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OPMT 340
Elements of Lean Production:
Small Lot Production
©The McGraw-Hill Companies, Inc., 2004
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LOT SIZING BASICS
• WHAT IS LOT SIZING?
• THE TERMS LOT AND BATCH ARE INTERCHANGEABLE.
• SMALLEST LOT SIZE IS ONE.
• IN MANUFACTURING, SCHEDULING MANUFACTURING BATCHES WITH ONE
UNIT IN EACH BATCH IS GENERALLY NOT ECONOMICAL.
• THE QUESTION THEN BECOMES HOW MANY IN A BATCH. THIS
DETERMINATION IS CALLED LOT SIZING.
• COSTS?
• SMALL BATCHES REQUIRE MORE FREQUENT SET-UPS, AND THEREFORE MORE
TIME.
• VERY LARGE BATCHES REDUCE SET UP CHANGES, BUT CREATE SIGNIFICANT
INVENTORIES BEFORE THE PRODUCTS ARE NEEDED.
• BOTH ADD COSTS
©The McGraw-Hill Companies, Inc., 2004
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ADVANTAGES (& DIS.) OF SMALL LOTS
•
L – LEAD TIME (AND LEAD TIME VARIABILITY)
•
•
H – HOLDING/CARRYING COST
•
•
•
•
•
MORE FREQUENT SET-UPS AND MORE HANDLING EQUALS HIGHER COSTS.
•
MAJOR GOAL FOR LEAN IS TO REDUCE SET-UP AND HANDLING COSTS.
Q – QUALITY
QUALITY GENERALLY IMPROVES THROUGH LESS SCRAP AND REWORK (SMALLER AMOUNTS PRODUCED IN A BATCH).
FLEXIBILITY – LITTLE’S LAW
•
ADAPT LITTLE’S LAW TO BE “WORK IN PROCESS INVENTORY = THROUGHPUT RATE X LEAD TIME”
•
NOTE THAT IF PRODUCTION LEAD TIME IS REDUCED, WIP IS DECREASED
BOTTLENECKS
•
•
SMALL BATCH SIZES CREATE SMALLER WIP INVENTORIES
S – SET-UP/HANDLING
•
•
SMALL BATCHES REDUCE OVERALL LEAD TIME AND OFTEN REDUCE VARIABILITY
REDUCING WIP REDUCES THE LOAD ON BOTTLENECK RESOURCES, ALLOWING BOTTLENECKS TO BE MORE EFFICIENT
SMALL BUFFER STOCKS
•
BUFFER STOCKS OF WIP, OR SAFETY STOCKS OF COMPONENTS AND RAW MATERIALS ARE REDUCED BECAUSE BATCH
SIZES ARE SMALL (LESS NEED).
©The McGraw-Hill Companies, Inc., 2004
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FACILITATING SMALL LOT SIZES
• PROCESS BATCHES
• PURCHASE/ORDER QUANTITIES (Q)
• TRANSFER BATCHES
• DELIVERY/SHIPPING BATCHES
©The McGraw-Hill Companies, Inc., 2004
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SMALL-LOT PRODUCTION
• HOW TO DETERMINE THE BEST LOT SIZE?
• EOQ MODEL
• EMQ MODEL
• BOTH MODELS MAKE ASSUMPTIONS
• BOTH MODELS USE RELATIVELY FIXED AMOUNTS FOR HOLDING AND
FOR ORDERING COST
©The McGraw-Hill Companies, Inc., 2004
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ASSUMPTIONS OF BASIC
EOQ/EMQ MODELS
• DEMAND IS CONSTANT, CONTINUOUS (INDEPENDENT) AND KNOWN
• FOR EOQ – THE ENTIRE LOT IS PRODUCED (OR RECEIVED) ALL AT ONCE
• FOR EMQ – THE LOT IS PRODCED (OR RECEIVED) OVER A PERIOD OF TIME
• NO STOCKOUTS (SHORTAGES) ARE ALLOWED
• SETUP (ORDER) COST IS FIXED, REGARDLESS OF LOT SIZE
• UNIT CARRYING COST IS KNOWN AND CONSTANT
• NO QUANTITY DISCOUNTS OR PRODUCTION ECONOMIES
©The McGraw-Hill Companies, Inc., 2004
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EOQ/EMQ MODEL COST CURVES
Slope = 0
Annual
cost ($)
Total Cost
Minimum
total cost
Carrying Cost = HQ/2
Ordering Cost = SD/Q
Optimal order
Qopt
Order Quantity, Q
©The McGraw-Hill Companies, Inc., 2004
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THE EOQ INVENTORY ORDER CYCLE
Inventory
Level
Demand
rate
Order qty, Q
Average
inventory
level
Q/2
0
Time
©The McGraw-Hill Companies, Inc., 2004
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EMQ
NONINSTANTANEOUS RECEIPT
Inventory
level
Q (p-d)
p
Q
(p-d)
2p
Maximum
inventory level
Begin
Order
Rate = -d
receipt
Average
inventory level
Rate = p-d
0
Order
receipt period = Q/p
End
Order
Time
receipt
©The McGraw-Hill Companies, Inc., 2004
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TRANSFER BATCHES
• A TRANSFER BATCH IS THE AMOUNT MOVED FROM WORK CENTER TO WORK CENTER
DURING PRODUCTION. THE TRANSFER BATCH AND THE LOT SIZE MAY BE EQUAL, OR A
LOT SIZE MAY BE DIVIDED INTO SEVERAL TRANSFER BATCHES.
• “BLOCKING” OCCURS WHEN A BATCH CANNOT BE TRANSFERRED TO THE NEXT
PROCESS BECAUSE THE NEXT PROCESS HAS NOT FINISHED THE PREVIOUS JOB. SO THE
BLOCKED BATCH MUST WAIT UNTIL THE NEXT PROCESS IS AVAILABLE.
• EXAMPLE
• WHAT IS THE IMPACT ON PRODUCTION IF WE MOVE FROM A TRANSFER BATCH SIZE OF
1,000 (EQUAL TO THE LOT SIZE) TO A TRANSFER BATCH OF 200 (20% OR 1/5TH OF THE LOT
SIZE)?
•
IN THIS CASE, WE WOULD NEED 5 PRODUCTION RUNS AT 200 EACH TO COMPLETE THE NECESSARY
LOT SIZE OF 1000 ITEMS.
• ONE PRODUCT
• 3 SEQUENTIAL OPERATIONS (A, B, C) TO COMPLETE THE PRODUCT
• PROCESSING TIME IS ONE MINUTE PER PIECE.
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EXAMPLE – 1 PRODUCT, 3 OPERATIONS
Time
(min)
Transfer Batch = 1000
0
1000
2000
3000
C
Operation
B
A
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EXAMPLE – 1 PRODUCT, 3 OPERATIONS
Time
(min)
Transfer Batch = 1000
0
1000
2000
3000
C
B
A
Transfer Batch = 1000
1200
1000
800
600
400
200
0
Quantity
Operation
0
1000
2000
3000
4000
Time
©The McGraw-Hill Companies, Inc., 2004
EXAMPLE – REDUCING BATCH SIZE
TRANSFER BATCH OF 200
Transfer Batch = 200
Time (min)
0
200
400
600
800
1000
1200
1600
1800
C
B
A
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Example – Reducing Batch Size
Transfer Batch of 200
Transfer Batch = 200
Time (min)
0
200
400
600
800
1000
1200
1400
1600
C
B
A
Quantity
Transfer Batch = 200
700
600
500
400
300
200
100
0
0
200
400
600
800
1000
1200
1400
1600
Time
©The McGraw-Hill Companies, Inc., 2004
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EFFECTS OF LOT SIZE REDUCTION
• TWO PRODUCTS (X,Y)
• 3 OPERATIONS (A, B, C)
Operation Capacity (units/day)
Product
A
B
C
X
1000
2000
1000
Y
2000
2000
2000
• EFFECTS OF HALVING PROCESS BATCH SIZE AND QUARTERING
TRANSFER BATCH SIZE?
©The McGraw-Hill Companies, Inc., 2004
CONVENTIONAL – 8,000 UNITS OF EACH PRODUCT AND
LOT SIZE AND TRANSFER BATCH ARE EQUAL. PROCESS
BATCH IS EQUAL TO CAPACITY
0
2
4
6
8
10
12
14
16
18
20
22
24
C
B
A
Blue = X Red = Y
Yellow = blocking
Quantity
Batch = 8000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0
2
4
6
8
10
12
14
16
18
20
22
24
Time
©The McGraw-Hill Companies, Inc., 2004
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PROCESS 4000, TRANSFER 2000
0
1
2
3
4
C
5
6
2000
B
2000
A
2000
2000
2000
2000
4000
4000
7
2000
2000
2000
2000
2000
6000
2000+
2000
8
9
2000
2000
2000
2000
2000
6000
8000
10
11
2000
2000
6000
12
6000
4000
13
2000
2000
2000
2000
2000
6000
2000+
2000
6000
14
15
2000
2000
16
2000
6000
4000
2000
0
Note: In periods 7, 8 and 13, 14, the first 2000 units of Y are blocked from being
sent to C. This causes a small build-up in inventory at B. When it’s finally sent to
C, it ends up as all 4000 units to begin with.
Quantity
Batch = 8000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Time
©The McGraw-Hill Companies, Inc., 2004