unit-4 production scheduling part-a 1. list out any five

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IE-6605 PRODUCTION PLANNING AND CONTROL UNIT-4 SRI VIDYA COLLEGE OF ENGG&TECH Page 1 UNIT-4 PRODUCTION SCHEDULING PART-A 1. List out any five priority sequencing rules. (Nov-2017) First come, first served (FCFS) Last come, first served (LCFS) Earliest due date (EDD) Shortest processing time (SPT) Longest processing time (LPT) 2. What is MRP? List the various inputs required for it. (Nov-2017) It is a computational technique that converts the master schedule for final product into a detailed schedule for the raw material and parts used in the final product. Various Inputs 1. MPS 2. Bill of materials 3. Inventory record file 3. What is master scheduling? (Apr-2017, Apr-2016, Apr-2012) It is a detailed plan that states how many end items will be available for sale (Or) distribution during specific periods 4. What is meant by Kanban system? (Apr-2017, Apr-2015) A Kanban is a card that is attached to a storage and transport container. It identifies the part number and container capacity, along with other information. 5. Differentiate between product sequencing or sequencing and scheduling. (Nov-2016, Nov-2015, Nov-2014) Scheduling refers to the setting of operation start dates so that jobs will be completed by their due date. Product Sequencing- It is a systematic procedure for determining the optimum sequence (order) of jobs that minimizes the total completion time. 6. Cite the meaning of the term line of balance. (Nov-2016, Nov-2015) Line-of-balance (LOB) is a charting technique that uses lead times and assembling sequencing to compare planned component completions with actual component completions.

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Page 1: UNIT-4 PRODUCTION SCHEDULING PART-A 1. List out any five

IE-6605 PRODUCTION PLANNING AND CONTROL UNIT-4

SRI VIDYA COLLEGE OF ENGG&TECH Page 1

UNIT-4 PRODUCTION SCHEDULING

PART-A

1. List out any five priority sequencing rules. (Nov-2017)

First come, first served (FCFS)

Last come, first served (LCFS)

Earliest due date (EDD)

Shortest processing time (SPT)

Longest processing time (LPT)

2. What is MRP? List the various inputs required for it. (Nov-2017)

It is a computational technique that converts the master schedule for final product into a

detailed schedule for the raw material and parts used in the final product.

Various Inputs

1. MPS

2. Bill of materials

3. Inventory record file

3. What is master scheduling? (Apr-2017, Apr-2016, Apr-2012)

It is a detailed plan that states how many end items will be available for sale (Or)

distribution during specific periods

4. What is meant by Kanban system? (Apr-2017, Apr-2015)

A Kanban is a card that is attached to a storage and transport container. It identifies the part

number and container capacity, along with other information.

5. Differentiate between product sequencing or sequencing and scheduling. (Nov-2016,

Nov-2015, Nov-2014)

Scheduling refers to the setting of operation start dates so that jobs will be completed by

their due date.

Product Sequencing- It is a systematic procedure for determining the optimum sequence

(order) of jobs that minimizes the total completion time.

6. Cite the meaning of the term line of balance. (Nov-2016, Nov-2015)

Line-of-balance (LOB) is a charting technique that uses lead times and assembling

sequencing to compare planned component completions with actual component

completions.

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7. Write a note on perpetual loading. (Nov-2014)

In perpetual loading, a copy of every order is placed in an open file which moves with the

job going to different facilities.

During the processing, the progress is reported with the help of tickets such as inspection

ticket, material requisition ticket, move ticket, etc.

8. What is Gantt chart and how it is constructed? (Apr-2014, Apr-2015)

Gantt charts are usual (bar chart) aids to depict the sequencing, load on facilities, or

progress associated with work effort over a well-defined time period.

9. With reference to line balancing, define the terms (a) line efficiency; (ii) balance

delay. (Apr-2014)

Line efficiency- is the ratio between the time needed and the time allocated in an assembly

line.

Balance delay-is the percentage of wasted time.

10. What is manufacturing lead time.

MLT is the total length of time used to process raw materials and components through all

upper levels in the bill of material into an end item.

11. Write down the advantages and disadvantages of master scheduling`

Advantages

1. It translates aggregate plans into specific end items.

2. It evaluates alternative schedules.

3. It generates material requirements.

Disadvantages

1. The complete information is available in gross, and thus it can sometimes mislead.

12. List the key functions of the production scheduling and control.

(i) Release orders;

(ii) Assign jobs;

(iii) Sequencing priorities;

(iv) MLT by expediting and tracking.

13. What is dispatching.

It is the routine of setting productive activities in motion through the release of orders and

instructions in accordance with previously planned times and sequences embodied in route

sheets and schedule charts.

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14. What are the advantages, disadvantages of Gantt load chart?

Advantages

i) This system is quite simple.

ii) ii) This could be maintained even by electrical staff after some training.

iii) iii) Overall cost of operation is small.

Disadvantages

From the load chart it is not possible to learn the exact time of a work. It tells only the total

load ahead of a department or a facility.

15. What are the main objectives of loading?

(i) To check the feasibility of production programs

(ii) To assist in the efficient planning of new work

(iii) To assist in balancing the plant to the existing load

(iv) To assist in fixing of reliable delivery promises.

16. List the function of expediting (Or) Follow up (Or) Progressing. (Apr-2012)

It is a control function that keeps track of the โ€œprogressโ€ of work in accordance with planned

schedule.

PART-B

1. Explain the process flow involved in Master scheduling. (Nov-2017)

or

Explain the scheduling procedure with suitable example. Discuss in detail about the

scheduling rules. (Apr-2012, Apr-2017)

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Basic scheduling techniques depend on the type of production type and frequency of jobs,

demand patterns and flexibility offered by available processing time.

Basic scheduling problems include:

โ€ข Job shop scheduling (also known as unit scheduling)

โ€ข Batch production scheduling

โ€ข Flow production scheduling

โ€ข Production scheduling

Major inputs of MPS

โ€ข Forecast of demand of end items

โ€ข Customer orders

โ€ข Inventory on-hand from the previous period

functions of MPS

โ€ข To translate aggregate plans in to specific end times

โ€ข To evaluate alternative schedules

โ€ข To generate material requirements.

โ€ข To generate capacity requirements

โ€ข To facilitate information processing

โ€ข To maintain valid priorities

โ€ข To utilize capacity effectively

Advantages of master scheduling

โ€ข The overall cost of operating is minimum than any other loading and scheduling

systems

โ€ข This method is very simple to understand

โ€ข This could be even maintained by clerical staff.

โ€ข It could be easily kept current.

dis-advantages of master scheduling

โ€ข The detailed information cannot be obtained.

โ€ข It is efficient for small units only

Scheduling Rules or Priority Rules

โ€ข When many jobs are waiting before an operational facility, there are some rules to

decide the priority while sequencing.

โ€ข FCFS โ€“ First Come First Served

โ€ข SOT โ€“ Shortest Opening Time

โ€ข SPT โ€“ Shortest Processing Time

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โ€ข Due Date โ€“ Earliest due date first

โ€ข Start Date โ€“ [Due Date โ€“Normal lead time]

โ€ข STR โ€“ Slack time remaining (Due date - Processing time)

โ€ข STR/OR โ€“ Slack Time Remaining Per Operation

โ€ข CR โ€“ Critical Ratio [difference b/w due date and current date and the no. of days

remaining]

โ€ข QR โ€“ Queue Ratio

โ€ข LCFS โ€“ Last Come First Serve

โ€ข Random Order or Whim.

2. Discuss in detail the method of obtaining the MPS for a system with example. Suitable

assumptions can be made. (Nov-2015, Nov-2016)

The Master Production Schedule (MPS) formalizes the production plan and translates it into

specificend-item requirements over a short to intermediate planning horizon. The end items

are then explodedCapacity Requirements Planning (CRP) systems. Thus, the MPS essentially

drives the entire production and inventory system.

The major inputs to the master production schedule are:

1. Forecasts of demand, e.g., of end items and service parts.

2. Customer orders, i.e., including any warehouse and interplant needs.

3. Inventory on-hand from the previous period.

Forecasts of demand are the major input for make-to-stock items. However, to be

competitive,many make-to-order firms must anticipate orders by using forecasts for long

lead-time items and by matching the forecasts with customer orders as the orders become

available.

Master Scheduling Planning Horizon

The time horizon of master scheduling depends upon the type of product, volume of

production, andcomponent lead times. It can be weeks, months, or some combination, but

the schedule must normally extend far enough into the future so that the lead times for all

purchased and assembled components are adequately encompassed, schedules frequently

have both firm and flexible (or tentative) portions. Table illustrates an MPS for a furniture

company that has one such schedule-where the firm and flexible portions have not open to

change.

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Two-time fence can be identified in MPS: A demand and a planning time fence.

(a) A demand time fence is the firm or โ€˜frozenโ€™ portion of the master schedule (beginning

with the current period) during which no changes can be made to the schedule without

managementapproval.

(b) A planning time fence is the portion of the master schedule (also beginning with the

current period) during which changes will not automatically be made (i.e., via computer) to

accommodate demand. This gives the master scheduler a manageable base to work from

and stillallows some discretion in overriding the constraint.

Question: How does master scheduling differ under manufacturing strategies of

(a) make-tostock,

(b) assemble-to-order, and

(c) make-to-order?

See Figure where the shorter line segments represent fewer items.

In (a) make-to-stock operations, the (fewer) end items are stocked, to support customer

service, and the master productionschedule (MPS) is structured around those end items.

In (b) assemble-to-order plants, such as inautomobile manufacturing, the master scheduling

is done for the major sub-assembly-level items.

In(c) make-to-order products, such as customized furniture, there are fewer raw materials

than enditems; the end items may even be one of a kind. Here, the master schedule is

typically structuredaround the raw material usage.

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3. (i) What is perpetual loading? Describe. (Apr-2015)

In perpetual loading, a copy of every order is placed in an open file which moves with the

job going to different facilities.

During the processing, the progress is reported with the help of tickets such as inspection

ticket, material requisition ticket, move ticket, etc.

Steps in making Perpetual Schedule

a. Preparation of load analysis sheet.

Load analysis can be prepared by posting the load information on the form.

b. Presentation in Gantt chart

The total load against each department is added up and knowing the weekly capacity of a

department, the number of weeksโ€™ load against each department is calculated.

These informations can be transferred in the form of chart, usually on a Gantt load chart.

Advantages

1. It is very simple and understandable.

2. It requires less overall cost.

3. These charts can be used for various type of work.

(ii) Describe Gantts chart. What are their used? (Nov-2014)

Gantt chart is simple bar graphs that can be used to schedule any type of operation.

Two basic types of Gantt charts

โ€ข Work Load Charts

โ€ข Scheduling Charts

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โ€“ A Gantt work load chart is usually used to depict work load levels for

equipment work station or departments.

โ€“ A Gantt scheduling chart is used to depict workload levels for equipment,

workstations (Or) departments.

Advantages

iv) This system is quite simple.

v) ii) This could be maintained even by electrical staff after some training.

vi) iii) Overall cost of operation is small.

Disadvantages

From the load chart it is not possible to learn the exact time of a work. It tells only the total

load ahead of a department or a facility.

(iii) Explain any one of techniques for aligning completion times and due dates. (Apr-

2015, Nov-2014)

MLT is the total length of time used to process raw materials and components through all

upper levels in the bill of material into an end item.

MLT = no (Tsu + Q Tc+Tno)

Tno= non operation time (min),

Tsu= setup time to prepare for the batch (min),

Q = batch quantity (pc), and

Tc= operation cycle time per work unit (min/cycle).

Example:

A certain part is produced in a batch size of 100 units. The batch must be routed

through five operations to complete the processing of the parts. Average setup time is 3

hr/operation, and average operation time is 6 min (0.1 hr). Average nonoperation time

due to handling, delays, inspections, etc., is 7 hours for each operation. Determine how

many days it will take to complete the batch, assuming the plant runs one 8-hr shift/day

Given data:

Number of operation, no = 5

Tsu= setup time to prepare for the batch (min)= 3

quantity, Q= 100

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Tc= operation cycle time per work unit (min/cycle) = 0.1 hr

Tno= Average non operation time =7 hr

Solution:

The manufacturing lead time,

MLT = no (Tsu + Q Tc +Tno) = 5 X (3+ 100X0.1 + 7) = 100 hours

At 8 hr/day, this amounts to 100/8 = 12.5 days

4. Discuss the following: (Nov-2014, Apr-2015)

(a) Flow production scheduling;

In flow shop scheduling problem, there are n jobs; each require processing on m different

machines.The order in which the machines are required to process a job is called process

sequence of that job. The process sequences of all the jobs are the same. But the processing

times for various jobs on a machine may differ. If an operation is absent in a job, then the

processing time of the operation of that job is assumed as zero.

The flow-shop scheduling problem can be characterized as given below:

1. A set of multiple-operation jobs is available for processing at time zero (Each job requires

moperations and each operation requires a different machine).

2. Set-up times for the operations are sequence independent, and are included in processing

times.

3. Job descriptors are known in advance.

4. m different machines are continuously available.

5. Each individual operation of jobs is processed till its completion without break.

The main difference of the flow shop scheduling from the basic single machine scheduling is

that the inserted idle time may be advantageous in flow shop scheduling. Though the

current machineis free, if the job from the previous machine is not released to the current

machine, we cannot startprocessing on that job. So, the current machine has to be idle for

some time. Hence, inserted idletime on some machines would lead to optimality.

(b) Periodic batch control

Batch Production

a. many planning steps

i. Aggregate planning

ii. master scheduling

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iii. material requirements planning (MRP)

iv. capacity requirements planning (CRP)

(c) Kanban.

A Kanban is a card that is attached to a storage and transport container. It identifies the

part number and container capacity, along with other information.

Production or (In-Process)-Kanban

โ€“ Provides production instructions for the work center

โ€“ Tells the workers exactly the quantity and the type of part to produce

โ€“ Used for work centers that produce only one-part number or have minimal setups in

spite of multiple part number production

โ€ข Rectangular โ€“ one-piece flow production

โ€ข Triangular โ€“ for small lot production

Withdrawal-Kanban

โ€“ Inter-Process Kanban

โ€ข Delivers order for parts from a preceding process

โ€ข Specifies quantity and type of parts to deliver from Location A to Location B

โ€“ Later replenishment system โ€“ kanban are filled from suppliers finished

goods shelf

โ€“ Sequenced withdrawal โ€“ supplier sequences parts in reverse order for

truck loading

โ€“ Supplier Kanban

โ€ข Same as an inter-process Kanban, except it signals conveyance of part from an

outside supplier

Job Order-Kanban

โ€“ Issued for each job order

Through-Kanban

โ€“ When two processes are very close, it doesnโ€™t make sense to issue two Kanbans. Used

where one process directly feeds (conveyor) the next process.

Common-Kanban

โ€“ Where a withdrawal kanban is used as a production ordering kanban if the distance

between two processes is very short and share the same supervisor.

Emergency-Kanban

โ€“ Temporary, when there is a defect or problem, can be withdrawal or production

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(d) Dispatching

It is the routine of setting productive activities in motion through the release orders and

instructions, in accordance with previously planned times and sequences embodied in route

sheets and scheduled charts.

Activities of Dispatching

โ€ข Movement of material from stores

โ€ข Issue of tool orders

โ€ข Issue of job order

โ€ข Issue of time tickets

โ€ข Issue of inspection orders

โ€ข Issue of move orders

Functions of dispatching

โ€ข To prepare manufacturing orders (shop order, move order, tool order)

โ€ข Issue of material from stores

โ€ข Issue of instructions to tool room

โ€ข Issue of orders authorising the commencement of operations in accordance with the

predicted dates

โ€ข Issue of time, time instruction cards, drawings

โ€ข Issue of order to the inspection department

โ€ข Ordering finished products to the stock room

โ€ข Time recording

โ€ข Issue of time tickets to finance department

โ€ข Recording of the idle time of machines and operations

Common Forms Used in Dispatching

โ€ข Material requisitions form

โ€ข Job card / job ticket

โ€ข Labour card / Tickets

โ€ข Move Card / Ticket

โ€ข Inspection Card / Tickets

โ€ข Tool and Gauge Tickets

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(e) Discuss in detail the various steps involved in Line of balance Technique. (Apr-

2016)

Line of balance (LOB) is a charging technique that uses lead times and assembly sequencing

to compare planned component completions with actual component completions

Uses of LOB

โ€ข Source of each component element (purchase, manufacture, assemble, test)

โ€ข Sequence of assembly, including sub-assembly, testing and inspection, packaging,

shipping and related activities.

โ€ข Comparison of scheduled versus actual finished product deliveries

โ€ข Comparison of scheduled versus actual component (element completion showing

present and shortages)

Input to LOB

โ€ข Schedule of Delivery.

โ€ข Key operations in making the product which needs to be controlled.

โ€ข The sequence in which the key events are controlled.

โ€ข Lead times of the above events.

Various charts used in LOB

โ€ข Operation programme chart/ or assembly chart

โ€ข Objective chart

โ€ข Progress chart

โ€ข Line or balance chart.

5. Discuss the concepts, inputs, characteristics, working, output and benefits of MRP.

Also Explain in detail the various components of MRP (Nov-2017, Apr-2017, Nov-

2016, Nov-2015, Apr-2012)

Material Requirement planning

Material requirements planning (MRP) is a computational technique that converts the

master schedule for end products into a detailed schedule for the raw materials and

components used in the end products. The distinction between independent demand and

dependent demand is important in MRP.

Independent demand means that demand for a product is unrelated to demand for other

items. Final products and spare parts are examples of items whose demand is independent.

Independent demand patterns must usually be forecasted.

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Dependent demand means that demand for the item is directly related to the demand for

some other item, usually a final product. The dependency usually derives from the fact that

the item is a component of the other product.

Inputs to the MRP System

To function, the MRP program must operate on data contained in several files. These files

serve as inputs to the MRP processor. They are:

(1) MPS,

(2) Bill of materials file and other engineering and manufacturing data, and

(3) Inventory record file.

Figure illustrates the flow of data into the MRP processor and its conversion into useful

output reports. In a properly implemented MRP system, capacity planning also provides

input to ensure that the MRP schedule does not exceed the production capacity of the firm.

(1) MPS

The MPS lists what end product, and how many of each are to be produced and when they

are to be ready for shipment. Manufacturing firms generally work toward monthly delivery

schedules, but the master schedule in our figure uses weeks as the time periods. 'Whatever

the duration, these time periods are called time buckets in MRP. Instead of treating time as a

continuous variable (which of course, it is). MRP makes its computations of materials and

parts requirements in terms of time buckets

(2) Bill of materials file

The bill of materials (BOM) file is used to compute the raw material and component

requirements for end products listed in the master schedule. It provides information on the

product structure by listing the component parts and subassemblies that make up each

product. The structure of an assembled product can be illustrated as in Figure. This is much

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simpler than most commercial products. but its simplicity will serve for illustration

purposes. Product PI is composed of two subassemblies, S1 and S2, each of which is made

up of components C1, C2, and C3, and C4, C5, and C6, respectively.

Finally, at the bottom level are the Jaw materials that go into each component. The items at

each successively higher level are called the parents of the items feeding into it from below.

For example, S1 is the parent of C1, C2, and C3. The product structure must also specify the

number of each subassembly, component, and raw material that go into its respective

parent. These numbers are shown in parentheses in our figure.

(3) Inventory record file

The inventory record file is referred to as the item master file in a computerized inventory

system. The types of data contained in the inventory record are divided into three segments:

1. Item master data

This provides the item's identification (part number) and other data about the part such as

order quantity and lead times.

2. Inventory status

This gives a time-phased record of inventory status. In MRP, it is important to know not only

the current level of inventory, but also any future changes that will occur against the

inventory. Therefore, the inventory status segment lists the gross requirements for the item,

scheduled receipts, on-hand status, and planned order releases.

3. Subsidiary data

The third file segment provides subsidiary data such as purchase orders, scrap or rejects,

and engineering changes.

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MRP Outputs and Benefits

Outputs include:

(1) Planned order releases, which provide the authority to place orders that have been

planned by the MRP system:

(2) Report of planned order releases in future periods

(3) Rescheduling notices, indicating changes in due dates for open orders

(4) Cancelation notices, indicating that certain open orders have been canceled because of

changes in the MPS; (5) reports on inventory status

(6) Performance reports of various types, indicating costs, item usage, actual versus planned

lead times

(7) Exception reports, showing deviations from the schedule, orders that are overdue, scrap,

and so on: and

(8) Inventory forecasts, indicating projected inventory levels in future periods.

Benefits

(1) Reduction in inventory

(2) Quicker response to changes in demand than is possible with a manual requirements

planning system.

(3) Reduced setup and product changeover costs,

(4) Better machine utilization,

(5) Improved capacity to respond to changes in the master Schedule, and

(6) As an aid in developing the master schedule.

6. Sequence the following jobs to minimize the processing times on the two machines.

Also compute the idle times of the machines. (Apr-2015)

Job 1 2 3 4 5 6

Machine -1 5 9 4 7 8 6

Machine -2 7 4 8 3 9 5

This sequencing problems can be solved using Johnsonโ€™s rule. The sequence of job can be

obtained as below.

J4

J2 J4

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J3 J2 J4

J3 J1 J2 J4

J3 J1 J6 J2 J4

J3 J1 J5 J6 J2 J4

Machine 1 Machine 2

Optimal sequence of job is

The final schedule for the above job sequence can be drawn as shown below.

From the above figure, we can write

Total elapsed time = 42 time units

Idle time for M1= 3 time units

Idle time for M2 = 4 + 2 = 6 time units

7. An assembly line is to be designed to operate 7.5 hours per day and supply a steady

demand of 300 units per day. The following table shows the tasks and their

performance times. (i) Draw the precedence diagram, (ii) What is the cycle time? (iii)

Assign tasks to work stations stating your logical rules, and (iv) What is the efficiency

of your line balance? (Apr-2014)

Task a b c d e f g h i j k l Preceding

tasks

- - - a b c d e f g h,i j,k Performance

time (sec)

70 40 45 10 30 20 60 50 15 25 20 25

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Given data

Working time = 7.5 hours per day

Demand = 300 units per day

(i) Precedence diagram

(ii) Cycle time (CT)

๐ถ๐‘‡ =๐‘‚๐‘๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘–๐‘›๐‘” ๐‘ก๐‘–๐‘š๐‘’ ๐‘๐‘’๐‘Ÿ ๐‘‘๐‘Ž๐‘ฆ

๐ท๐‘’๐‘ ๐‘–๐‘Ÿ๐‘’๐‘‘ ๐‘œ๐‘ข๐‘ก๐‘๐‘ข๐‘ก ๐‘๐‘’๐‘Ÿ ๐‘‘๐‘Ž๐‘ฆ=

7.5 ๐‘‹ 60 ๐‘‹ 60

300= 90 ๐‘ ๐‘’๐‘๐‘œ๐‘›๐‘‘๐‘  = 1.5 ๐‘š๐‘–๐‘›

(iii) Assigning tasks to workstations

Workstation Assign task Idle time (in seconds) 1 a, d 20 10 2 c, f, i 45 25 10 3 g, j 30 5 4 b, h 50 0 5 e, k, l 60 40 15 = 40

(iv) Efficiency of line balance

Percentage of idle time (balance decay) for the line

=๐‘ฐ๐’…๐’๐’† ๐’•๐’Š๐’Ž๐’† ๐’‘๐’†๐’“ ๐’„๐’š๐’„๐’๐’†

๐‘ต๐’.๐’๐’‡ ๐’˜๐’๐’“๐’Œ๐’”๐’•๐’‚๐’•๐’Š๐’๐’๐’” ๐‘ฟ ๐‘ช๐’š๐’„๐’๐’† ๐’•๐’Š๐’Ž๐’† ๐‘ฟ ๐Ÿ๐ŸŽ๐ŸŽ =

๐Ÿ’๐ŸŽ

๐Ÿ“ ๐‘ฟ ๐Ÿ—๐ŸŽ ๐‘ฟ ๐Ÿ๐ŸŽ๐ŸŽ = ๐Ÿ–.๐Ÿ— %

Efficiency of the line = 100 โ€“ Percentage of idle line=1 โ€“ 8.9 = 91.1%

8. There are seven jobs which are to be processed first on Machine I and then on

Machine II. Process time in hours is given below. Find the optimal sequence and total

elapsed time. (Apr-2014)

Task a b c d e f g

Machine I 6 24 30 12 20 22 18

Machine II 16 20 20 13 24 2 6

This sequencing problems can be solved using Johnsonโ€™s rule. The sequence of job can be

obtained as below.

Page 18: UNIT-4 PRODUCTION SCHEDULING PART-A 1. List out any five

IE-6605 PRODUCTION PLANNING AND CONTROL UNIT-4

SRI VIDYA COLLEGE OF ENGG&TECH Page 18

f

a f

a g f

a d g f

a d b c g f

a d e b c g f

Machine 1 Machine 2

Optimal sequence of job is a--- d----e---b---c---g----f

The final schedule for the above job sequence can be drawn as shown below.

From the above figure, we can write

Total elapsed time = 132 time units

Idle time for M1= 2 hours

Idle time for M2 = 6 + 3 +10 + 14 = 33 hours