Chapter 2 – Manufacturing Operations
John L. Evans, Ph.D.
INSY 4700
6/21/2016
Assembly Systems
1
Introduction to Assembly Systems
• Definition of the term assembly
– The aggregation of all processes by which various parts and subassemblies are built together to form a complete, geometrically
designed assembly or product either by an individual, batch, or
continuous process.
• Assembly of manufactured goods accounts for:
– over 50% of total production time,
– 20% of the total unit production cost, and
– 33%-50% of labor costs
6/21/2016
Assembly Systems
2
Types of Manufacturing Industries
•
•
•
•
•
•
•
•
•
Aerospace
Basic Metals
Chemicals
Appliances
Fab Metals
Machinery
Pharmaceuticals
Publishing
Wood Furniture
6/21/2016
Apparel
Beverages
Computers
Electronics
Food
Paper
Plastics
Textiles
Assembly Systems
Automotive
Building Materials
Construction
Equipment
Glass
Petroleum
Power Utilities
Tire and Rubber
3
Processing and Assembly Operations
• Solidification Processes
– Casting and Molding
• Particulate Processing
– Pressing Powers and Sintering
• Deformation Processes
– Forging, Extrusion, Rolling, Drawing, Forming, Bending
• Material Removal
– Turning, Drilling, Milling, Gringing
• Material Finishing
– Heat Treatment, Cleaning, Surface Treatment
• Assembly Operations
– Welding, Brazing, Soldering, Adhesive, Rivets, Press, Threaded Fastners
6/21/2016
Assembly Systems
4
Product Assembly
• Virtually all end products go through some assembly
process.
• Approaches
– Craftsman approach
l
Output = l parts/unit time
6/21/2016
Assembly Systems
5
Product Assembly
• Virtually all end products go through some assembly
process.
• Approaches
– Craftsman approach
l
l
l
Output = 3l parts/unit time
6/21/2016
Assembly Systems
6
Product Assembly
• Virtually all end products go through some assembly
process.
• Approaches
– Craftsman approach
– Assembly line
3l
3l
l
l
l
Output = 3l parts/unit time
6/21/2016
Assembly Systems
3l
Output = 3l
parts/unit time
7
Example
m1
m2
m3
l
l
l
n1
3l
n2
3l
l = 2 parts/hour
3l = 6 parts/hour (each)
n = 1/3l = 1/6 hour
l = 2 part/hour (each)
3l = 6 parts/hour
m = 1/l = 1/2 hour
n3
Assume m1=m2=m3=m
Assume n1=n2=n3=n
6/21/2016
3l
Assembly Systems
8
Assembly Line
• Each part moves sequentially
down the line, visiting each
workstation.
• Assembly (or inspection) tasks
are performed at each station.
2
1
6
4
3
5
• Tc is defined as the cycle time. At steady state, one unit is produced every
Tc time units (i.e., TC = 1/required number of assemblies per unit time).
• Paced lines vs. unpaced lines
• Single product vs. mixed lines
• Flexible flow lines
6/21/2016
Assembly Systems
9
Assembly Line Balancing
• Assembly line balancing problems:
– ALB-1 - Assign tasks to the minimum number of stations such that
the workload assigned to each station does not exceed the cycle
time, TC.
– ALB-2 - Assign tasks to a fixed number of stations such that the
cycle time, TC, is minimized.
• An assembly consists of a set of tasks.
• Task precedence relationships
– Precedence relationships are described by a graph
G = (N, A) where njN represents task j, and aijA indicates that
task i is an immediate predecessor of task j.
6/21/2016
Assembly Systems
10
Production Concepts and Models
• Production Rates
TC= TO + Th + Tth
Where TC = Operation Cycle Time
TO = Time of Actual Processing
Th = Handling Time
Tth = Tool Handling Time
For total batch processing time
Tb = Tsu + QTc
Where Q = Batch Quantity
Tsu = Total Setup Time
6/21/2016
Assembly Systems
11
Production Concepts and Models (2)
The Average Production Time for a Part (Batch)
Tp = Tb/Q
The Average Production Rate (pc/hr)
Rp = 60/Tp
For Job Shop Production
Tp= Tsu + Tc
For Mass Production – Q is very large making
Rp ~ = Rc = 60/Tc
Where Rc =Operation Rate of the Machine
6/21/2016
Assembly Systems
12
Production Concepts and Models (3)
• For Multiple Stations Dividing work evenly is not realistic
• Bottleneck Station is the “Gating” or limiting operation
Tc = Tr + Max To
Where Tr = time to transfer work between stations
Max To = operation time at bottleneck operation
Therefore the theoretical production rate is approximately
Rc = 60/Tc
6/21/2016
Assembly Systems
13
Production Concepts and Models (4)
• Production Capacity is defined as
PC = nSHRp
Where n = number of work stations
S = number of shifts per period
H = hr/shift
Rp= hourly production rate of each center
• Utilization is defined as
U = Q/PC
• Availability is defined as
A = (MTBF – MTTR)/MTBF
Where MTBF is mean time between failure (hr)
MTTR is mean time to repair (hr)
6/21/2016
Assembly Systems
14
Manufacturing Lead Time
• The Lead Time for Manufacturing a Product Through the
Entire Operation is defined as
MLTj = Sum of (Tsuij + QiTcji + Tnoji) i = 1 to oj
Where Tsuji = Setup Time for Operation i
Qj = Quantity of product j
Tcji = Operation cycle time for operation i
Tnoji = Nonoperation time with operation i
6/21/2016
Assembly Systems
15
Manufacturing Lead Time
• Lead Time for Job Shop – Q = 1
MLT = no(Tsu + Tc + Tno)
• Lead Time in Mass Production
MLT = no(Tr + Max To) = noTc
6/21/2016
Assembly Systems
16
Work-in-Process
• Work-in-Process is the quantity of products currently in the process of
production
• WIP = [ AU(PC)(MLT)] / SH
Where A is Availability
U is Utilization
PC is Production Capacity
MLT is Manufacturing Lead Time
S is number of Shifts per Week
H is the number of Hours per Shift
6/21/2016
Assembly Systems
17
Costs of Manufacturing
• Fixed and Variable Costs
TC = FC + VC (Q)
Where TC is the Total Cost
FC is the Total Fixed Cost
VC is the Variable Cost per unit
Q is the Quantity
6/21/2016
Assembly Systems
18
Manufacturing Analysis
• Evaluate or Optimize
–
–
–
–
–
–
6/21/2016
Minimize Throughput Time
Minimize Labor
Minimize Capital Investment
Maximize Capacity
Minimize Operational Cost
Minimize Cost Per Unit
Assembly Systems
19
Types of Analysis Problems
•
•
•
•
•
•
•
•
Capacity of Process Time
Analyze Lead Time to Production
“Optimize” Process Steps or Sequence
Evaluate WIP
Evaluate Cost of Operation
“Optimize” Capital Investment
Minimize Travel Time
Minimize Floorspace
6/21/2016
Assembly Systems
20
Example Problem
Task
a
b
c
d
e
6/21/2016
ti
3
2
3
2
1
Predecessors
a,b
a
d
Assembly Systems
a
d
e
c
b
21
Assembly Line Balancing
• Problem (ALB-1): Assign tasks to workstations
• Objective: Minimize assembly cost
– f(labor cost while performing tasks, idle time cost)
• Constraints:
– Total time for all tasks assigned to a workstation can not exceed C.
– Precedence constraints between individual tasks.
– Zoning constraints
• Same workstation
• Different workstation
6/21/2016
Assembly Systems
22
Parameters / Inputs
• Parameters / Inputs
–
–
–
–
–
–
P parts/unit time are required
m parallel lines are to be designed (usually 1)
C = m/P is the required cycle time
ti is the assembly time required by task i, i = 1,…,N
IP = {(u,v) | task u must precede task v}
ZS = {(u,v) | tasks u and v must be assigned to the same
workstation}
– ZD = {(u,v) | tasks u and v can not be assigned to the same
workstation}
– S(i) is the set of successors for task i.
6/21/2016
Assembly Systems
23
Parameters / Decision Variables (cont.)
• Decision Variables
– k is the number of workstations required (unknown).
– x  1, if task i is assigned to station k

ik
0, otherwise
• cik is a set of cost coefficients such that:
Ncik  ci , k 1 , k  1,2,, n  1
• cik is the cost of assigning task i to station k
6/21/2016
Assembly Systems
24
Problem Formulation
N
min
K
c
ik
xik
i 1 k 1
N
t x
i 1
i
K
x
ik
ik
 C,
 1,
k  1, , k
i  1,, N
k 1
h
xvh   xuj ,
h  1,, K ; and (u, v )  IP
j 1
K
x
uk
xvk  1,
( u, v )  ZS
k 1
xuk  xvk  1,
k  1,, K; and (u, v) ZD
xik (0,1)  i , k
6/21/2016
Assembly Systems
25
Solving the Problem
• Very difficult to solve optimally
– Integer variables
– Non-linear constraints
• Heuristic Solutions
– COMSOAL
– Ranked positional weight
• Enumeration Methods
– Tree Generation
• Niave approach
• Fathoming rules
6/21/2016
Assembly Systems
26
Example Problem
j
tj
1
2
3
4
5
6
7
8
9
10
11
5
35
25
60
30
10
60
25
35
70
30
6/21/2016
Pj
1
1
2
2
2,3
6
4,5
8
7,9
10
4
2
1
8
9
5
10
11
3
6
Assembly Systems
7
27
Example Problem (cont.)
j
tj
1
2
3
4
5
6
7
8
9
10
11
5
35
25
60
30
10
60
25
35
70
30
6/21/2016
Pj
1
1
2
2
2,3
6
4,5
8
7,9
10
All Predecessors
1
1
1,2
1,2
1
1,2,3
1,2,3,6
1,2,4,5
1,2,4,5,8
1,2,3,4,5,6,7,8,9
1,2,3,4,5,6,7,8,9,10
4
2
8
9
5
10
11
3
6
Assembly Systems
7
28
Ranked Positional Weight Example
C = 72
j
tj
1
2
3
4
5
6
7
8
9
10
11
5
35
25
60
30
10
60
25
35
70
30
6/21/2016
Pj
1
1
2
2
2,3
6
4,5
8
7,9
10
All Predecessors
1
1
1,2
1,2
1,2,3
1,2,3,6
1,2,4,5
1,2,4,5,8
1,2,3,4,5,6,7,8,9
1,2,3,4,5,6,7,8,9,10
S(j)
2,3,4,5,6,7,8,9,10,11
4,5,6,7,8,9,10,11
6,7,10,11
8,9,10,11
8,9,10,11
7,10,11
10,11
9,10,11
10,11
11
-
Assembly Systems
PW(j)
Rank
Station
385
355
195
220
190
170
160
160
135
100
30
1
2
4
3
5
6
7
8
9
10
11
1
1
1
2
3
2
4
3
5
6
7
29