Multiple-Objective Linear Programming And Analytic Hierarchy Process For Optimization Problems

Q1a							Total	Estimated Recycleble Garbage
		x1	x2	x3	x4	x5
Objective	Decision	1.28E-07	8.93E-08	1.91E-07	1.53E-07	7.65E-08
	Capacity	10	7	15	12	6	7.07E-06


constrains
	sectors
	1	2630472	1096030	3726502	5699356	7124195	2.56398	4.6
	2	1863251	1644045	6356974	7014592	6795386	3.19449	4.6
	3	1096030	2192060	2849678	7233798	6576180	2.491283	4.7
	4	1972854	2740075	3507296	6247371	6795386	2.643668	4.2
	5	1205633	2411266	1644045	6028165	6795386	2.126398	3.8
	6	3178487	3726502	5041738	5918562	4712929	2.969408	3.9
	7	3726502	4712929	7562607	4712929	4384120	3.4	3.4
	8	4164914	4603326	3945708	5808959	3726502	2.871546	3.3
	9	2411266	3178487	5041738	5808959	5480150	2.864556	3.9
	10	2411266	5041738	5480150	4603326	6356974	2.997368	4.1

suburb	x	y	Wh1	Wh2	Wh3	Distance
Ascot Vale	25	13.8	0	1	0	3.21	1
Avondale	19.7	14.2	0	1	0	5.42	1
Brooklyn	18.2	9.4	1	0	0	5.21	1
Burnside	10.7	16.2	1	0	0	6.29	1
Caroline	9.7	16.8	1	0	0	7.25	1
Derrimut	10.7	10.2	1	0	0	2.4	1
Flemington	24.3	11.8	0	1	0	1.09	1
Footscray	22.4	11	0	1	0	1.52	1
Footscray	23.7	11.1	0	1	0	0.38	1
Hoppers	6.3	4.7	0	0	1	1.28	1
Leverton	13.5	7.2	1	0	0	3.21	1
Melbourne	28.6	8.9	0	1	0	5.06	1
Seabrook	10.9	2.3	0	0	1	6.33	1
Southbank	29.8	8.1	0	1	0	6.48	1
St Kilda	30.4	3.4	0	1	0	9.83	1
Sunshine	16.6	10.2	1	0	0	3.52	1
Tameit	5.2	8.1	0	0	1	3.46	1
Tameit	5.1	6.6	0	0	1	1.96	1
Werribee	0.5	0	0	0	1	6.48	1
Wyndham	0	2	0	0	1	5.68	1

Wh1	13.1	10.4		Total		86.06
Wh2	23.9	10.8
Wh3	5	4.6


Q3

			price	safety	economy	comfort	GM	PV	price	A	B	C	GM	PV
		price	1	0.166667	0.333333	0.2	0.324668	0.061042	A	1	0.333333	4	1.100642	0.262753
		safety	6	1	4	2	2.632148	0.494876	B	3	1	7	2.758924	0.65863
		economy	3	0.25	1	0.333333	0.707107	0.132945	C	0.25	0.147619	1	0.332936	0.079481
		comfort	5	0.5	3	1	1.654875	0.311137	SUM=	4.25	1.480952	12	4.188883
		sum =	15	1.916667	8.333333	3.533333	5.318798	1	SUM PV =	1.116701	0.975399	0.95377
		sum PV =	0.915624	0.948513	1.107873	1.099351			LAMBA MAX =	3.032367
		Labda max	4.071362						CI	0.016183
		CI	0.023787						RI	0.58
		CR	0.02643						CR	0.027902




		price	A	B	C	GM	PV		price	A	B	C	GM	PV
		A	1	0.333333	2	0.87358	0.210251		A	1	0.166667	0.333333	0.381572	0.10253
		B	3	1	8	2.884499	0.694235		B	6	1	0.333333	1.259921	0.338545
		C	0.5	0.125	1	0.39685	0.095513		C	3	3	1	2.080084	0.558926
		SUM=	4.5	1.458333	11	4.15493			SUM=	10	4.166667	1.666666	3.721576
		SUM PV =	0.946132	1.012426	1.050644				SUM PV =	1.025296	1.410604	0.931542
		LAMBA MAX =	3.009202						LAMBA MAX =	3.367442
		CI	0.004601						CI	0.183721
		RI	0.58						RI	0.58
		CR	0.007933						CR	0.31676



		price	A	B	C	GM	PV
		A	1	0.125	0.25	0.31498	0.07892
		B	8	1	0.333333	1.386722	0.347451
		C	4	3	1	2.289428	0.573629
		SUM=	13	4.125	1.583333	3.991131
		SUM PV =	1.025961	1.433235	0.908246
		LAMBA MAX =	3.367442
		CI	0.183721
		RI	0.58
		CR	0.31676



			price	economy	safety	comfort
		Pv of factors	0.061052	0.132945	0.494876	0.311137
		A	0.262753	0.10253	0.210252	0.07892	0.158276
		B	0.65863	0.338545	0.694235	0.347451	0.536884
		C	0.078617	0.558925	0.095513	0.573629	0.30485


	Land Cost	Labor cost	Labor availability	Construction cost	Transportation	Access to customers	Long – range goals
Smithfield, NSW	5	7	6	5	6	8	5
Eagle farm, QLD	7	6	7	6	6	7	7
Derrimut, VIC	6	6	5	7	7	7	6
weight	4	6	8	5	5	9	7

squares

	Land Cost	Labor cost	Labor availability	Construction cost	Transportation	Access to customers	Long – range goals
Smithfield, NSW	25	49	36	25	36	64	25
Eagle farm, QLD	49	36	49	36	36	49	49
Derrimut, VIC	36	36	25	49	49	49	36

Total	110	121	110	110	121	162	110

sum square root	29.05168

	Land Cost	Labor cost	Labor availability	Construction cost	Transportation	Access to customers	Long – range goals
Smithfield, NSW	0.17211	0.24095	0.20653	0.17211	0.20653	0.27537	0.17211
Eagle farm, QLD	0.24095	0.20653	0.24095	0.20653	0.20653	0.24095	0.24095
Derrimut, VIC	0.20653	0.20653	0.17211	0.24095	0.24095	0.24095	0.20653


multiply each of the columns by the respective weights given to the criterion.

	Land Cost	Labor cost	Labor availability	Construction cost	Transportation	Access to customers	Long – range goals
Smithfield, NSW	0.68843	1.4457	1.65223	0.86054	1.03264	2.47834	1.20475
Eagle farm, QLD	0.9638	1.23917	1.9276	1.03264	1.03264	2.16855	1.68665
Derrimut, VIC	0.82611	1.23917	1.37686	1.20475	1.20475	2.16855	1.4457




	Ideal solution	Negative ideal solution
Smithfield, NSW	0.15	0.29
Eagle farm, QLD	0.21	0.31
Derrimut, VIC	0.39	0.09



	Closeness
Smithfield, NSW	0.34
Eagle farm, QLD	0.41
Derrimut, VIC	0.81

Q1c							Total	Estimated Recycleble Garbage
		x1	x2	x3	x4	x5
Objective	Decision	0	2.68E-07	4.93E-07	8.91E-07	2.3E-07
	Capacity	10	7	15	12	6	2.13E-05


constrains
	sectors
	1	2630472	1096030	3726502	5699356	7124195	8.8478	13.8
	2	1863251	1644045	6356974	7014592	6795386	11.38884	13.8
	3	1096030	2192060	2849678	7233798	6576180	9.951034	14.1
	4	1972854	2740075	3507296	6247371	6795386	9.593112	12.6
	5	1205633	2411266	1644045	6028165	6795386	8.390731	11.4
	6	3178487	3726502	5041738	5918562	4712929	9.84283	11.7
	7	3726502	4712929	7562607	4712929	4384120	10.2	10.2
	8	4164914	4603326	3945708	5808959	3726502	9.212987	9.9
	9	2411266	3178487	5041738	5808959	5480150	9.774482	11.7
	10	2411266	5041738	5480150	4603326	6356974	9.616332	12.3

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