Case 4.2 New Frontier and Case 4.3 Assigning Students to Schools Solutions

Solution of Case 4.2 New Frontier and Case 4.3 Assigning Students to Schools LPP

(in book Introduction to Operation Research, Hillier and Lieberman)

Download CASE Study 4.3 : Assigning Students to school EXCEL FILE 

CASE 4.2 Solution

New Frontiers Case Study Analysis Or by Kaushik Mandal

CASE 4.3 Solutions 

Download CASE Study 4.3 : Assigning Students to school EXCEL FILE 

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Overview

Part a-c
Part d
Part e
Part f
Scen1
Part g

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Sheet 1: Part a-c

Case Study 4.3: Assigning Students to Schools
		# of	% in 6th	% in 7th	% in 8th		Bussing Cost ($/student)
	Area	Students	Grade	Grade	Grade	School 1	School 2	School 3
	1	450	0.32	0.38	0.30	300	0	700
	2	600	0.37	0.28	0.35	N/A	400	500
	3	550	0.30	0.32	0.38	600	300	200
	4	350	0.28	0.40	0.32	200	500	N/A
	5	500	0.39	0.34	0.27	0	N/A	400
	6	450	0.34	0.28	0.38	500	300	0
Best Assignment:
			# of Students Assigned				Total # of
	Area	School 1	School 2	School 3	Total		Students
	1	0.00	450.00	0.00	450	=	450
	2	0.00	422.22	177.78	600	=	600
	3	0.00	227.78	322.22	550	=	550
	4	350.00	0.00	0.00	350	=	350
	5	366.67	0.00	133.33	500	=	500
	6	83.33	0.00	366.67	450	=	450
	Total	800	1100	1000
	School Capacity	900	1100	1000				Total Bussing Cost:	$555,555.56
			# of Students by Grade
		School 1	School 2	School 3
	6th Graders	269.33	368.56	339.11
	7th Graders	288.00	362.11	300.89
	8th Graders	242.67	369.33	360.00
	30% of Total	240	330	300
	36% of Total	288	396	360

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Sheet 2: Part d

Case Study 4.3: Assigning Students to Schools
		# of	% in 6th	% in 7th	% in 8th		Bussing Cost ($/student)
	Area	Students	Grade	Grade	Grade	School 1	School 2	School 3
	1	450	0.32	0.38	0.30	300	0	700
	2	600	0.37	0.28	0.35	N/A	400	500
	3	550	0.30	0.32	0.38	600	300	200
	4	350	0.28	0.40	0.32	200	500	N/A
	5	500	0.39	0.34	0.27	0	N/A	400
	6	450	0.34	0.28	0.38	500	300	0
Best Assignment:
			# of Students Assigned				Total # of
	Area	School 1	School 2	School 3	Total		Students
	1	0.00	450.00	0.00	450	=	450
	2	0.00	600.00	0.00	600	=	600
	3	0.00	0.00	550.00	550	=	550
	4	350.00	0.00	0.00	350	=	350
	5	500.00	0.00	0.00	500	=	500
	6	0.00	0.00	450.00	450	=	450
	Total	850	1050	1000
	School Capacity	900	1100	1000				Total Bussing Cost:	$420,000.00
			# of Students by Grade
		School 1	School 2	School 3
	6th Graders	293.00	366.00	318.00
	7th Graders	310.00	339.00	302.00
	8th Graders	247.00	345.00	380.00
	30% of Total	255	315	300
	36% of Total	306	378	360

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Sheet 3: Part e

Case Study 4.3: Assigning Students to Schools
		# of	% in 6th	% in 7th	% in 8th		Bussing Cost ($/student)
	Area	Students	Grade	Grade	Grade	School 1	School 2	School 3
	1	450	0.32	0.38	0.30	300	0	700
	2	600	0.37	0.28	0.35	N/A	400	500
	3	550	0.30	0.32	0.38	600	300	0
	4	350	0.28	0.40	0.32	0	500	N/A
	5	500	0.39	0.34	0.27	0	N/A	400
	6	450	0.34	0.28	0.38	500	300	0
Best Assignment:
			# of Students Assigned				Total # of
	Area	School 1	School 2	School 3	Total		Students
	1	0	450	0	450	=	450
	2	0	600	0	600	=	600
	3	0	0	550	550	=	550
	4	350	0	0	350	=	350
	5	318	0	182	500	=	500
	6	132	50	268	450	=	450
	Total	800	1100	1000
	School Capacity	900	1100	1000				Total Bussing Cost:	$393,636.36
			# of Students by Grade
		School 1	School 2	School 3
	6th Graders	266.91	383.00	327.09
	7th Graders	285.09	353.00	312.91
	8th Graders	248.00	364.00	360.00
	30% of Total	240	330	300
	36% of Total	288	396	360

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Sheet 4: Part f

Case Study 4.3: Assigning Students to Schools
		# of	% in 6th	% in 7th	% in 8th		Bussing Cost ($/student)
	Area	Students	Grade	Grade	Grade	School 1	School 2	School 3
	1	450	0.32	0.38	0.30	0	0	700
	2	600	0.37	0.28	0.35	N/A	400	500
	3	550	0.30	0.32	0.38	600	0	0
	4	350	0.28	0.40	0.32	0	500	N/A
	5	500	0.39	0.34	0.27	0	N/A	400
	6	450	0.34	0.28	0.38	500	0	0
Best Assignment:
			# of Students Assigned				Total # of
	Area	School 1	School 2	School 3	Total		Students
	1	39	411	0	450	=	450
	2	0	237	363	600	=	600
	3	0	78	472	550	=	550
	4	350	0	0	350	=	350
	5	435	0	65	500	=	500
	6	76	374	0	450	=	450
	Total	900	1100	900
	School Capacity	900	1100	1000				Total Bussing Cost:	$340,053.76
			# of Students by Grade
		School 1	School 2	School 3
	6th Graders	306.00	369.75	301.25
	7th Graders	324.00	352.25	274.75
	8th Graders	270.00	378.00	324.00
	30% of Total	270	330	270
	36% of Total	324	396	324

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Sheet 5: Scen1

0	450	0
	422.2222222222	177.7777777778
0	227.7777777778	322.2222222222
350	0
366.6666666667		133.3333333333
83.3333333333	0	366.6666666667

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Sheet 6: Part g

	# Students Walking:		Bussing
Case	1 - 1.5 mi.	1.5 - 2 mi.	Cost
Base	0	0	$555,556
Option 1	900	0	$393,636
Option 2	822	491	$340,054

Download CASE Study 4.3 : Assigning Students to school EXCEL FILE 

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