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Title: Production Planning and Control


1
Production Planning and Control
Chapter 5 Operations Scheduling
Professor JIANG Zhibin Department of Industrial
Engineering Management Shanghai Jiao Tong
University
2
Chapter 5 Operations Scheduling
  • Contents
  • Introduction
  • Job Shop Scheduling Terminology
  • Sequencing Rules
  • Sequencing Theory for a Single Machine
  • Sequencing Theory for Multiple Machines
  • Assembly Line Balancing
  • Advanced Topics for Operations scheduling

3
Introduction-What is Operations Scheduling ?
  • Implement the production orders generated in MRP
    under given objectives
  • Allocate production resources (machine, workers
    et al.) to production orders (jobs or tasks and
    their due dates) in an optimized manners
  • The results are time allocations of production
    resources to different jobs (job sequences on
    each production resources)
  • All the orders can be completed while all
    production resources are utilized with their
    loads being balanced.

4
Introduction-Objectives of Job Shop Scheduling
  • Objectives of operations scheduling
  • Meet due date
  • Minimize WIP inventory
  • Minimize the average flow time through the
    systems
  • Provide for high machine/worker (time)
    utilization (minimize idle time)
  • Reduce setup cost
  • Minimize production and worker costs
  • Discussion
  • 1) and 3) aim at providing a high level of
    costumer service
  • 2), 4), 5) and 6) are to provide a high level of
    plant efficiency
  • Impossible to optimize all above objectives
    simultaneously
  • Proper trade off between cost and quality is
    one of the most challenging strategic issues
    facing a firm today

5
Introduction-Objectives of operations Scheduling
  • Discussion (Cont.)
  • Some of these objectives conflicts, e.g.
  • Reduce WIP inventory ? Worker idle time may
    increase or machine utilization may decrease
  • Reasons differences in the throughput rate from
    one part of the system to the another may force
    the faster operations to wait, if there is no
    buffer for WIP between 1 and 2 .

6
Introduction-Functions of Scheduling and Control
is SF
  • The following functions must be performed in
    scheduling and control a shop floor
  • Allocating orders, equipments, and personnel to
    work centers or other specified location-Short
    term capacity planning
  • Determining the sequence of orders (i. e. job
    priorities)
  • Initializing performance of the scheduled work,
    commonly termed the dispatching of jobs
  • Shop-floor control, involving
  • Reviewing the status and controlling the progress
    of orders as they are being worked on
  • Expediting the late and critical orders
  • Revising the schedules in light of changes in
    order status.

7
Introduction-Elements of the Shop Floor
Scheduling Problems
  • The classic approaches to shop floor scheduling
    focuses on the following six elements
  • Job arrival patterns static or dynamic
  • Static jobs arrive in batch
  • Dynamic jobs arrive over time interval according
    to some statistical distribution.
  • Numbers and variety of machines in the shop floor
  • If there is only one machine or if a group of
    machines can be treated as one machine, the
    scheduling problem is much more simplified
  • As number of variety of machines increase, the
    more complex the scheduling problems is likely to
    become.

8
Introduction-Elements of the Shop Floor
Scheduling Problems
  • The classic approaches to job shop scheduling
    focuses on the following six elements (cont.)
  • Ratio of workers to machines
  • Machine limited system more workers than machine
    or equal number workers and machines
  • Labor-limited system more machines than worker.
  • Flow pattern of jobs flow shop or job shop
  • Flow shop all jobs follow the same paths from
    one machine to the next
  • Job shop no similar pattern of movement of jobs
    from one machine to the next.

9
Introduction-Elements of the Job Shop Scheduling
Problems
  • Flow shop
  • Each of the n jobs must be processed through the
    m machines in the same order.
  • Each job is processed exactly once on each
    machine.
  • An assembly line is a classic example of flow
    shop
  • Every cars go through all the stations one by one
    in the same sequences
  • Same tasks are performed on each car in each
    station
  • Its operations scheduling is simplified as
    assembly line balancing
  • An assembly balancing problem is to determine the
    number of stations and to allocate tasks to each
    station.

10
Introduction-Job Shop
A job shop is organized by machines which
are grouped according to their functions.
11
Introduction-Job Shop
Job A
Job B
  • Not all jobs are assumed to require exactly the
    same number of operations, and some jobs may
    require multiple operations on a single machine
    (Reentrant system, Job B twice in work center 3
    ).
  • Each job may have a different required sequencing
    of operations.
  • No all-purpose solution algorithms for solving
    general job shop problems
  • Operations scheduling of shop floor usually means
    job shop scheduling

12
Introduction-Elements of the Shop Floor
Scheduling Problems
  • The classic approaches to shop floor scheduling
    focuses on the following six elements
  • Job sequencing
  • Sequencing or priority sequencing the process of
    determining which job is started first on some
    machines or work center by priority rule
  • Priority rule the rule used in obtaining a job
    sequencing
  • Priority rule evaluation criteria
  • To meet corresponding objectives of scheduling
  • Common standard measures
  • Meeting due date of customers or downstream
    operations
  • Minimizing flow time (the time a job spends in
    the shop flow)
  • Minimizing WIP
  • Minimizing idle time of machines and workers
    (Maximizing utilization).

13
Job Shop Scheduling Terminology
  • Parallel processing versus sequential processing
  • Sequencing Processing the m machines are
    distinguishable, and different operations are
    performed by different machines.
  • Parallel processing The machines are identical,
    and any job can be processed on any machine.
  • M1, M2, M3, and M4 are different
  • Job A has 2 operations which should be processed
    on different Machines M1and M2
  • Job B has 3 operations which should be processed
    on different Machines M3, M2 and M4
  • M1, M2, M3, and M4 are identical
  • Jobs A and B can be processed on any one of the 4
    machines

14
Job Shop Scheduling Terminology
  • 2 Flow time
  • The flow time of job i is the time that elapses
    from the initiation of the that job on the first
    machine to the completion of job i.
  • The mean flow time, which is a common measure of
    system performance, is the arithmetic average of
    the flow times for all n jobs

Mean Flow Time(F1F2F3)/3
15
Job Shop Scheduling Terminology
  • 2. Make-span
  • The make-span is the time required to complete a
    group of jobs (all n jobs).
  • Minimizing the make-span is a common objective in
    multiple-machine sequencing problems.

Make-span of the 3 jobs
16
Job Shop Scheduling Terminology
  • 3. Tardiness and lateness
  • Tardiness is the positive difference between the
    completion time and the due date of a job.
  • Lateness refers to the difference between the job
    completion time and its due date and differs from
    tardiness in that lateness can be either positive
    or negative.
  • If lateness is positive, it is tardiness when it
    is negative, it is earliness

Latenessgt0---Tardiness
Latenesslt0---Earliness
When the completion of Job is earlier than due
date, the tardiness is 0
17
Sequencing Rules
  • FCFS (first come-first served)
  • Jobs are processed in the sequence in which they
    entered the shop
  • The simplest and nature way of sequencing as in
    queuing of a bank
  • SPT (shortest processing time)
  • Jobs are sequenced in increasing order of their
    processing time
  • The job with shortest processing time is first,
    the one with the next shortest processing time is
    second, and so on
  • EDD (earliest due date)
  • Jobs are sequenced in increasing order of their
    due dates
  • The job with earliest due date is first, the one
    with the next earliest due date is second, and so
    on

18
Sequencing Rules
  • CR (Critical ratio)
  • Critical ration is the remaining time until due
    date divided by processing time
  • Scheduling the job with the largest CR next

CRiRemaining time of Job i/Processing time of
Job i (Due date of Job i-current
time)/Processing time of Job i
  • CR provides the balance between SPT and EDD, such
    that the task with shorter remaining time and
    longer processing time takes higher priority
  • CR will become smaller as the current time
    approaches due date, and more priority will given
    to one with longer processing time..
  • For a job, if the numerator of its CR is negative
    ( the job has been already later), it is
    naturally scheduled next
  • If more jobs are later, higher priority is given
    to one that has shorter processing time (SPT).

19
Sequencing Rules
  • Example 5.1
  • A machine center in a job shop for a local
    fabrication company has five unprocessed jobs
    remaining at a particular point in time. The jobs
    are labeled 1, 2, 3, 4, and 5 in the order that
    they entered the shop. The respective processing
    times and due date are given in the table below.
  • Sequence the 5 jobs by above 4 rules and compare
    results based on mean flow time, average
    tardiness, and number of tardy jobs

Job number Processing Time Due Date
1 2 3 4 5 11 29 31 1 2 61 45 31 33 32
20
Sequencing RulesFCFS
Job number Processing Time Due Date
1 2 3 4 5 11 29 31 1 2 61 45 31 33 32
Mean Flow time268/553.6 Average
tardiness121/524.2 No. of tardy jobs3.
Job Completion Time Due Date Tardiness

1 11
61 0
2 40
45 0
3 71
31 40
4 72
33 39
5 74
32 42
Totals 268

121
21
Sequencing RulesSPT
Job number Processing Time Due Date
1 2 3 4 5 11 29 31 1 2 61 45 31 33 32
Mean Flow time135/527.0 Average
tardiness43/58.6 No. of tardy jobs1.
Job Processing Time Completion Time Due Date Tardiness

4 1 1
33
0
5 2 3
32
0
1 11 14
61
0
2 29 43
45
0
3 31 74
31
43
Totals 135

43
22
Sequencing RulesEDD
Job number Processing Time Due Date
1 2 3 4 5 11 29 31 1 2 61 45 31 33 32
Mean Flow time235/547.0 Average
tardiness33/56.6 No. of tardy jobs4.
Job Processing Time Completion Time Due Date Tardiness

3 31 31
31
0
5 2 33
32
1
4 1 34
33
1
2 29 63
45
18
1 11 74
61
13
Totals 235

33
23
Sequencing RulesCR
Current time t0 Current time t0 Current time t0 Current time t0
Job number Processing Time Due Date Critical Ratio
1 2 3 4 5 11 29 31 1 2 61 45 31 33 32 61/11(5.545) 45/29(1.552) 31/31(1.000) 33/1 (33.00) 32/2 (16.00)
Current time should be reset after scheduling one
job
Current time t31 Current time t31 Current time t31 Current time t31
Job number Processing Time Due Date-Current Time Critical Ratio
1 2 4 5 11 29 1 2 30 14 2 1 30/11(2.727) 14/29(0.483) 2/1 (2.000) 1/2 (0.500)
24
Sequencing RulesCR
Mean Flow time289/557.8 Average
tardiness87/517.4 No. of tardy jobs4.
Current time60 Current time60 Current time60 Current time60
Job number Processing Time Due Date-Current Time Critical Ratio
1 4 5 11 1 2 1 -27 -28 1/11(0.0909) -27/1lt0 -28/2lt0
Both Jobs 4 and 5 are later, however Job 4 has
shorter processing time and thus is scheduled
first
Job number Processing Time Completion Time Tardiness
3 2 4 5 1 31 29 1 2 11 31 60 61 63 74 0 15 28 31 13
Totals 289 87
25
Sequencing RulesSummary
Rule Mean Flow Time Average Tardiness Number of Tardy Jobs
FCFS SPT EDD CR 53.6 27.0 47.0 57.8 24.2 8.6 6.6 17.4 3 1 4 4
  • Discussions
  • SPT results in smallest mean flow time
  • EDD yields the minimum maximums tardiness (42,
    43, 18, and 31 for the 4 different rules)
  • Always true? Yes!

26
Sequencing Theory for A Single Machines
Assuming that n jobs are to be processed through
one machine. For each job i, define the following
quantities
  • tiProcessing time for job i, constant for job
    i
  • diDue date for job i, constant for job i
  • WiWaiting time for job i, the amount of time
    that the job must wait before its processing can
    begin.
  • When all the jobs are processed continuously, Wi
    is the sum of the processing times for all of the
    preceding jobs
  • FiFlow time for job i, the waiting time plus
    the processing time Fi Wi ti
  • LiLateness of job i , Li Fi- di, either
    positive or negative
  • TiTardiness of job i, the positive part of Li,
    TimaxLi,0
  • EiEarliness of job i, the negative part of Li,
    Ei max- Li,0

27
Sequencing Theory for A Single Machines
  • Suppose that 4 jobs J1, J2, J3, J4 need to be
    scheduled
  • For example a schedule is J3-J2-J1-J4
  • Cindered as a permutation of integers 1, 2, 3, 4
    3, 2, 1, 4.
  • For only a single machine, every schedule can be
    represented by a permutation (ordering) of the
    integers 1, 2, 3, , n.
  • There are totally n! (the factorial of n)
    different permutations.
  • A permutation of integers 1, 2, ?, n is expressed
    by 1, 2, ?, n, which represents a schedule
  • In case of a schedule 3, 2, 1, 4, 13, 22,
    31, and 44

28
Sequencing Theory for A Single Machines
  • Shortest-Processing-Time Scheduling
  • Theorem 5.1 The scheduling rule that minimizes
    the mean flow time F is SPT
  • The mean flow time of all jobs on the schedule is
    given by

29
Sequencing Theory for A Single Machines
  • Shortest-Processing-Time Scheduling
  • Theorem 5.1 The scheduling rule that minimizes
    the mean flow time F is SPT
  • The mean flow time is given by
  • The double summation term may be written in a
    different form. Expanding the double summation,
    we obtain
  • k1t1
  • k2t1 t2
  • knt1 t2 tn
  • By summing down the column rather than across the
    row, we may rewrite F in the form
  • nt1(n-1)t2tn

SPT sequencing rule the job with shortest
processing time t is set first
30
Sequencing Theory for A Single Machines
  • Shortest-Processing-Time Scheduling (Cont.)
  • Corollary 5.1 The following measures are
    equivalent
  • Mean flow time
  • Mean waiting time
  • Mean lateness
  • SPT minimizes mean flow time, mean waiting
    time, and mean lateness for single machine
    sequencing.
  • Earliest-Due-Date Scheduling If the objective is
    to minimize the maximum lateness, then the jobs
    should be sequenced according to their due dates.
    That is, d1? d2? dn.

31
Sequencing Theory for A Single Machines
  • 3. Minimizing the number of Tardy Jobs An
    algorithm from Moore(1968) that minimizes the
    number of tardy jobs for the single machine
    problem.
  • Step1. Sequence the jobs according to the
    earliest due date to obtain the initial solution.
    That is d1? d2?,, ? dn
  • Step2. Find the first tardy job in the current
    sequence, say job i. If none exists go to step
    4.
  • Step3. Consider jobs 1, 2, , i. Reject the
    job with the largest processing time. Return to
    step2. (Why ?)
  • Reason It has the largest effect on the
    tardiness of the Jobi.
  • Step4. Form an optimal sequence by taking the
    current sequence and appending to it the rejected
    jobs. (Can be appended in any order?)
  • Yes, because we only consider the number of
    tardiness jobs rather than tardiness.

32
Sequencing Theory for A Single Machines
Example 8.3
Job 1 2 3 4 5 6
Due date 15 6 9 23 20 30
Processing time 10 3 4 8 10 6
Solution
Job 2 3 1 5 4 6
Due date 6 9 15 20 23 30
Processing time 3 4 10 10 8 6
Completion time 3 7 17 27 35 41
33
Sequencing Theory for A Single Machines
Example 8.3 Solution (Cont.)
Job 2 3 5 4 6
Due date 6 9 20 23 30
Processing time 3 4 10 8 6
Completion time 3 7 17 25 31
Job 2 3 4 6
Due date 6 9 23 30
Processing time 3 4 8 6
Completion time 3 7 15 21
The optimal sequence 2, 3, 4, 6, 5, 1 or 2, 3,
4, 6, 1, 5. In each case the number of tardy jobs
is exactly 2.
34
Sequencing Theory for A Single Machines
Precedence constraints Lawlers Algorithm
Minimizing maximum lateness
Minimizing maximum tardiness
gi is any non-decreasing function of the flow
time Fi
The Algorithm
  • First schedules the job to be completed last,
    then the job to be completed next to last, and so
    on. At each stage one determines the set of jobs
    not required to precede any other. Call this set
    V. among the set V, choose the job k that
    satisfies

35
Sequencing Theory for A Single Machines
The Algorithm (Cont.)
  • Consider the remaining jobs and again determine
    the set of jobs that are not required to precede
    any other remaining job.
  • The value of t is reduced by tk and the job
    scheduled next to last is now determined.
  • The process is continued until all jobs are
    scheduled.

Note As jobs are scheduled, some of the
precedence constraints may be relaxed, so the set
V is likely to change at each iteration.
36
Sequencing Theory for A Single Machines
Example 8.4
Job 1 2 3 4 5 6
Processing time 2 3 4 3 2 1
Due date 3 6 9 7 11 7
37
Sequencing Theory for A Single Machines
Example 8.4
Step1 find the job scheduled last(sixth)
Job 1 2 3 4 5 6
Processing time 2 3 4 3 2 1
Due date 3 6 9 7 11 7
3 5 6
Tardiness 15-96 15-114 15-78
t 23432115
Step2 find the job scheduled fifth
Job 1 2 3 4 6
Processing time 2 3 4 3 1
Due date 3 6 9 7 7
3 6
Tardiness 13-94 13-76
t 15-213
38
Sequencing Theory for A Single Machines
Example 8.4
Step3 find the job scheduled fourth
Job 1 2 4 6
Processing time 2 3 3 1
Due date 3 6 7 7
Because job3 is no longer on the list, job 2 now
because a candidate.
2 6
Tardiness 9-63 9-72
t 13-49
Step4 find the job scheduled third
Because job6 has been scheduled, so job
4 now because a candidate along with job 2.
Job 1 2 4
Processing time 2 3 3
Due date 3 6 7
2 4
Tardiness 8-62 8-71
t 9-18
39
Sequencing Theory for A Single Machines
Example 8.4
Step5 find the job scheduled second
Job 1 2
Processing time 2 3
Due date 3 6
The optimal sequence 1-2-4-6-3-5
Job Processing time Flow time Due date Tardiness
1 2 4 6 3 5 2 3 3 1 4 2 2 5 8 9 13 15 3 6 7 7 9 11 0 0 1 2 4 4
40
Sequencing Theory for Multiple Machines
  • Assume that n jobs are to be processed through m
    machines. The number of possible schedules is
    staggering, even for moderate values of both n
    and m.
  • For each machine, there is n! different ordering
    of the jobs if the jobs may be processed on the
    machines in any order, there are totally (n!)m
    possible schedules. (n5, m5, 25 billion
    possible schedules)
  • Even with the availability of inexpensive
    computing today, enumerating all feasible
    schedules for even moderate-sized problems is
    impossible or, at best, impractical.

41
Sequencing Theory for Multiple Machines
  • Gantt chart
  • Suppose that two jobs, I and J, are to be
    scheduled on two machines, 1 and 2, the
    processing times are

Machine 1 Machine 2
Job I 4 1
Job J 1 4
  • Assume that both jobs must be processed first on
    machine 1 and then on machine 2. There are four
    possible schedules.

42
Sequencing Theory for Multiple Machines
Schedule Total flow time Mean flow time Mean idle time
1 9 (59)/27 (44)/24
2 6 5.5 1
3 10 8 5
4 10 9.5 5
43
Sequencing Theory for Multiple Machines
  • Scheduling n Jobs on Two Machines
  • Theorem 8.2 The optimal solution for
    scheduling n jobs on two machines is always a
    permutation schedule.
  • A very efficient algorithm for
    solving the two-machine problem was discovered by
    Johnson(1954).
  • Denote the machines by A and B
  • The jobs must be processed first on machine A and
    then on machine B.
  • Define
  • AiProcessing time of job i on machine A
  • BiProcessing time of job i on machine B
  • Rule Job i precedes job i1 if min(Ai,
    Bi-1)ltmin(Ai1,Bi)
  • List the values of Ai and Bi in two columns.
  • Find the smallest remaining element in the two
    columns. If it appears in column A, then schedule
    that job next. If it appears in column B, then
    schedule that job last.
  • Cross off the jobs as they are scheduled. Stop
    when all jobs have been scheduled.

44
Sequencing Theory for Multiple Machines
Job Machine A Machine B
1 5 2
2 1 6
3 9 7
4 3 8
5 10 4
Example 8.5
Optimal sequence 2 4 3 5
1
45
Sequencing Theory for Multiple Machines
  • Extension to Three Machines
  • The three-machine problem can be reduced to a
    two-machine problem if
  • the following condition is satisfied
  • min Ai?max Bi or min Ci?max Bi
  • It is only necessary that either one of these
    conditions be satisfied. If that is the case,
    then the problem is reduced to a two-machine
    problem
  • Define AiAiBi, BiBiCi
  • Solve the problem using the rules described above
    for two-machines, treating Ai and Bi as the
    processing times.
  • The resulting permutation schedule will be
    optimal for the three-machine problem.
  • If the condition are not satisfied, this method
    will usually give reasonable, but possibly
    sub-optimal results.

46
Sequencing Theory for Multiple Machines
  • The Two-Job Flow Shop Problem assume that two
    jobs are to be processed through m machines. Each
    job must be processed by the machines in a
    particular order, but the sequences for the two
    jobs need not be the same.
  • Draw a Cartesian coordinate system with the
    processing times corresponding to the first job
    on the horizontal axis and the processing times
    corresponding to the second job on the vertical
    axis.
  • Block out areas corresponding to each machine at
    the intersection of the intervals marked for that
    machine on the two axes.
  • Determine a path from the origin to the end of
    the final block that does not intersect any of
    the blocks and that minimizes the vertical
    movement. Movement is allowed only in three
    directions horizontal, vertical, and 45-degree
    diagonal. The path with minimum vertical distance
    corresponds to the optimal solution.

47
Sequencing Theory for Multiple Machines
Example 8.7 A regional manufacturing firm
produces a variety of household products. One is
a wooden desk lamp. Prior to packing, the lamps
must be sanded, lacquered, and polished. Each
operation requires a different machine. There are
currently shipments of two models awaiting
processing. The times required for the three
operations for each of the two shipments are
Job 1 Job 1 Job2 Job2
Operation Time Operation Time
Sanding(A) 3 A 2
Lacquering(B) 4 B 5
Polishing( C ) 5 C 3
48
Minimizing the flow time is the same as
maximizing the time that both jobs are being
processed.that is equivalent to finding the path
from the origin to the end of block C that
maximizes the diagonal movement and therefore
minimizes either the horizontal or the vertical
movement.
or 10616
or 10(32)15
49
Assembly Line Balancing
  • The problem of balancing an assembly line is a
    classic industrial engineering problem.
  • The problem is characterized by a set of n
    distinct tasks that must be completed on each
    item
  • The time required to complete task i is a known
    constant ti.
  • The goal is to organize the tasks into groups,
    with each group of tasks being performed at a
    single workstation
  • In most cases, the amount of time allotted to
    each workstation is determined in advance, based
    on the desired rate of production of the assembly
    line.

50
Assembly Line Balancing
  • Assembly line balancing is traditionally thought
    of as a facilities design and layout problem.
  • There are a variety of factors that contribute to
    the difficulty of the problem.
  • Precedence constrains some tasks may have to be
    completed in a particular sequence.
  • Zoning restriction Some tasks cannot be
    performed at the same workstation.
  • Let t1, t2, , tn be the time required to
    complete the respective tasks.
  • The total work content (time) associated with the
    production of an item, say T, is given by
  • For a cycle time of C, the minimum number of
    workstations possible is T/C, where the
    brackets indicate that the value of T/C is to be
    rounded to the next larger integer.
  • Ranked positional weight technique the method
    places a weight on each task based on the total
    time required by all of the succeeding tasks.
    Tasks are assigned sequentially to stations based
    on these weights.

51
Assembly Line Balancing
Example 8.11 The Final assembly of Noname
personal computers, a generic mail-order PC
clone, requires a total of 12 tasks. The assembly
is done at the Lubbock, Texas, plant using
various components imported from the Far East.
The network representation of this particular
problem is given in the following figure.
52
Assembly Line Balancing
Precondition The job times and precedence
relationships for this problem are summarized in
the table below.
Task Immediate Predecessors Time
1 _ 12
2 1 6
3 2 6
4 2 2
5 2 2
6 2 12
7 3, 4 7
8 7 5
9 5 1
10 9, 6 4
11 8, 10 6
12 11 7
  • ?ti70, and the production rate is a unit/15
    minutes
  • The minimum number of workstations 70/155

53
Assembly Line Balancing
The solution precedence requires determining the
positional weight of each task. The positional
weight of task i is defined as the time required
to perform task i plus the times required to
perform all tasks having task i as a predecessor.
t3t7t8t11t1231
Task Positional Weight
1 70
2 58
3 31
4 27
5 20
6 29
7 25
8 18
9 18
10 17
11 13
12 7
The ranking 1, 2, 3, 6, 4, 7, 5, 8, 9, 10, 11, 12
54
Assembly Line Balancing
Profile 1 C15
Station 1 2 3 4 5 6
Tasks 1 2, 3, 4 5, 6, 9 7, 8 10, 11 12
Processing time 12 14 15 12 10 7
Idle time 3 1 0 3 5 8
Task Immediate Predecessors Time
1 _ 12
2 1 6
3 2 6
4 2 2
5 2 2
6 2 12
7 3, 4 7
8 7 5
9 5 1
10 9, 6 4
11 8, 10 6
12 11 7
The ranking 1, 2, 3, 6, 4, 7, 5, 8, 9, 10, 11, 12
55
Assembly Line Balancing
Profile 1 C15
Station 1 2 3 4 5 6
Tasks 1 2,3,4 5,6,9 7,8 10,11 12
Processing time 12 14 15 12 10 7
Idle time 3 1 0 3 5 8
  • Evaluate the balancing results by the efficiency
    ?ti/NC
  • The efficiencies for Profiles 1 3 are 77.7,
    87.5, and 89.7. Thus the profile 3 is the best
    one.

Cycle Time15
T26
T112
T26
T36
T42
T52
T52
T612
T91
T85
T77
T104
T104
T116
T127
T127
56
Assembly Line Balancing
Alternative 1 Change cycle time to ensure 5
station balance
Profile 1 Increasing cycle time from 15 to 16
Station 1 2 3 4 5
Tasks 1 2,3,4,5 6,9 7,8,10 11,12
Idle time 4 0 3 0 3
  • Increasing the cycle time from 15 to 16, the
    total idle time
  • has been cut down from 20 min/units to 10
    resulting in a substantial improvement in
    balancing rate.
  • However, the production rate has to be reduced
    from one unit/15 minutes to one unit/16minute

57
Assembly Line Balancing
Alternative 2 Staying with 6 stations, see if a
six-station balance could be obtained by cycle
time less that 15 minutes
Profile 2 C13
Station 1 2 3 4 5 6
Tasks 1 2,3 6 4,5,7,9 8,10 11,12
Idle time 1 1 1 1 4 0
  • 13 minutes appear to be the minimum cycle time
    with six station balance.
  • Increasing the number of stations from 5 to 6
    results in a great improvement in production rate
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