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PRODUCTION SCHEDULING
UNIT 7
• DR. RASHMI PANWAR
Production control
• Design and use of systematic
procedure for establishing plans and
controlling all the elements of an
activity
• Follow up procedure for determining
how closely is the plan followed
Objectives of production
control
• Issuing the necessary orders to concerned
personnel
• Arrange necessary items like materials
,machines,man power and jigs
• To ensure instructions are followed so that
time limit is managed
DEFINITION
In production scheduling the products to be
manufactured and their
quantities are determined initially.
• The sequence of manufacturing processes required
for the production of these items are also
established.
• The manufacturing resources are then allocated to
perform production processes to realise various
items.
• This is spread over a predetermined time. This
function is known as production scheduling.
OVERVIEW OF PRODUCTION SCEDULING
Scheduling: is the process of arranging, controlling and
optimizing work and workloads in a production process or
manufacturing process.
• Scheduling: is used to allocate plant and machinery
resources, plan human resources, plan production
processes and purchase materials.
• It is an important tool for manufacturing and engineering,
where it can have a major impact on the productivity of
a process.
• In manufacturing, the purpose of scheduling is to
minimize the production time and costs, by telling a
production facility when to make, with which staff, and
on which equipment.
• Production scheduling aims to maximize the efficiency of
the operation and reduce costs..
OVERVIEW
• Scheduling is the process of arranging, controlling and
optimizing work and workloads in a production process.
Companies use backward and forward scheduling to
allocate plant and machinery resources, plan human
resources, plan production processes and purchase
materials.
• Forward scheduling is planning the tasks from the date
resources become available to determine the shipping
date or the due date.
• Backward scheduling is planning the tasks from the due
date or required-by date to determine the start date
and/or any changes in capacity required.
THE BENEFITS OF PRODUCTION SCHEDULING
• Process change-over reduction
• Inventory reduction, leveling
• Reduced scheduling effort
• Increased production efficiency
• Labor load leveling
• Accurate delivery date quotes
• Real time information
• It greatly outperform older manual scheduling methods.
• These provide the production scheduler with powerful graphical
interfaces which can be used to visually optimize real-time work
loads in various stages of production, and pattern recognition
allows the software to automatically create scheduling
opportunities which might not be apparent without this view into
the data.
SHOP FLOOR CONTROL
• LOADING: Check availability of material ,labour and
machines
• SEQUENCING: Release work order to shops and issue
dispatch list for individual lists
• MONITORING: Maintain progress reports of each job
until I is complete
LOADING:
• Another important technique of production planning is
loading. In planning the production process the
management-must know when a particular
equipment/machine will be available for work on each order
or item. For this information a list of the number of machines
capable of performing similar operations is prepared.
• Knowing the number of machine shifts available for each
kind of operation and number of shifts required for such
operations in the production process to complete the
schedule, the planning staff can evaluate whether the work
load is greater or less than the capacity of the equipment.
OBJECTIVES OF LOADING
• (i) To plan new work orders on the basis of spare
capacity available.
• (ii) To balance the work load in a plant.
• (iii) To maintain the delivery promises.
• (iv) To check the feasibility of production programmes.
• and load charts:
LOADING DEVICES:
THERE ARE TWO MAIN APPROACHES FOR LOADING VIZ. LOADING STEP BY STEP,
AND MACHINE LOADING
Loading Step by Step:
• Sometimes an individual production order may require a
finite number of operations and the order of these operations
may vary too much from item to item. In such cases
overloads are scheduled to account for interaction among
various operations by identifying the operation which
imposes maximum delay on the order.
Following are the steps in this approach:
(a) Find the earliest date and the hours required that can be
scheduled onto each operation.
(b) Determine the hours required at each operation and the
time thereafter to complete the job if no loading delay occurs.
(c) Schedule the bottleneck operation as early as possible.
• (d) Schedule subsequent operations as early as possible.
• B. Machine Loading:
• Using information from schedules, weekly/periodic load in hours
is determined for each machine and is then recorded on
machine load chart. The chart also gives the time for which the
machine is busy for parts pertaining to different work orders.
• A machine load chart for all the machines in a production
department shows the future spare capacity of machines. The
machines should be loaded to full capacities as idle capacities
of machines are sources of loss to the organisation and also
increase the cost of production.
• C. Load Charts:
• Load charts shows the work assigned to various departments,
machines or components of an organisation.
• During “periods of peak/heavy loads information from load
charts can be used to Determine”:
(i) Priorities to future orders and to decide whether to sub-
contract or refuse new orders.
(ii) Provision of overtime or multi-shift operations.
(iii) Acquisition of extra men or equipment for additional
capacity.
One common procedure for Loading is to maintain a register
at each machine center. When any order is loaded on a
machine a entry is made in the register showing the estimated
time, the order is likely to devote on the machine and the
estimated time off. The information can also be presented with
the help of Gantt chart.
• Finite Capacity Planning and Scheduling
• Finite capacity planning recognizes that every business has a
fixed amount of available resources with which it can
produce its products or services, at least in the short run.
Because of this, providing its services or producing its
products requires careful planning and scheduling to stay
within its resource constraints. In this context, resources refer
to people, tools and expertise. This approach to planning is
finite planning, based on the finite amount of resource
capacity to apply to the production of products or services
to customers.
• Examples of businesses with finite capacity in the near-term
are window cleaners, construction contractors, automobile
manufacturers, specialized product shops and software
developers.
• Infinite Capacity Planning
• Infinite capacity planning ignores any resource
constraints and plans production or servicing activities
backward from a customer due date or another fixed
end date. Infinite scheduling and capacity planning
uses the lead times or work times of the production flow
to back-schedule work to each resource, whether a
work center or one or more individuals. In doing so,
infinite capacity loading disregards any existing work or
commitments of the resources.
• One example of a business operating with infinite
capacity planning is an online retail vendor.
TECHNIQUES OF
SCHEDULING
• Priority rules in scheduling: PRIORITY SEQUENCING
• When several jobs compete for the capacity of a
machine or a work center, the question of sequencing
the jobs rises. This question is answered by determining
the priority for all the jobs waiting in the queue by
applying priority sequencing rules.
THE RULES OF SINGLE CRITERION SEQUENCING ARE EXPLAINED
IN DETAIL IN THE FOLLOWING PARAGRAPHS
• i) First come-first served (FCFS) rule: Jobs are scheduled for work
in the same sequence as they arrive at the facility or work
center. This rule is commonly applied in service centers such s
banks, super bazaars and barber shops.
• ii) Shortest process time job (SPT) first: The job which has the
shortest processing/ operation time on the mchine or at the
work center is given the highest priority to be loaded as the next
job for processing. This rule minimizes the in-process-inventory,
however, at the expense of keeping the jobs having longer
processing time for a longer time in the work center, there-by
increasing the job through-put time (i.e. manufacturing cycle
time).
• iii) Longest processing time (LPT) job first: The job with the longest
processing/ operation time is scheduled as the first job to be
loaded on the machine among the jobs waiting in queue.
• iv) Least slack (LS) job first: In this rule, the highest priority is
given to the job which has the least slack. Slack is the
difference between available time and the duration of
processing the job.
• Slack = Available time - Processing time.
• v) Earliest due date (EDD) job first:
• This rule sequences the jobs waiting in the queue at the work
centre or machine according to their due dates and the jobs
are processed according to their due dates i.e. having
earliest due date is given highest priority while loading the
job on the machine (or work center). This rule does not
ensure that all jobs will be completed on time i.e. within their
due dates.
• vi) Truncated shortest processing time (TSPT) job first: This rule
sequences the jobs according to the SPT rule, except that
the jobs that have been waiting for time period longer than
a specified truncation time are given higher priority than
other jobs.
• vii) Preferred customer order (PCO) rule: Jobs belonging to a
preferred customer are given higher priority than other jobs.
• viii) Random-selection: This rule is not used normally. It may
be used when no other consideration is important.
• ix) COVERT (cost over time) rule: This rule uses the ratio of
expected delay cost (C) to the processing time (T). The job
with the largest ratio is given the highest priority
JOHNSONS RULE
• In operations research, Johnson's rule is a method of
scheduling jobs in two work centers.
• Its primary objective is to find an optimal sequence of
jobs to reduce make span (the total amount of time it
takes to complete all jobs).
• It also reduces the amount of idle time between the
two work centers. The method minimizes the makespan
in the case of two work centers.
• Furthermore, the method finds the shortest makespan in
the case of three work centers if additional constraints
are met.
The technique requires several preconditions:
• The time for each job must be constant.
• Job times must be mutually exclusive of the job
sequence.
• All jobs must be processed in the first work center
before going through the second work center.
• All jobs are equally prioritised.
• Johnson's rule is as follows:
• List the jobs and their times at each work center.
• Select the job with the shortest activity time. If that
activity time is for the first work center, then schedule
the job first. If that activity time is for the second work
center then schedule the job last. Break ties arbitrarily.
• Eliminate the shortest job from further consideration.
• Repeat steps 2 and 3, working towards the center of
the job schedule until all jobs have been scheduled.
• Example
• Each of five jobs needs to go through work center A and B. Find the
optimum sequence of jobs using Johnson's rule.
• FIND :total runtime/elapse time.
• Total idle time.
• Job times (hours)
• Job Work center A Work center B
• A 3 4
• B 4 1
• C 2 5
• D 5 4
• E 3 2
• The smallest time is located in Job B (1 hours). Since the time is in Work
Center B, schedule this job last.
• Eliminate Job B from further consideration.
• ? ? ? ? B
• The next smallest time is located in Job C (2hours). Since the time is in Work
Center A, schedule this job first.
• Eliminate Job C from further consideration.
• C ? ? ? B
• The next smallest time after that is located in Job E (2hours). Since the time is in Work
Center B, schedule this job last.
• Eliminate Job E from further consideration.
• C ? ? E B
• The next smallest time after is located in Job A (3hours). Since the time is in Work Center
A, schedule this job first.
• Eliminate Job A from further consideration.
• C A ? E B
• The only job left to consider is Job D.
• C A D E B
• So, the jobs must be processed in the order C → A → D → E → B, and must be
processed in the same order on both work centers.
• Job times (hours)
• Job Work center A Work center B
• A 3 4
• B 4 1
• C 2 5
• D 5 4
• E 3 2
• Total idle time:M1:1 hr
• Total idle time :M2:2 hr
order C → A → D → E → B,
JOBS M1 IN-OUT M2 IN-OUT
C 0-2 2-7
A 2-5 7-11
D 5-10 11-15
E 10-13 15-17
B 13-17 17-18
Total run
time
18 hrs
THREE MACHINES
• This case is similar to the previous case except that instead of two
machines, there are three machines. Problems falling under this
category can be solved by the method developed by Johnson.
Following are the two conditions of this approach:
• The smallest processing time on machine A is greater than or equal to
the greatest processing time on machine B, i.e.,
• Min. (Ai) ≥ Max. (Bi)
The smallest processing time on machine C is greater than or equal to
the greatest processing time on machine B, i.e.,
• Max. (Bi) ≤ Min. (Ci)
• At least one of the above two conditions must be satisfied.
If either or both of the above conditions are satisfied, then we replace
the three machines by two fictitious machines G & H with
corresponding processing times given by
Gi = Ai + Bi
Hi = Bi + Ci
Where Gi & Hi are the processing times for ith job on machine G and H
respectively.
After calculating the new processing times, we determine the optimal
sequence of jobs for the machines G & H in the usual manner.
• The MDH Masala company has to process five items on three
machines:- A, B & C. Processing times are given in the
following table:
• Item Ai Bi Ci
• 1 4 4 6
• 2 9 5 9
• 3 8 3 11
• 4 6 2 8
• 5 3 6 7
• Find the sequence that minimizes the total elapsed time.
Here, Min. (Ai) = 3, Max. (Bi) = 6 and Min. (Ci) = 6. Since the condition of
Max. (Bi) ≤ Min. (Ci) is satisfied, the problem can be solved by the above
procedure
• . The processing times for the new problem are given
below.
• Item Gi = Ai + Bi Hi = Bi + Ci
• 1 8 10
• 2 14 14
• 3 11 14
• 4 8 10
• 5 9 13
• The optimal sequence is
• 1 4 5 3 2
5 3 2
EM AI BI CI
4 4 6
9 5 9
8 3 11
6 2 8
3 6 7
It
e
m
Machine A Machine B Machine C
Time
in
Time
out
Time
in
Time
out
Time
in
Time
out
1 0 4 4 8 8 14
4 4 10 10 12 14 22
5 10 13 13 19 22 29
3 13 21 21 24 29 40
2 21 30 30 35 40 49
Total elapsed time = 49
Idle time for machine A = 49 – 30 = 19 hours
Idle time for machine B = 4 + (10 - 8) + (13 - 12) + (21 - 19)+ (30 - 24) + (49 - 35) = 29 hours
Idle time for machine C = 8 + (14 - 14) + (22 - 22) + (29 - 29)+ (40 - 40) = 8 hours
Thank you

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Unit 7 production scheduling

  • 2. Production control • Design and use of systematic procedure for establishing plans and controlling all the elements of an activity • Follow up procedure for determining how closely is the plan followed
  • 3. Objectives of production control • Issuing the necessary orders to concerned personnel • Arrange necessary items like materials ,machines,man power and jigs • To ensure instructions are followed so that time limit is managed
  • 4. DEFINITION In production scheduling the products to be manufactured and their quantities are determined initially. • The sequence of manufacturing processes required for the production of these items are also established. • The manufacturing resources are then allocated to perform production processes to realise various items. • This is spread over a predetermined time. This function is known as production scheduling.
  • 5. OVERVIEW OF PRODUCTION SCEDULING Scheduling: is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process. • Scheduling: is used to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials. • It is an important tool for manufacturing and engineering, where it can have a major impact on the productivity of a process. • In manufacturing, the purpose of scheduling is to minimize the production time and costs, by telling a production facility when to make, with which staff, and on which equipment. • Production scheduling aims to maximize the efficiency of the operation and reduce costs..
  • 6. OVERVIEW • Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process. Companies use backward and forward scheduling to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials. • Forward scheduling is planning the tasks from the date resources become available to determine the shipping date or the due date. • Backward scheduling is planning the tasks from the due date or required-by date to determine the start date and/or any changes in capacity required.
  • 7. THE BENEFITS OF PRODUCTION SCHEDULING • Process change-over reduction • Inventory reduction, leveling • Reduced scheduling effort • Increased production efficiency • Labor load leveling • Accurate delivery date quotes • Real time information • It greatly outperform older manual scheduling methods. • These provide the production scheduler with powerful graphical interfaces which can be used to visually optimize real-time work loads in various stages of production, and pattern recognition allows the software to automatically create scheduling opportunities which might not be apparent without this view into the data.
  • 8. SHOP FLOOR CONTROL • LOADING: Check availability of material ,labour and machines • SEQUENCING: Release work order to shops and issue dispatch list for individual lists • MONITORING: Maintain progress reports of each job until I is complete
  • 9. LOADING: • Another important technique of production planning is loading. In planning the production process the management-must know when a particular equipment/machine will be available for work on each order or item. For this information a list of the number of machines capable of performing similar operations is prepared. • Knowing the number of machine shifts available for each kind of operation and number of shifts required for such operations in the production process to complete the schedule, the planning staff can evaluate whether the work load is greater or less than the capacity of the equipment.
  • 10. OBJECTIVES OF LOADING • (i) To plan new work orders on the basis of spare capacity available. • (ii) To balance the work load in a plant. • (iii) To maintain the delivery promises. • (iv) To check the feasibility of production programmes. • and load charts:
  • 11. LOADING DEVICES: THERE ARE TWO MAIN APPROACHES FOR LOADING VIZ. LOADING STEP BY STEP, AND MACHINE LOADING Loading Step by Step: • Sometimes an individual production order may require a finite number of operations and the order of these operations may vary too much from item to item. In such cases overloads are scheduled to account for interaction among various operations by identifying the operation which imposes maximum delay on the order. Following are the steps in this approach: (a) Find the earliest date and the hours required that can be scheduled onto each operation. (b) Determine the hours required at each operation and the time thereafter to complete the job if no loading delay occurs. (c) Schedule the bottleneck operation as early as possible.
  • 12. • (d) Schedule subsequent operations as early as possible. • B. Machine Loading: • Using information from schedules, weekly/periodic load in hours is determined for each machine and is then recorded on machine load chart. The chart also gives the time for which the machine is busy for parts pertaining to different work orders. • A machine load chart for all the machines in a production department shows the future spare capacity of machines. The machines should be loaded to full capacities as idle capacities of machines are sources of loss to the organisation and also increase the cost of production. • C. Load Charts: • Load charts shows the work assigned to various departments, machines or components of an organisation.
  • 13. • During “periods of peak/heavy loads information from load charts can be used to Determine”: (i) Priorities to future orders and to decide whether to sub- contract or refuse new orders. (ii) Provision of overtime or multi-shift operations. (iii) Acquisition of extra men or equipment for additional capacity. One common procedure for Loading is to maintain a register at each machine center. When any order is loaded on a machine a entry is made in the register showing the estimated time, the order is likely to devote on the machine and the estimated time off. The information can also be presented with the help of Gantt chart.
  • 14. • Finite Capacity Planning and Scheduling • Finite capacity planning recognizes that every business has a fixed amount of available resources with which it can produce its products or services, at least in the short run. Because of this, providing its services or producing its products requires careful planning and scheduling to stay within its resource constraints. In this context, resources refer to people, tools and expertise. This approach to planning is finite planning, based on the finite amount of resource capacity to apply to the production of products or services to customers. • Examples of businesses with finite capacity in the near-term are window cleaners, construction contractors, automobile manufacturers, specialized product shops and software developers.
  • 15. • Infinite Capacity Planning • Infinite capacity planning ignores any resource constraints and plans production or servicing activities backward from a customer due date or another fixed end date. Infinite scheduling and capacity planning uses the lead times or work times of the production flow to back-schedule work to each resource, whether a work center or one or more individuals. In doing so, infinite capacity loading disregards any existing work or commitments of the resources. • One example of a business operating with infinite capacity planning is an online retail vendor.
  • 16. TECHNIQUES OF SCHEDULING • Priority rules in scheduling: PRIORITY SEQUENCING • When several jobs compete for the capacity of a machine or a work center, the question of sequencing the jobs rises. This question is answered by determining the priority for all the jobs waiting in the queue by applying priority sequencing rules.
  • 17. THE RULES OF SINGLE CRITERION SEQUENCING ARE EXPLAINED IN DETAIL IN THE FOLLOWING PARAGRAPHS • i) First come-first served (FCFS) rule: Jobs are scheduled for work in the same sequence as they arrive at the facility or work center. This rule is commonly applied in service centers such s banks, super bazaars and barber shops. • ii) Shortest process time job (SPT) first: The job which has the shortest processing/ operation time on the mchine or at the work center is given the highest priority to be loaded as the next job for processing. This rule minimizes the in-process-inventory, however, at the expense of keeping the jobs having longer processing time for a longer time in the work center, there-by increasing the job through-put time (i.e. manufacturing cycle time). • iii) Longest processing time (LPT) job first: The job with the longest processing/ operation time is scheduled as the first job to be loaded on the machine among the jobs waiting in queue.
  • 18. • iv) Least slack (LS) job first: In this rule, the highest priority is given to the job which has the least slack. Slack is the difference between available time and the duration of processing the job. • Slack = Available time - Processing time. • v) Earliest due date (EDD) job first: • This rule sequences the jobs waiting in the queue at the work centre or machine according to their due dates and the jobs are processed according to their due dates i.e. having earliest due date is given highest priority while loading the job on the machine (or work center). This rule does not ensure that all jobs will be completed on time i.e. within their due dates.
  • 19. • vi) Truncated shortest processing time (TSPT) job first: This rule sequences the jobs according to the SPT rule, except that the jobs that have been waiting for time period longer than a specified truncation time are given higher priority than other jobs. • vii) Preferred customer order (PCO) rule: Jobs belonging to a preferred customer are given higher priority than other jobs. • viii) Random-selection: This rule is not used normally. It may be used when no other consideration is important. • ix) COVERT (cost over time) rule: This rule uses the ratio of expected delay cost (C) to the processing time (T). The job with the largest ratio is given the highest priority
  • 20. JOHNSONS RULE • In operations research, Johnson's rule is a method of scheduling jobs in two work centers. • Its primary objective is to find an optimal sequence of jobs to reduce make span (the total amount of time it takes to complete all jobs). • It also reduces the amount of idle time between the two work centers. The method minimizes the makespan in the case of two work centers. • Furthermore, the method finds the shortest makespan in the case of three work centers if additional constraints are met.
  • 21. The technique requires several preconditions: • The time for each job must be constant. • Job times must be mutually exclusive of the job sequence. • All jobs must be processed in the first work center before going through the second work center. • All jobs are equally prioritised.
  • 22. • Johnson's rule is as follows: • List the jobs and their times at each work center. • Select the job with the shortest activity time. If that activity time is for the first work center, then schedule the job first. If that activity time is for the second work center then schedule the job last. Break ties arbitrarily. • Eliminate the shortest job from further consideration. • Repeat steps 2 and 3, working towards the center of the job schedule until all jobs have been scheduled.
  • 23. • Example • Each of five jobs needs to go through work center A and B. Find the optimum sequence of jobs using Johnson's rule. • FIND :total runtime/elapse time. • Total idle time. • Job times (hours) • Job Work center A Work center B • A 3 4 • B 4 1 • C 2 5 • D 5 4 • E 3 2 • The smallest time is located in Job B (1 hours). Since the time is in Work Center B, schedule this job last. • Eliminate Job B from further consideration. • ? ? ? ? B • The next smallest time is located in Job C (2hours). Since the time is in Work Center A, schedule this job first. • Eliminate Job C from further consideration.
  • 24. • C ? ? ? B • The next smallest time after that is located in Job E (2hours). Since the time is in Work Center B, schedule this job last. • Eliminate Job E from further consideration. • C ? ? E B • The next smallest time after is located in Job A (3hours). Since the time is in Work Center A, schedule this job first. • Eliminate Job A from further consideration. • C A ? E B • The only job left to consider is Job D. • C A D E B • So, the jobs must be processed in the order C → A → D → E → B, and must be processed in the same order on both work centers.
  • 25. • Job times (hours) • Job Work center A Work center B • A 3 4 • B 4 1 • C 2 5 • D 5 4 • E 3 2 • Total idle time:M1:1 hr • Total idle time :M2:2 hr order C → A → D → E → B, JOBS M1 IN-OUT M2 IN-OUT C 0-2 2-7 A 2-5 7-11 D 5-10 11-15 E 10-13 15-17 B 13-17 17-18 Total run time 18 hrs
  • 26. THREE MACHINES • This case is similar to the previous case except that instead of two machines, there are three machines. Problems falling under this category can be solved by the method developed by Johnson. Following are the two conditions of this approach: • The smallest processing time on machine A is greater than or equal to the greatest processing time on machine B, i.e., • Min. (Ai) ≥ Max. (Bi) The smallest processing time on machine C is greater than or equal to the greatest processing time on machine B, i.e., • Max. (Bi) ≤ Min. (Ci) • At least one of the above two conditions must be satisfied. If either or both of the above conditions are satisfied, then we replace the three machines by two fictitious machines G & H with corresponding processing times given by Gi = Ai + Bi Hi = Bi + Ci Where Gi & Hi are the processing times for ith job on machine G and H respectively. After calculating the new processing times, we determine the optimal sequence of jobs for the machines G & H in the usual manner.
  • 27. • The MDH Masala company has to process five items on three machines:- A, B & C. Processing times are given in the following table: • Item Ai Bi Ci • 1 4 4 6 • 2 9 5 9 • 3 8 3 11 • 4 6 2 8 • 5 3 6 7 • Find the sequence that minimizes the total elapsed time.
  • 28. Here, Min. (Ai) = 3, Max. (Bi) = 6 and Min. (Ci) = 6. Since the condition of Max. (Bi) ≤ Min. (Ci) is satisfied, the problem can be solved by the above procedure
  • 29. • . The processing times for the new problem are given below. • Item Gi = Ai + Bi Hi = Bi + Ci • 1 8 10 • 2 14 14 • 3 11 14 • 4 8 10 • 5 9 13 • The optimal sequence is • 1 4 5 3 2
  • 30. 5 3 2 EM AI BI CI 4 4 6 9 5 9 8 3 11 6 2 8 3 6 7 It e m Machine A Machine B Machine C Time in Time out Time in Time out Time in Time out 1 0 4 4 8 8 14 4 4 10 10 12 14 22 5 10 13 13 19 22 29 3 13 21 21 24 29 40 2 21 30 30 35 40 49 Total elapsed time = 49 Idle time for machine A = 49 – 30 = 19 hours Idle time for machine B = 4 + (10 - 8) + (13 - 12) + (21 - 19)+ (30 - 24) + (49 - 35) = 29 hours Idle time for machine C = 8 + (14 - 14) + (22 - 22) + (29 - 29)+ (40 - 40) = 8 hours