Description	4188915	Description	4188915	Description	4188915	Description
APT12	5148302	Picture	5156065	Picture	5156065	Picture	5156065	Picture
APT12	5148302	Description	5156065	Description	5156065	Description	5156065	Description
APT13	3493072	Picture	3498302	Picture	3498302	Picture	3498302	Picture
APT13	3493072	Description	3498302	Description	3498302	Description	3498302	Description
APT14	4458052	Picture	4463550	Picture	4463550	Picture	4463550	Picture
APT14	4458052	Description	4463550	Description	4463550	Description	4463550	Description
APT15	6028426	Picture	6047188	Picture	6047188	Picture	6047188	Picture
APT15	6028426	Description	6047188	Description	6047188	Description	6047188	Description
APT16	7533987	Picture	7566719	Picture	7566719	Picture	7566719	Picture
APT16	7533987	Description	7566719	Description	7566719	Description	7566719	Description
APT17	4529371	Picture	4535302	Picture	4535302	Picture	4535302	Picture
APT17	4529371	Description	4535302	Description	4535302	Description	4535302	Description
APT18	5807988	Picture	5825956	Picture	5825956	Picture	5825956	Picture
APT18	5807988	Description	5825956	Description	5825956	Description	5825956	Description
APT19	6811338	Picture	6826674	Picture	6826674	Picture	6826674	Picture
APT19	6811338	Description	6826674	Description	6826674	Description	6826674	Description
APT20	5490828	Picture	5545818	Picture	5545818	Picture	5545818	Picture
APT20	5490828	Description	5545818	Description	5545818	Description	5545818	Description
APT21	3479634	Picture	3484406	Picture	3491545	Picture	3491545	Picture
APT21	3479634	Description	3484406	Description	3491545	Description	3491545	Description
APT22	4111542	Picture	4145317	Picture	4153426	Picture	4153426	Picture
APT22	4111542	Description	4145317	Description	4153426	Description	4153426	Description
APT23	3494778	Picture	3546535	Picture	3546535	Picture	3546535	Picture
APT23	3494778	Description	3546535	Description	3546535	Description	3546535	Description
APT24	3898694	Picture	3948037	Picture	3948037	Picture	3948037	Picture
APT24	3898694	Description	3948037	Description	3948037	Description	3948037	Description
APT25	3485589	Picture	3507615	Picture	3507615	Picture	3507615	Picture
APT25	3485589	Description	3507615	Description	3507615	Description	3507615	Description
APT26	2639964	Picture	2683689	Picture	2683689	Picture	2683689	Picture
APT26	2639964	Description	2683689	Description	2683689	Description	2683689	Description
APT27	2382270	Picture	2438174	Picture	2438174	Picture	2438174	Picture
APT27	2382270	Description	2438174	Description	2438174	Description	2438174	Description
APT28	3969356	Picture	4065011	Picture	4065011	Picture	4065011	Picture
APT28	3969356	Description	4065011	Description	4065011	Description	4065011	Description
APT29	3619071	Picture	3652858	Picture	3652858	Picture	3652858	Picture
APT29	3619071	Description	3652858	Description	3652858	Description	3652858	Description
B1	7990710	Picture	7993031	Picture	7993031	Picture	7993031	Picture
B1	7990710	Description	7993031	Description	7993031	Description	7993031	Description
B2	7984124	Picture	7993849	Picture	7993849	Picture	7993849	Picture
B2	7984124	Description	7993849	Description	7993849	Description	7993849	Description
B3	7966146	Picture	7991615	Picture	7991615	Picture	7991615	Picture
B3	7966146	Description	7991615	Description	7991615	Description	7991615	Description
B4	7979928	Picture	7989673	Picture	7989673	Picture	7989673	Picture
B4	7979928	Description	7989673	Description	7989673	Description	7989673	Description
B5	7978160	Picture	7994752	Picture	7994752	Picture	7994752	Picture
B5	7978160	Description	7994752	Description	7994752	Description	7994752	Description
B6	7989831	Picture	7992075	Picture	7992075	Picture	7992075	Picture
B6	7989831	Description	7992075	Description	7992075	Description	7992075	Description
B7	7999488	Picture	8000000	Picture	8000000	Picture	8000000	Picture
B7	7999488	Description	8000000	Description	8000000	Description	8000000	Description

Other large instances

Results for some large size instances presented in Birgin, Lobato and Morabito (2012).

Results for some large size instances presented in Birgin, Lobato and Morabito (2012).
Instance	Two-stage cuts		Guillotine cuts		First-order non-guillotine cuts
Instance	Optimal value	Optimal solution	Optimal value	Optimal solution	Solution value	Solution
APT10	3585612	Picture	3589703	Picture	3589833	Picture
APT10	3585612	Description	3589703	Description	3589833	Description
APT11	4175414	Picture	4188915	Picture	4189860	Picture
APT11	4175414	Description	4188915	Description	4189860	Description
APT12	5148302	Picture	5156065	Picture	5156618	Picture
APT12	5148302	Description	5156065	Description	5156618	Description
APT13	3493072	Picture	3498302	Picture	3498302	Picture
APT13	3493072	Description	3498302	Description	3498302	Description
APT14	4458052	Picture	4463550	Picture	4463550	Picture
APT14	4458052	Description	4463550	Description	4463550	Description
APT15	6028426	Picture	6047188	Picture	6052277	Picture
APT15	6028426	Description	6047188	Description	6052277	Description
APT16	7533987	Picture	7566719	Picture	7571590	Picture
APT16	7533987	Description	7566719	Description	7571590	Description
APT17	4529371	Picture	4535302	Picture	4536372	Picture
APT17	4529371	Description	4535302	Description	4536372	Description
APT18	5807988	Picture	5825956	Picture	5829172	Picture
APT18	5807988	Description	5825956	Description	5829172	Description
APT19	6811338	Picture	6826674	Picture	6826674	Picture
APT19	6811338	Description	6826674	Description	6826674	Description
APT20	5490828	Picture	5545818	Picture	5548505	Picture
APT20	5490828	Description	5545818	Description	5548505	Description
APT21	3479634	Picture	3484406	Picture	3491545	Picture
APT21	3479634	Description	3484406	Description	3491545	Description
APT22	4111542	Picture	4145317	Picture	4161384	Picture
APT22	4111542	Description	4145317	Description	4161384	Description
APT23	3494778	Picture	3546535	Picture	3559028	Picture
APT23	3494778	Description	3546535	Description	3559028	Description
APT24	3898694	Picture	3948037	Picture	3956498	Picture
APT24	3898694	Description	3948037	Description	3956498	Description
APT25	3485589	Picture	3507615	Picture	3507615	Picture
APT25	3485589	Description	3507615	Description	3507615	Description
APT26	2639964	Picture	2683689	Picture	2683689	Picture
APT26	2639964	Description	2683689	Description	2683689	Description
APT27	2382270	Picture	2438174	Picture	2443696	Picture
APT27	2382270	Description	2438174	Description	2443696	Description
APT28	3969356	Picture	4065011	Picture	4065011	Picture
APT28	3969356	Description	4065011	Description	4065011	Description
APT29	3619071	Picture	3652858	Picture	3652858	Picture
APT29	3619071	Description	3652858	Description	3652858	Description

Recursive partitioning approach for the Distributor's Pallet Loading Problem

Results

Moderate size instances

Large instances

Other large instances

Recursive partitioning approach
for the Distributor's Pallet Loading Problem