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

Overview

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

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

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

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

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

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

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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Munshi Premchand (Hindi: मुंशी प्रेमचंद,

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Born Dhanpat Rai, he began writing under the pen name "Nawab Rai", but subsequently switched to "Premchand", while he is also known as "Munshi Premchand", Munshi being an honorary prefix. A novel writer, story writer and dramatist, he has been referred to as the "Upanyas Samrat" ("Emperor of Novels") by some Hindi writers. His works include more than a dozen novels, around 250 short stories, several essays and translations of a number of foreign literary works into Hindi.

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