Heuristic Approach for Packing Identical Rectangular Tiles in an Irregular Marble Slab

Table 1

Computational results.

No.	Irregular region		Rectangle item		Number of items	CPU time in seconds
	Description	Area	Dimensions	Area
1	{(0,0), (40,0), (20,20)}	400	3 × 2	6	56	10.211
2	{(0,0), (20,0), (18,20),(2,20)}	360	4 × 4	16	20	2.022
3	{(0,0), (15,0), (18,12), (3,12)}	180	2 × 3	6	28	3.411
4	{(0,0), (30,0), (15,15), (15,30)}	337.5	3 × 3	9	29	1.252
5	{(0,0), (20,0), (24,24), (10,16), (0,22)}	422	4 × 3	12	29	4.429
6	{(0,0), (14,0), (30,−10), (26,20), (6,16)}	508	3 × 3	9	42	9.774
7	{(0,0), (21,0), (30,20), (6,30), (−4,20)}	720	4 × 3	12	50	17.719
8	{(0,0), (10,0), (15,12), (10,24), (0,24), (−5,12)}	360	3 × 3	9	32	7.841
9	{(0,0), (15,0), (7.5,18), (15,36), (0,36), (−7.5,18)}	540	4 × 3	12	36	11.012
10	{(0,0), (24,0), (21.6,12), (24,24), (0,24), (4.8,12)}	489.6	4 × 2	8	54	13.033
11	{(0,0), (10,0), (15,−6), (22,10), (14,24), (0,24), (−5,12)}	526	3 × 3	9	46	23.234
12	{(0,0), (6,−6), (4,−20), (20,−12), (36,−20), (30,−6), (40,0), (24,0), (20,16), (10,0)}	568	2 × 2	4	105	44.236