Home-Work #3 Solution Set

Home-work #3 Solution Set

PROBLEMS from chapter 6:

5.a.

b. The minimum cycle time = maximum task time =1.2 minutes

The maximum cycle time = .2 +.4 +.2 +.4 +1.2 +1.2 + 1.0 = 4.6 minutes

Task / Number of following tasks
A / 4
B / 3
C / 2
D / 2
E / 1
F / 1
G / 0

Assembly Line Balancing Table (CT = 2 minutes)

Work Station / Task / Task Time / Time Remaining / Feasible tasks Remaining
I / A / 0.2 / 1.8 / B,D
B / 0.4 / 1.4 / C, D
D / 0.4 / 1.0 / C
C / 0.2 / 0.8 / –
II / E / 1.2 / 0.8 / –

III

/ F / 1.2 / 0.8 / –

IV

/ G / 1.0 / 1.0 / –

b.

Station / Tasks / Time / Idle/Time
1 / a,b / 1.9 / .1
2 / c,d / 1.9 / .1
3 / e,f,i / 2.0 / 0
4 / g,h,j / 1.5 / .5
5 / k,m / 1.2 / .8
1.5
c. / Tasks / Positional Weight
a / 8.5
b / 4.6
c / 4.4
d / 4.2
e / 3.2
f / 3.5
g / 1.9
h / 1.5
i / 2.5
j / 2.0
k / 1.2
m / .3

Solutions (continued)

Work Station / Task / Task Time / Time Remaining / Feasible tasks Remaining
I / a / .5 / 1.5 / b, c, d
b / 1.4 / .1 / –
II / c / 1.2 / .8 / d, e
d / .7 / .1
III / f / 1.0 / 1.0 / e, i
e / .5 / .5 / i, g
i / .5 / 0 / –
IV / j / .8 / 1.2 / g
g / .4 / .8 / h
h / .3 / .5 / –
k / .9 / 1.1 / m
m / .3 / .8 / –

Total idle time = .1 + .1 + 0 + .5 + .8 = 1.5 minutes

d.Balance delay: part b and c 1.5/10 = 15%

11. / 1 / 5 / 4
3 / 8 / 7
6 / 2

17.Two-way trips can not be used here because of the one-way route restriction. Consequently, we need a heuristic that will yield reasonable assignments. One possible heuristic is the following:

Beginning with Department 1, identify the department which receives the greatest number of trips from that department (e.g., 40 to Department 2). Assign that department to the next location counter-clockwise.

For that department (e.g., 2) identify the department which receives the greatest number of trips (e.g., 5) and assign it to the next position.

Continue in this manner until all departments have been assigned.

The resulting set of assignments for this problem is: A–1, 2–B, 5–C, 4–D, 9–E, 8–F, 6–G, 10–H, 7–I, 3–J.

IFreturn trips to the original departments after delivery are added to the cost/objective, which would seem to make all locations comparable. Why they are excluded can be explained by one of these reasons:

1.Return trips cost less because they are unloaded.

PROBLEMS from Chapter 8:

4. / A / B / C
FC/year / $250,000 / $50,000
VC/unit / 500 / 2,500 / 1,000
a.
b. / C (from graph)
c. / Subcontracting prices are probably more precise, subcontracting provides another source of supply. Expansion would allow more control and flexibility.
6. / Memphis / Biloxi / Birmingham
Lease, equipment / $40,000 / $60,000 / $100,000
Transportation / 50,000 / 60,000 / 25,000
“Fixed” Costs / $90,000 / $120,000 / $125,000
VC/unit / $8 / $4 / $5
Memphis / Biloxi / Birmingham
TC = VC/unit x Q + FC: / $170,000 / $160,000 / $175,000
7. / City / Outside
FC/month / $7,000 / $4,700
VC/unit / $30 / $40
Rev/unit / $90 / $90
Profit = (rev/unit – VC/unit) – FC
City / Outside
a. / P200 / $5,000 / $5,300*
P300 / 11,000* / 10,300
b. / ($90 – $30)Q – $7,000 = ($90 – $40)Q – 4,700
Solving, Q = 230 cars
8. / Factor / Local bank / Steel mill / Food warehouse / Public school
1. / Convenience for customers / H / L / M–H / M–H
2. / Attractiveness of building / H / L / M / M–H
3. / Nearness to raw materials / L / H / L / M
4. / Large amounts of power / L / H / L / L
5. / Pollution controls / L / H / L / L
6. / Labor cost and availability / L / M / L / L
7. / Transportation costs / L / M–H / M–H / M
8. / Construction costs / M / H / M / M–H
9. / 1 / 4 / 3
2 / 5 / 6
11. / 1 / 5 / 4
3 / 8 / 7
6 / 2
12. / Location / x / y / 0
A / 5 / 7 / 15
B / 6 / 9 / 20
C / 3 / 9 / 25
D / 9 / 4 / 30
Totals / 23 / 29 / 90
= / xiQi / = / 5(15) + 6(20) + 3(25) + 9(30) / = / 540 / = 6.0
Qi / 90 / 90
= / xiQi / = / 7(15) + 9(20) + 9(25) + 4(30) / = / 630 / = 7.0
Qi / 90 / 90

The center of gravity and optimal location is (6,7).

Case: Hello Wal-Mart?

1. Owners of small businesses.

Pro: restaurants and other businesses that do not compete directly with Wal-Mart would

generally welcome the additional traffic Wal-Mart would attract.

Con: businesses that directly compete would not fare well unless they provided a product

or service value that would offset Wal-Mart’s lower price.

2. Residents.

Pro: another shopping option, lower prices, and other, non-competing businesses that

would be attracted by the increased traffic Wal-Mart would generate.

Con: Increased traffic and noise, construction inconveniences, loss of small-town

atmosphere, and loss of local businesses and jobs.

Wal-Mart responses: The company would be a “good neighbor,” supporting the community

and providing jobs for low-skilled and handicapped workers. Construction would create

construction jobs and generate taxes and revenues for the community. Shoppers would benefit

from Wal-Mart’s low prices. Also, there would be an increase in the tax base.