Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems with Incremental Quantity Discount

Table 4

Comparison with DSSP and CPLEX.

Instance	RHH		DSSP		CPLEX		DP
	RE (%)	CPU (sec)	RE (%)	CPU (sec)	RE (%)	CPU (sec)	Value	CPU (sec)
𝐺1−1	0.0	0.094	2.225	1.062	11.881	5.110	11452.16	0.985
𝐺1−2	0.0	0.109	2.299	0.907	10.441	5.063	11653.62	0.984
𝐺1−3	0.0	0.094	2.581	1.062	9.555	5.015	11685.286	0.984
𝐺2−1	0.0	0.516	1.986	2.172	0.619	25.750	22602.25	4.719
𝐺2−2	0.0	0.516	2.583	2.438	3.800	24.093	23408.59	4.719
𝐺2−3	0.0	0.500	3.040	2.094	6.103	24.110	23259.73	4.719
𝐺3−1	0.0	1.140	1.947	4.578	0.645	111.891	45820.49	22.187
𝐺3−2	0.0	1.125	2.845	4.250	1.162	114.657	46665.20	22.172
𝐺3−3	0.0	1.125	3.104	4.406	0.858	113.641	47492.82	22.218
𝐺4−1	0.704	0.140	0.721	1.015	3.744	3.391	7285.71	0.656
𝐺4−2	0.110	0.140	0.893	0.828	15.302	3.375	7916.02	0.656
𝐺4−3	0.035	0.140	1.089	0.735	13.440	3.297	8279.95	0.641
𝐺5−1	0.867	0.515	0.484	3.313	3.334	37.516	21619.82	7.453
𝐺5−2	0.174	0.500	0.632	2.796	1.199	38.265	23767.47	7.422
𝐺5−3	0.198	0.516	1.163	3.110	0.814	37.703	24543.10	7.438
𝐺6−1	0.202	6.063	0.401	8.781	0.800	414.046	65133.43	82.640
𝐺6−2	0.068	6.109	0.747	11.453	1.879	412.860	70243.82	82.375
𝐺6−3	0.022	6.110	1.034	11.157	0.843	419.937	74203.32	82.563
𝐺7−1	0.201	0.360	0.716	1.078	4.300	4.250	6681.52	0.828
𝐺7−2	0.0	0.359	0.889	0.859	1.742	4.172	7480.93	0.812
𝐺7−3	0.0	0.344	1.368	1.188	1.188	4.2347	7980.60	0.828
𝐺8−1	0.367	2.204	0.429	4.578	3.918	86.125	26885.65	17.265
𝐺8−2	0.082	2.172	0.579	4.812	0.741	87.125	30213.60	17.234
𝐺8−3	0.0	2.171	1.060	5.594	1.111	89.468	32503.12	17.157