A Network Flow Algorithm for Solving Generalized Assignment Problem

Table 1

Computational behavior of randomly generated GAP with various values of , and a density valued 0.8 (times in seconds).

	0.2	5.620	0.046	0.040	5.940	0.047	0.014	4.971	0.040	0.012	5.837	0.043	0.006
	0.4	5.683	0.048	0.019	6.168	0.048	0.021	5.008	0.042	0.017	5.906	0.045	0.016
	0.6	5.926	0.052	0.052	6.186	0.053	0.035	5.255	0.045	0.021	6.183	0.050	0.018
	0.8	5.911	0.059	0.041	6.003	0.067	0.030	5.216	0.053	0.022	5.985	0.062	0.019
	0.9	6.098	0.060	0.050	6.064	0.072	0.040	5.343	0.053	0.029	6.090	0.066	0.024
	1.0	6.122	0.061	0.042	6.109	0.077	0.040	5.379	0.054	0.043	6.040	0.071	0.027
	Average	5.893	0.054	0.041	6.078	0.061	0.028	5.195	0.048	0.024	6.142	0.056	0.018
	0.2	5.855	0.108	0.040	6.187	0.111	0.025	5.168	0.095	0.011	6.007	0.108	0.015
	0.4	5.906	0.109	0.030	5.971	0.126	0.014	5.173	0.097	0.018	5.955	0.115	0.016
	0.6	6.101	0.112	0.070	6.128	0.128	0.032	5.382	0.099	0.023	5.910	0.119	0.020
	0.8	6.201	0.127	0.053	5.986	0.136	0.021	5.449	0.113	0.026	5.922	0.139	0.025
	0.9	6.440	0.135	0.063	6.030	0.139	0.045	5.705	0.123	0.030	5.917	0.145	0.025
	1.0	6.361	0.139	0.047	5.947	0.143	0.041	5.644	0.123	0.031	6.000	0.151	0.027
	Average	6.144	0.122	0.051	6.042	0.131	0.030	5.423	0.108	0.023	5.952	0.130	0.021
	0.2	5.951	0.551	0.178	7.246	0.667	0.083	5.247	0.567	0.050	6.977	0.850	0.045
	0.4	6.071	0.554	0.263	7.322	0.681	0.123	5.394	0.586	0.097	7.274	0.867	0.064
	0.6	6.114	0.565	0.331	7.385	0.692	0.152	5.418	0.590	0.125	7.230	0.885	0.119
	0.8	6.935	0.582	0.358	7.411	0.696	0.194	6.098	0.603	0.127	7.411	0.886	0.120
	0.9	7.311	0.584	0.358	7.272	0.701	0.206	6.417	0.618	0.210	7.232	0.952	0.128
	1.0	8.068	0.607	0.384	7.398	0.732	0.214	7.074	0.651	0.242	7.187	0.984	0.111
	Average	6.742	0.574	0.312	7.339	0.695	0.162	5.941	0.603	0.142	7.222	0.899	0.098
	0.2	6.737	0.846	0.344	8.624	1.105	0.064	5.896	0.746	0.080	8.305	1.082	0.042
	0.4	6.956	0.852	0.544	8.714	1.112	0.142	6.155	0.751	0.127	8.529	1.114	0.089
	0.6	6.872	0.920	0.686	8.893	1.124	0.194	6.026	0.817	0.169	8.669	1.207	0.113
	0.8	8.446	0.959	0.723	8.989	1.137	0.207	7.427	0.846	0.191	8.773	1.239	0.138
	0.9	9.252	1.051	0.803	9.057	1.146	0.214	8.153	0.925	0.234	8.667	1.304	0.203
	1.0	11.576	1.112	0.884	9.051	1.368	0.227	10.136	0.977	0.239	8.961	1.348	0.213
	Average	8.307	0.957	0.561	8.888	1.165	0.175	7.314	0.884	0.173	8.651	1.216	0.133
	0.2	6.760	2.264	0.782	8.940	3.038	0.168	5.944	1.988	0.322	8.604	2.843	0.183
	0.4	6.849	2.368	2.697	10.983	3.398	0.479	6.051	2.107	0.517	10.566	3.055	0.257
	0.6	6.994	2.413	3.322	11.534	3.440	0.583	6.150	2.148	0.642	11.053	3.136	0.382
	0.8	8.673	2.891	3.545	11.692	4.230	0.630	7.621	2.602	0.663	11.375	3.929	0.465
	0.9	9.286	3.107	3.714	11.943	4.661	0.854	8.181	2.796	0.866	11.744	4.018	0.587
	1.0	11.676	3.268	3.727	11.926	5.033	0.882	10.255	2.983	1.092	11.588	4.237	0.616
	Average	8.373	2.719	2.965	11.170	3.967	0.559	7.367	2.422	0.667	10.822	3.536	0.415
	0.2	9.555	15.103	5.256	11.826	18.724	0.343	8.411	11.700	0.769	11.597	16.087	0.212
	0.4	9.084	15.217	8.981	12.132	20.537	0.715	7.957	12.150	1.225	11.781	16.940	0.424
	0.6	9.357	16.467	11.173	12.238	23.267	0.977	8.231	13.530	1.470	11.881	19.305	0.599
	0.8	12.586	18.525	11.642	15.406	25.901	1.003	11.050	15.725	1.495	15.023	22.801	0.550
	0.9	12.845	19.637	11.963	15.714	27.588	1.099	11.283	17.052	1.758	15.302	25.578	0.744
	1.0	17.236	20.208	12.195	20.010	31.029	1.155	15.115	18.187	1.775	19.212	27.281	0.932
	Average	11.777	17.511	10.202	14.554	24.508	0.882	10.341	4.724	1.145	14.193	21.212	0.577
	0.2	9.670	22.612	34.092	12.301	28.250	1.826	8.498	18.316	3.673	12.087	24.907	0.847
	0.4	9.782	23.107	59.843	12.213	29.217	3.158	8.571	19.173	6.142	11.859	26.842	1.707
	0.6	9.825	24.750	70.225	12.693	34.423	4.208	8.676	21.285	7.608	12.318	30.225	2.446
	0.8	13.742	27.695	73.291	16.275	37.131	5.208	12.045	23.364	7.748	15.784	32.478	2.434
	0.9	14.158	28.733	74.686	16.692	42.157	5.658	12.420	24.952	9.039	16.286	33.167	4.569
	1.0	18.843	31.203	76.188	21.245	45.208	7.306	16.530	27.007	10.678	20.643	35.247	4.576
	Average	12.670	26.350	64.723	15.237	36.064	4.561	11.123	22.350	7.481	14.830	30.478	2.763
	0.2	9.529	108.531	127.211	12.686	145.807	3.993	8.375	93.961	12.338	12.139	133.425	1.628
	0.4	10.327	113.421	218.291	12.719	154.826	7.552	9.055	94.692	20.583	12.450	134.219	3.125
	0.6	10.135	120.280	266.023	12.518	164.904	9.913	8.941	102.241	24.847	12.293	143.627	4.389
	0.8	15.123	133.514	275.431	18.226	172.927	11.495	13.271	105.821	25.050	17.707	151.292	4.306
	0.9	16.541	139.770	285.422	18.824	180.619	11.870	14.486	122.327	27.784	18.184	156.443	5.852
	1.0	23.668	151.022	286.511	26.359	194.231	11.990	20.766	129.863	28.139	25.409	160.126	6.457
	Average	14.221	127.356	243.148	16.889	168.886	9.946	12.482	108.151	23.124	16.364	146.522	4.248