Linear Programming & Model with Binary Variables

Product-MixProblemforstudentstoworkon_Final.xlsx

Home >Mathematics homework help >Statistics homework help >Linear Programming & Model with Binary Variables

Prod-Mix

A Production-Mix Problem
		Department					Minimum
	PRODUCT	Wiring	Drilling	Assembly	Inspection	Unit Profit	Requirement
	XJ201	0.5	3	2	0.5	$ 9	150
	XM897	1.5	1	4	1.0	$ 12	100
	TR29	1.5	2	1	0.5	$ 15	200
	BR788	1.0	3	2	0.5	$ 11	400
	Capacity	1500	2350	2600	1200
Decision		Wiring	Drilling	Assembly	Inspection	Total Profit
XJ201	150	75	450	300	75	1350
XM897	300	450	300	1200	300	3600
TR29	200	300	400	200	100	3000
BR788	400	400	1200	800	200	4400
Total		1225	2350	2500	675	12350
Surplus Capacity		275	0	100	525

Failsafe Electronics Corporation (FEC) primarily manufactures mainly four highly technique products, which supplies to aerospace firms that hold NASA contracts. each of the products must pass through the following departments before they are shipped: Wiring, Drilling, Assembly, and Inspection. The time requirements in each department (in hours) for each unit produced and its corresponding profit value are summarized in the below table:

Workforce Scheduling 539 #7

Workforce-Scheduling Model
Input Data
	Hour	Min Staff Required
	8-9	5
	9-10	12
	10-11	15
	11-Noon	12
	Noon-1	11
	1-2	18
	2-3	17
	3-4	19
	4-5	14
	PT Hours per shift=		4	hours
	Full-time employees=		5	people
Model
	Hour	Shift 1	Shift 2	Shift 3	Shift 4	Shift 5	Shift 6
	8-9
	9-10
	10-11
	11-noon
	noon-1
	1-2
	2-3
	3-4
	4-5
		x1	x2	x3	x4	x5	x6
	Decision	1	6	3	0	5	9
	Objective	1	1	1	1	1	1	24		RHS	Slack
	8-9	1						1	>=	0	-1
	9-10	1	1					7	>=	7	0
	10-11	1	1	1				10	>=	10	0
	11-noon	1	1	1	1			10	>=	7	-3
	noon-1		1	1	1	1		14	>=	6	-8
	1-2			1	1	1	1	17	>=	13	-4
	2-3				1	1	1	14	>=	12	-2
	3-4					1	1	14	>=	14	0
	4-5						1	9	>=	9	0
											-8
	Homework	Page 539 #7 -cant find
	7 days a week scheduling
			shift 1	shift 2	shift 3	shift 4	shift 5	shift 6	shift 7
		Monday										RHS	Slack
		Tuesday
		Wednesday
		Thursday
		Friday
		Saturday
		Sunday
			Shift 1	Shift 2	Shift 3	Shift 4	Shift 5	Shift 6	Shift 7
		Decision
		Objective	1	1	1	1	1	1	1
		Monday	1			1	1	1	1
		Tuesday	1	1			1	1	1
		Wednesday	1	1	1			1	1
		Thursday	1	1	1	1			1
		Friday	1	1	1	1	1
		Saturday		1	1	1	1	1
		Sunday			1	1	1	1	1

Brewer Services contracts with outsoursing partners to handle various customer-service functions. The customer-service dpartment is open Monday through Friday from 8 a.m. to 5 p.m.. Calls vary over the course of a typical day. Vased on a study of call volumes provided by one of firm's partners, the minimum number of staff needed each hour of the day are as follows:

Transportation

Linear Programing Problems
Transportation Model
	From	Albuquerque	Bostone	Cleveland	Capacity
	Des Moines	$ 5	$ 4	$ 3	100
	Evansville	$ 8	$ 4	$ 3	300
	Fort Lauderdale	$ 9	$ 7	$ 5	300
	Dummy	$ - 0	$ - 0	$ - 0	200
	Demand	300	200	400
		1	2	3
Decision	From	Albuquerque	Bostone	Cleveland
A	Des Moines	XA1	XA2	XA3
B	Evansville	XB1	XB2	XB3
C	Fort Lauderdale	XC1	XC2	XC3
Decision	From	Albuquerque	Bostone	Cleveland	Total
A	Des Moines	100	0	0	100
B	Evansville	0	200	100	300
C	Fort Lauderdale	0	0	300	300
	Dummy	200	0	0	200
	Total	300	200	400
	Total Transportation Cost:				3100

Page 513 #28

A Production-Mix Problem
		Product				Capacity
	PRODUCT	Ferrari	BMW	Lotus	Tesla	Minutes/day
	Molding	5.00	3.50	1.00	3.00	600
	Sanding	4.00	3.20	2.00	3.65	600
	Polishing	3.00	2.00	3.00	1.00	480
	Painting	3.75	3.25	1.75	2.00	480
	Finishing	4.00	1.00	2.00	3.00	480
	Prices	$ 350	$ 330	$ 270	$ 255

The Martinez Model Car Company produces four different radio-controlled model cars based on exotic production models. Each model required production in five departments. See the table below and answer the following three questions: a. How many of each type of car should be produced to maximize profit? (Run solver once); b. What happens if market requires that at least 50 units of each be produced each day? (run solver twice with 50 instead of 40).

Page 554 #6

Workforce-Scheduling Model
Input Data
	Hour	Min Nurses Needed
	12:00 a.m. - 4:00 am	5
	4 a.m. - 8:00 a.m.	10
	8 a.m. - 12:00 p.m.	14
	12 p.m. - 4:00 p.m.	8
	4 p.m. - 8:00 p.m.	12
	8 p.m. - 12:00 a.m.	10

Van Nostrand Hospital must schedule nurses to provide the adaquate care but also keep the cost down. From historical records, we can project the minimum number of nurses required. Nuses work for consecutive 8 hours shift. Find the optimal solution first, then fixed the total number of nurses and find the smallest over staffing in all hours (just like the second part of the workforce scheduling video example).

Page 516 # 37Transportation

		Destination
		Seattle	San Francisco	Las Vegas	Tucson	Denver	Charlotte	Minneapolis	Fayetteville	Birmingham	Orlando	Cleveland	Philadelphia	Supply
Distribution Center	Atlanta	2.15	2.1	1.75	1.5	1.2	0.65	0.9	0.8	0.35	0.15	0.6	0.5	39200
	Lexington	1.95	2	1.7	1.53	1.1	0.55	0.6	1.05	0.6	0.5	0.25	0.3	32500
	Milwaukee	1.7	1.85	1.5	1.41	0.95	0.4	0.4	0.95	0.7	0.7	0.35	0.4	15200
	Salt Lake City	0.6	0.55	0.35	0.6	0.4	0.95	1	1.1	1.35	1.6	1.6	1.7	17000
	Demand	5500	17000	3900	3400	4500	7500	3000	8500	3300	12000	9000	14000