Production Scheduling
Penjadwalan Produksi
N Job M Mesin
3 4 5 6 7 8
B2 [----------]
E5
[-------------P9
[---]
D1 [-------X8
----]
C6
[-
Algoritma Johnson

Digunakan untuk menjadwalkan
pekerjaan N job di dua mesin flow shop
dengan tujuan minimasi Makespan.
Algoritma Johnson


Diketahui N job dikerjakan di 2 mesin dengan
urutan yang sama dengan waktu proses (Pi).
(I: Job ke 1,2,…n).
(J: Mesin 1, atau 2).
Pilih Pij terkecil
- Jika Pij terkecil ada dimesin 1, tetapkan
pada prioritas I
- Jika Pij terkecil ada dimesin 2, tetapkan
pada prioritas terakhir.


Pilih Pij terkecil berikutnya, lakukan hal
yang sama.
Teruskan sampai semua job
memperoleh prioritas pengerjaan.
N job di 3 Mesin Flow Shop
Algoritma Campbel (Perluasan Johnson).

Periksa apakah syarat terpenuhi, jika
ada N job dimesin A, B dan D dengan
waktu proses Ai, Bi, Di
Ai minimum  Bi Maximum
dan / atau
Di Minimum  Bi Maximum



Jika syarat terpenuhi jadikan 2
kelompok mesin K dan N
Ki= gabungan Ai dan Bi
Ni= Gabungan Bi dan Di
Selesaikan dengan aturan Johnson
Buat schedule dengan Gantt Chart
N job di M mesin Flow Shop
Perluasan campbel oleh Dudeck & Smith

Jika ada M mesin ambil mesin 1 dan
mesin M (mesin lain dianggap tidak
ada) Lakukan Algoritma Johnson
Diperoleh sequence 1 hitung Makespan


Ambil mesin 1, mesin 2 dan mesin M, M-1
Gabungkan waktu proses mesin 1 dan 2.
Ki = M1i + M2i
Gabungkan waktu proses mesin M dan m-1
Li=Mmi + MM-1i
Lakukan Algoritma Johnson diperoleh
sequence 2
Hitung Makespan.


Ambil Mesin 1, 2, 3 dan mesin M, M-1,
M-2
Gabungkan waktu proses
Pi
= M1i + M2i + M3i
Qi
= MMi + MM-1i + MM-2i
Lakukan Algoritma Johnson diperoleh
sequence 3
Hitung Makespan


Lakukan terus sampai semua mesin
teranalisa.
Diperoleh M-1 sequence 3
Hitung Makespan
Pilih Makespan terkecil
Urutan pengerjaan yang menghasilkan makespan terkecil tersebut
yang terpilih.

CONTOH PENJADWALAN DI M (>1)
MESIN
Contoh penjadwalan 5 Job 2 Mesin
JOB
1
MESIN 1
2
MESIN 2
10
2
3
8
3
7
5
4
9
1
5
6
4
Scheduling
Product-Focused
Manufacturing
Product-Focused Scheduling

Two general types of product-focused
production:


Batch - large batches of several
standardized products produced
Continuous - few products produced
continuously.... minimal changeovers
Scheduling Decisions

If products are produced in batches on
the same production lines:



How large should production lot size be for
each product?
When should machine changeovers be
scheduled?
If products are produced to a delivery
schedule:

At any point in time, how many products
should have passed each operation if time
Batch
Scheduling
EOQ for Production Lot Size

How many units of a single product should be
included in each production lot to minimize
annual inventory carrying cost and annual
machine changeover cost?
Example: EOQ for Production
Lots
CPC, Inc. produces four standard electronic
assemblies on a produce-to-stock basis. The annual
demand, setup cost, carrying cost, demand rate, and
production rate for each assembly are shown on the
next slide.
a) What is the economic production lot size for each
assembly?
b) What percentage of the production lot of power
units is being used during its production run?
c) For the power unit, how much time will pass
between production setups?
Example: EOQ for Production
Lots
Power Unit
Converter
Equalizer
Transformer
Annual
Demand
Setup
Cost
Carry
Cost
5,000
10,000
12,000
6,000
$1,200
600
1,500
400
$6
4
10
2
Demand Prod.
Rate Rate
20
40
48
24
200
300
100
50
Example: EOQ for Production
Lots
EOQ=Economic
(2DS/C[p/(p-d)]
Production Lot Sizes
EOQ1 = (2(5,000)(1,200)/6[200/(200-20)]  1, 490.7
EOQ2 = (2(10,000)(600)/4[300/(300-40)]  1,860.5
EOQ3 = (2(12,000)(1,500)/10[100/(100-48)]  2,631.2
EOQ4 = (2(6,000)(400)/2[50/(50-24)]  2,148.3
Example: EOQ for Production
Lots

% of Power Units Used During Production
d/p = 20/200 = .10 or 10%

Time Between Setups for Power Units
EOQ/d = 1,490.7/20 = 74.535 days
Batch Scheduling

Limitations of EOQ Production Lot Size



Uses annual “ballpark” estimates of
demand and production rates, not the
most current estimates
Not a comprehensive scheduling technique
– only considers a single product at a time
Multiple products usually share the same
scarce production capacity
Batch Scheduling

Run-Out Method

Attempts to use the total production
capacity available to produce just enough
of each product so that if all production
stops, inventory of each product runs out
at the same time
Example: Run-Out Method
QuadCycle, Inc. assembles, in batches, four
bicycle models on the same assembly line. The
production manager must develop an assembly
schedule for March.
There are 1,000 hours available per month for
bicycle assembly work. Using the run-out method
and the pertinent data shown on the next slide,
develop an assembly schedule for March.
Example: Run-Out Method
Bicycle
Razer
Splicer
Tracker
HiLander
Inventory
On-Hand
(Units)
Assembly
Time
Required
(Hr/Unit)
100
600
500
200
.3
.2
.6
.1
March
April
Forec.
Forec.
Demand Demand
(Units)
(Units)
400
900
1,500
500
400
900
1,500
500
Example: Run-Out Method
(1)

(2)
(3)
(4)
(5)
Convert inventory and forecast into assembly hours
Bicycle
Invent.
On-Hand
(Units)
Assemb.
Time
Req’d.
(Hr/Unit)
March
Forec.
Dem.
(Units)
Invent.
On-Hand
(Hours)
Razer
Splicer
Tracker
HiLander
100
600
500
200
.3
.2
.6
.1
400
900
1,500
500
30
120
300
20
120
180
900
50
Total
470
1,250
(1) x (2)
(2) x (4)
March
Forec.
Dem.
(Hours)
Example: Run-Out Method

Compute aggregate run-out time in months
Aggregate Run-out Time =
= [(Total Inventory On-Hand in Hours)
+ (Total Assembly Hours Available per Month)
- (March’s Forecasted Demand in Hours)]
/ (April’s Forecasted Demand in Hours)
= (470 + 1,000 - 1,250)/1,250 = .176 months
Example: Run-Out Method

Develop March’s Production Schedule
Bicycle
Razer
Splicer
Tracker
HiLander
(3) x .176
(6)
(7)
March’s
Desired
Ending
Inventory
(Units)
70
158
264
88
(3) + (6)
(8)
(9)
March’s
Desired
End.Inv.
& Forec.
(Units)
Required
Production
(Units)
Assembly
Time
Allocated
(Hours)
470
1,058
1,764
588
370
458
1,264
388
(7) - (1)
(8) x (2)
111.0
91.6
758.4
38.8
999.8
Computerized Scheduling




Develops detailed schedules for each
work center indicating starting and
ending times
Develops departmental schedules
Generates modified schedules as orders
move
Many packages available.... select one
most appropriate for your business
Wrap-Up: World-Class
Practice



In process-focused factories:
 MRP II refined.... promises are met, shop loading
is near optimal, costs are low, quality is high
In product-focused factories:
 EOQ for standard parts containers, this sets S, lot
sizes are lower, inventories slashed, customer
service improved
Scheduling is integral part of a computer information
system