Precedence Diagram and Line Balancing

This document discusses the concepts of precedence diagram and line balancing in production planning. It explains how to balance a production line and calculate efficiency. It also provides study material and solved assignments on Desklib.

Answer 1
a. The precedence diagram.
b. Workstation cycle time
C = production time per day/required output per day
= (450 minutes/day)/360units per day
= 1.25 minutes per unit or 75 seconds per unit
a. Balancing the line
Work station Task Task time Idle time
I
A
C
E
30
30
15 0

II F 65 10
III
B
G
35
40 0
IV
D
H
35
25 15
b.
d. Efficiency of line balance
Efficiency =
= 275 / 4(75)
= 0.917 or 91.7%

Answer-2
C = (5 Hours X 5 Days X 60 min/hr)/ 3000 units / day
= 0.5 min/ unit
N = 1.9 min / 0.5 min
= 3.8
= 4

Answer -3
average number = lambda = lambda / u - lamba
lambda = arrival rate; u = repair rate
hence ( from table)
average = 2/(4-2) =1
No of
Repairs
Arrival
Rate
Repair Rate Avg No. of
Repair
Downtime
Loss @
40/hr
costs of
repairers @
$20/hr
Total costs
in $/hr
1 2 2 Infinite Infinite 20 Infinite
2 2 3 2 80 40 120
3 2 4 1 40 60 100
Answer - 4

Januar
y
February
Marc
h
Apri
l
Ma
y
Jun
e
Jul
y
Augu
st
Septembe
r
Octobe
r
Nov
ember e
Forecast 600 800 900 600 400 300 200 200 300 700 800
Beginni
ng
inventory
200
181 -38 -357 -376 -195 86 71 452 733 614
Availabl
e
productio
n
581 581 581 581 581 581 185 581 581 581 581
Ending
inventory
181 -38 -357 -376 -195 86 71 452 733 614 395
Costs
US$
116,200.0
0
US$
116,200.00
US$
116,200
.00
US$
116,20
0.00
US$
116,20
0.00
US$
116,20
0.00
US$
37,00
0.00
US$
116,200.
00
US$
116,200.00
US$
116,200.
00
US$
116,20
0.00
1
Lost
sales
US$ -
US$
(760.00)
US$
(7,140.0
0)
US$
(7,520.
00)
US$
(3,900
.00)
US$ US$
US$
-
US$ -
US$
-
US$ U

Inventor
y
US$
905.00
US$ - US$ - US$ US$
US$
US$
355.0
0
US$
2,260.00
US$
3,665.00
US$
3,070.00
US$
1,975.
00
Total
US$
1,308,920
.00
Answer - 5
Productivity = 0.5 units/hour, 8 hours/day, 50 days/season
Labor RT = $10/hour, OT = $15/hour
RT unit cost = $10/0.5 units = $20/unit, OT unit cost = $15/0.5 units = $30/unit
Inventory holding = $20/unit/quarter, Backorder = $8/unit
Hiring = $100/worker, Firing = $200/worker, Spring Inventory = 1,000 units
Number of units produced by 1 worker in one season = 0.5*8*50 = 200 units
*Laid off 20 workers at the beginning of summer
** Hired 20 workers at the end of summer to begin regular work in the fall
*** Hired 25 workers at the end of summer to begin regular work in the fall

PRODUCTION PLAN 1:
Seasons Spring Summer Fall Winter Total Cost
Beginning
Inventory
1000 1000 1000 0
Demand
Forecast
20000 10000 15000 18000
Production
RT
14000 10000 14000 14000 52000
Production
OT
60000 6000 180000
Ending
Inventory
1000 1000 0 2000 40000
Back Orders 0 0 4000 4000 32000

# of Workers
used
70 50 70 70
# of Workers
hired
20 20 2000
# of Workers
laid off
20 20 4000
Totals 1,298,000
PRODUCTION PLAN 2:
Seasons Spring Summer Fall Winter Total Cost
Beginning
Inventory
1000 0 0 0
Demand
Forecast
20000 10000 15000 18000
Production
RT
14000 10000 15000 15000 54000

Production
OT
50000 5000 150000
Ending
Inventory
0 0 0 0 0
Back Orders 0 0 3000 3000 24000
# of Workers
used
70 50 75 75
# of Workers
hired
25 25 2500
# of Workers
laid off
20 20 4000
Totals 1,260,500