## (Solved) EIN 4401 Lean Production Home Work # 2 Due March 1, 201 1. The demand for a product is 1000 units per day. The external setup for a punch press is...

The daily demand is known to be 400 units per day. It is also known that the batch size for thisÂ line is 25 units per container. The line operates 24 hours each day without breaks.Â a)Â Calculate the needed number of Kanban cards if each station will be controlled byÂ

Kanban. Use 10% safety factor.Â b)Â If the entire line is to be controlled by Conwip system what should be the number ofÂ cards needed. For this, use 10% safety factor, and assume the card travel time fromÂ machine 5 to machine 1 is 10 minutes.Â c)Â Which machine is the bottleneck machine on this line? Why?Â d)Â Now assume that we will implement DBR technique to this line. I.e., the machines fromÂ Machine #1 to the bottleneck machine (inclusive) will be controlled by Conwip. Once theÂ batch clears the bottleneck machine, it will travel the remaining machines in a pushÂ fashion without any delay (pull-push system). Calculate the number of cards needed onÂ the Conwip side of the line. Again use 10% for safety factor and assume that the cardÂ transfer time from your bottleneck machine to machine #1 is 10 minutes.Â

EIN 4401 Lean Production
Home Work # 2
Due March 1, 201 1. The demand for a product is 1000 units per day. The external setup for a punch press is
approximately 1.75 hours. The internal setup time is 15 minutes. The facility operates on a
single 8-hr shift. The punch press feeds the downstream operation grinder by placing its lot
production into containers of size 50. We will make the grinder be responsible to inform the
punch process for the start of a new production batch as well as the signal for the material
order.
- Kanban waiting time at the receiving post at grinder is 10 minutes
Kanban transfer time to punch press ordering post is 15 min
Kanban wait time at the ordering post 5 minutes
Processing time at the punch press 0.1 minutes per unit
In process batch waiting time 10 minutes
Lot transfer time to final buffer is 0
We want to build 10 % safety to our card calculations.
Material kanban waiting time at the grinder receiving post is 7 minutes
Material kanban transfer time to raw material storage is 13 minutes
Material kanban waiting time at the raw material post is 18 minutes
Time to withdraw material for punch press lot size is 12 minutes
Time to convey the raw material to punch press is 10 minutes
The system operates 8-hour shift a day. a)
b)
c)
d) Find the minimum production lot size at the punch press.
Find the kanban cycle time at the punch press.
Where should the production ordering signal kanban be placed at the grinding station.
Where the material ordering kanban be placed at the grinding station. 3. Consider a flow line below 1 2 3 4 5 The following table provides all the information need for designing Kanban control or Conwip
control on this line. All times are in minutes. Kanban waiting at
the receiving post
Transfer of Kanban
to Ordering Post
Wait at the
Ordering Post
Internal Setup time
Unit processing
time
Container transfer
time to downstream
buffer
Waiting time in the
buffer 1
2 Machines (all data in minutes)
2
3
4
5
3
4
3
2 5 5 5 5 5 6 7 6 5 4 10 12 14 8 7 1 2 3 2 2 4 4 4 4 6 6 4 7 5 4 The daily demand is known to be 400 units per day. It is also known that the batch size for this
line is 25 units per container. The line operates 24 hours each day without breaks.
a) Calculate the needed number of Kanban cards if each station will be controlled by
Kanban. Use 10% safety factor.
b) If the entire line is to be controlled by Conwip system what should be the number of
cards needed. For this, use 10% safety factor, and assume the card travel time from
machine 5 to machine 1 is 10 minutes.
c) Which machine is the bottleneck machine on this line? Why?
d) Now assume that we will implement DBR technique to this line. I.e., the machines from
Machine #1 to the bottleneck machine (inclusive) will be controlled by Conwip. Once the
batch clears the bottleneck machine, it will travel the remaining machines in a push
fashion without any delay (pull-push system). Calculate the number of cards needed on
the Conwip side of the line. Again use 10% for safety factor and assume that the card
transfer time from your bottleneck machine to machine #1 is 10 minutes.
2. Consider the data provided below for three products. Product A
B
C Selling
price
(\$) Unit direct
material
(\$) Unit
direct
labor
(\$) Unit
outsourcin
g cost (\$) Unit
(\$) 125
250
200 25
100
110 35
35
35 25
25
25 12
12
12 Unit
processing
time at the
bottleneck
(hrs.)
1
2.5
2 There is 600 total available machine-hours on the bottleneck machine. The sales department
estimates the maximum sales for each product to be as follows:
A : maximum 70
B : maximum 120
C : maximum 220
a) What is the unit profit of each product in the sense of classical cost accounting? Show work.
b) What is the contribution margin of each product in the TOC sense? Show work.
c) What is the best product mix that will maximize the throughput (in the TOC sense)? Show
work.
d) Write down the corresponding LP problem, when solved will give the optimal product mix.
3. Consider the data below:
Daily demand matrix:
F08958
F00121
000331
F51354
F09584
F09688 Parts
A
B
C
D
E
F Daily demand (parts)
900
1,200
1,800
2,400
600
300 Setup time matrix:
Machine
Parts
F08958
F00121
000331
C
F51354
F09584
F09688 A
B
D
E
F Cut
(sec) Mold
(sec) 300
300
300
300
300
300 20
30
10
20
20
10 Assembly
(sec)
90
90
90
90
90
90 (e.g. It takes 300 sec. to setup the cut machine to cut part A.
It takes 90 sec. to setup the assembly machine to assemble part C )
Processing time matrix:
Machine
Parts
F08958 A Cut
(sec)
1 Mold
(sec)
10 Assembly
(sec)
20 F00121
000331
C
F51354
F09584
F09688 B
D
E
F 1
1
1
1
1 10
10
10
10
10 20
20
20
20
20 (e.g. It takes 1 sec. for cut machine to cut 1 unit of A.
It takes 20 sec. to assemble 1 unit C.)
Available time matrix:
Working time
per shift
Cut
Mold
Assembly 480 min (8 hrs)
480 min (8 hrs)
480 min (8 hrs) No. of
shifts
per day
3
3
3 No. of
machine
allocated
1
1
2 Total working
time per day
(sec)
86,400
86,400
172,800 Efficiency 85%
85%
85% Total
available time
per day (sec)
73,440
73,440
146,880 Total working time per day = working time per shift * no. of shifts per day * no. of machines
allocated
Total available time per day = Total working time per day * efficiency a) What are the daily demand ratios for this problem?
b) How many slots will you have on the repeating production cycle (nA, nB, nC, nD, nE, nF)?
What will be your optimum batch size?
c) Given the number of slots, find the sequencing of these cards so that the most smoothed
our production schedule is at hand.

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