Operations Management Assignment Solution - MGX 3771, Semester 1

This document presents solutions to an Operations Management assignment, addressing key topics within the field. The solutions cover precedence diagrams and assembly line balancing, calculating cycle times, and efficiency. The assignment also includes problems related to capacity planning, queuing theory, and aggregate planning. The solutions demonstrate how to calculate the optimal number of servers, analyze costs, and develop production plans considering factors such as labor costs, inventory, and demand fluctuations. The assignment covers topics from Jacobs and Chase's "Operations and Supply Chain Management" textbook, providing a comprehensive overview of operations strategy, manufacturing processes, service processes, and capacity management.

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