Module-III

Production Planning [10]

Routing, Loading, and scheduling with their different
techniques, dispatching, Progress reports, Expediting, and
corrective measures.
PRODUCTION PLANNING AND CONTROL

"Production planning and control is the co-ordination of series of functions

according to a plan which will economically utilize the plant facilities and
regulate the orderly movement of goods through the entire manufacturing
cycle from the procurement of all materials to the shipping of finished goods
at a predetermined rate”

Functions of production planning and control

1. Planning,
2. Routing,
3. Scheduling,
4. Dispatching,
5. Follow-up and
6. Inspection.
Planning
• It is deciding in advance what to do, how to do it, when to do it and who is to do it.
• It bridges the gap from where we are, to where we want to go.
• It makes it possible for things to occur which would not otherwise happen.

Routing
• Routing may be defined as the selection of path which each part of the product will
follow, while being transformed from raw material to finished products.
• Routing determines the most advantageous path to be followed from department to
department and machine to machine till raw material gets its final shape.

Scheduling
• Scheduling is the determining of starting and finishing time for each operation,
assembly and finish product.
• It includes the scheduling of materials, machines and all other requisites of production.
So, it is like a time-table of production.
It also means to :
 Fix the amount of work to do.
 Arrange the different manufacturing operations in order of priority.
 Fix the starting and completing, date and time, for each operation
Dispatching
• Dispatching is concerned with starting the processes.
• It gives necessary authority so as to start a particular work, which has already been
planned under ‘Routing’ and ‘Scheduling’.
• Therefore, dispatching is ‘release of orders and instruction for the starting of
production of any item in acceptance with the route sheet and schedule charts’.

Follow-up
The function of follow-up is to report daily the progress of work in each shop in a
prescribed proforma and to investigate the causes of deviations from the planned
performance.

Inspection
• Inspection is also an important function of control.
• The purpose of inspection is to see whether the products manufactured are of requisite
quality or not.
• It is carried on at various levels of production process so that pre-determined standards
of quality are achieved. Inspection is undertaken both of products and inputs.
Objectives of production planning and control functions:
1. Systematic planning of production activities to achieve the highest efficiency in the
production of goods/services.
2. Organize the production facilities like machines, men, etc., to achieve stated
production objectives with respect to quantity and quality, time and cost.
3. Optimum scheduling of resources.
4. Coordinate with other departments relating to production to achieve regularly
balanced and uninterrupted production flow.
5. To conform to delivery commitments.
6. Materials planning and control.
7. To be able to make adjustments due to changes in demand and rush orders.
 Limitations of production planning and control

1. Based on Assumptions: - Production planning and control are based on certain

assumptions. In case the assumptions prove correct then the planning and control
will go smoothly, otherwise it may not. The assumptions generally are about plant
capacity, orders, availability of raw materials and power, etc.

2. Rigidity: - Under production planning and control things are pre-decided and fixed.
There is rigidity in the behavior of employees and it may not help in smoothening
the flow of work.

3. Difficult for Small Firms: - This process is time-consuming and small firms may not
be able to make use of production planning and control.

4. Costly: - It is a costly device as its implementation requires separate persons to

perform the functions of planning, dispatching, expediting, etc.

5. Dependence on External Factors: - The external factors sometimes reduce the

effectiveness of production planning and control. The factors like natural calamities,
change in technology, change in fashion, breakdown of power, government controls
etc. limit the use of production planning and control.
 Functions of Production Planning and Control

PPC
PRIOR PLANNING
Prior planning means pre-production planning. This includes all the planning efforts,
which are taking place prior to the active planning.

The modules of prior planning are as follows:

Product development and design is the process of developing a new product with all
the features, which are essential for effective use in the field, and designing it
accordingly. At the design stage, one has to take several aspects of design like, design
for selling, design for manufacturing and design for usage.

Forecasting is an estimate of demand, which will happen in future. Since, it is only an

estimate based on the past demand, proper care must be taken while estimating it.
Given the sales forecast, the factory capacity, the aggregate inventory levels and size
of the work force, the manager must decide at what rate of production to operate
the plant over an intermediate planning horizon.

Aggregate planning aims to find out a product wise planning over the intermediate
planning horizon.

Material requirement planning is a technique for determining the quantity and

timing for the acquisition of dependent items needed to satisfy the master
production schedule.
ACTIVE PLANNING

The modules of active planning are: Process planning and routing, Materials
planning. Tools planning, Loading, Scheduling etc.

Process planning and routing is a complete determination of the specific

technological process steps and their sequence to produce products at the desired
quality, quantity and cost.

It determines the method of manufacturing a product, selects the tools and

equipment's, analyses how the manufacturing of the product will fit into the
facilities.

Routing in particular prescribes the flow of work in the plant and it is related to the
considerations of layout, temporary locations for raw materials and components and
materials handling systems.

A material planning is a process which determines the requirements of various raw

materials/subassemblies by considering the trade-off between various cost
components like, carrying cost, ordering cost, shortage cost, and so forth.
1. Tools’ planning determines the requirements of various tools by taking
process specification (surface finish, length of the job, overall depth of cut
etc.), material specifications (type of material used, hardness of the material,
shape and size of the material etc.) and equipment specifications (speed
range, feed range, depth of cut range etc.).

2. Loading is the process of assigning jobs to several machines such that there is
a load balance among the machines. This is relatively a complex task, which
can be managed with the help of efficient heuristic procedures.

3. Scheduling is the time phase of loading and determines when and in what
sequence the work will be carried out. This fixes the starting as well as the
finishing time for each job.
 Action Phase
Action phase has the major step of dispatching. Dispatching is the transition
from planning phase to action phase. In this phase, the worker is ordered to
start manufacturing the product. The tasks which are included in dispatching
are job order, store issue order, tool order, time ticket, inspection order, move
order etc.
Control Phase
The control phase has the following two major modules:

PROGRESS REPORTING
In progress reporting, the data regarding what is happening with the job is collected. The
various data pertaining to materials rejection, process variations, equipment failures,
operator efficiency, operator absenteeism, tool life, etc., are collected and analyzed for the
purpose of progress reporting. These data are used for performing variance analysis, which
would help us to identify critical areas that deserve immediate attention for corrective
actions.

CORRECTIVE ACTION
The tasks under corrective action primarily make provisions for an unexpected event.
Some examples of corrective actions are creating schedule flexibility, schedule
modifications, capacity modifications, make or buy decisions, expediting the work, pre-
planning, and so on. Due to unforeseen reasons such as, machine breakdown, labor
absenteeism, too much rejection due to poor material quality etc., it may not be possible
to realize the schedule as per the plan. Under such condition, it is better to reschedule the
whole product mix so that we get a clear picture of the situation to progress further. Under
such situation, it is to be re-examined for selecting appropriate course of action.
Expediting means taking action if the progress reporting indicates deviations from the
originally set targets. Pre-planning of the whole affair becomes essential in case the
expediting fails to bring the deviated plan to its right path.
Aggregate planning makes decisions regarding the use of
facilities, inventory, people, and outside contractors.
Aggregate plans are typically monthly, and resources are
allocated in terms of an aggregate measure such as total
units, tons, or shop hours.

Master schedule breaks down the aggregate plan and

develops a schedule for specific products or product lines
for each week.

Short-term schedules then translate capacity decisions,

aggregate (intermediate) planning, and master schedules
into job sequences and specific assignments of personnel,
materials, and machinery.

The objective of scheduling is to allocate and prioritize

demand (generated by either forecasts or customer orders)
to available facilities.
 ROUTING

Routing may be defined as the selection of path which each part of the product will
follow while being transformed from raw materials to finished products.
Path of the product will also give sequence of operation to be adopted while being
manufactured.
In other way, routing means determination of most advantageous path to be
followed from department to department and machine to machine till raw material
gets its final shape, which involves the following steps:
a) Type of work to be done on product or its parts.
b) Operation required to do the work.
c) Sequence of operation required.
d) Where the work will be done.
e) A proper classification about the personnel required and the machine for
doing the work.

Routing provides the basis for scheduling, dispatching and follow-up.

Main Factors Affecting Routing Procedure

1. Type of Manufacturing Process/Technique Employed

In line type of layout the production process is serialized according to the sequence of
operations making routing automatic

2. Plant Equipment Characteristics

The same process may be possible on many machines available in the plant. In such cases the
cheapest one should be selected for routing purpose.

3. Availability of plant and equipment

Sometimes the services of cheapest processing machines or processes may not be available.
In such conditions, the routing must have alternatives available to keep the materials moving for
manufacturing of the product. This alternative may be in the form of bypassing the breakdown
machines/operations or changing the sequence of operations

4. Difficulties in Routing due to Non-Availability of Requisite Skilled Manpower

Manpower required in the plant may be highly skilled, semiskilled, or unskilled. On certain
particular machines, where high precision work is done, only services of experienced highly
skilled workers can be utilized.
Advantages of routing
• Routing gives a very systematic method of converting raw-materials into
finished goods.
• It leads to smooth and efficient work.
• It leads to optimum utilization of resources; namely, men, machines,
materials, etc.
• It leads to division of labor.
• It ensures a continuous flow of materials without any backtracking.
• It saves time and space.
• It makes the work easy for the production engineers and foremen.
• It has a great influence on design of factory's building and installed
machines.
Techniques of Routing

1. Route card:
• This card always accompanies with the job throughout all operations.
• This indicates the material used during manufacturing and their progress
from one operation to another.
• In addition to this, the details of scrap and good work produced are also
recorded.
Route card
2. Work sheet: It contains
a) Specifications to be followed while manufacturing.
b) Instructions regarding routing of every part with identification number of
machines and work place of operation.
This sheet is made for manufacturing as well as for maintenance.
3. Route sheet: It deals with specific production order. Generally made from operation
sheets. One sheet is required for each part or component of the order. These
includes the following:
(a) Number and other identification of order.
(b) Symbol and identification of part.
(c) Number of pieces to be made.
(d) Number of pieces in each lot—if put through in lots.
(e) Operation data which includes:
(i) List of operation on the part.
(ii) Department in which operations are to be performed.
(iii) Machine to be used for each operation.
(iv) Fixed sequence of operation, if any.
(f) Rate at which job must be completed, determined from the operation sheet.
 Use of Route Sheet
• In some production control systems, route sheets serve as the basis for
recording the progress of the part through a cycle of operation.
• It acts as a record of material flow.
• Route sheets are also used to
• load and schedule,
• determine labour efficiency,
• secure tooling, and
• arrange material moves.
 Scheduling
Scheduling encompasses allocating workloads to specific work centers and
determining the sequence in which operations are to be performed.
Scheduling can be defined as “prescribing of when and where each operation
necessary to manufacture the product is to be performed.”
It is also defined as the “establishing of times at which to begin and complete
each event or operation comprising a procedure”.

The objective of scheduling is to allocate and prioritize demand to available facilities.

Two significant factors in achieving this allocation and prioritizing are
(1) the type of scheduling, forward or backward, and
(2) the criteria for priorities.
Forward and Backward Scheduling

Forward scheduling
Forward scheduling is used in a variety of organizations where, jobs are performed to
customer order, and delivery is often requested as soon as possible i.e. job shop.

Forward scheduling determines the start and finish time of the next priority job by
assigning it the earliest available time slot and from that time, determines when the
job will be finished in that work center.

• Since the job and its components start as early as possible, they will typically be
completed before they are due at the subsequent work centers in the routing.

• The forward method generates in-process inventory and higher inventory costs.

• Forward scheduling is simple to use and it gets jobs done in shorter lead times,
compared to backward scheduling.
Backward scheduling
• Backward scheduling is often used in assembly type industries and commit in
advance to specific delivery dates.
• Backward scheduling begins with the due date, scheduling the final operation
first. Steps in the job are then scheduled, one at a time, in reverse order.
• By subtracting the lead time for each item, the start time is obtained.
• However, the resources necessary to accomplish the schedule may not exist.
• Backward scheduling is used in many manufacturing environments, as well as
service environments such as catering a banquet or scheduling surgery.
 Scheduling Criteria

The correct scheduling technique depends on the volume of orders, the nature of
operations, and the overall complexity of jobs, as well as the importance placed on
each of four criteria. These four criteria are:
1. Minimize completion time: This criterion is evaluated by determining the average
completion time per job.
2. Maximize utilization: This is evaluated by determining the percent of the time the
facility is utilized.
3. Minimize work-in-process (WIP) inventory: This is evaluated by determining the
average number of jobs in the system. The fewer the number of jobs that are in
the system, the lower the inventory.
4. Minimize customer waiting time: This is evaluated by determining the average
number of late days.
Inputs to Scheduling

1. Performance standards: Standard times for operations helps to know the

capacity in order to assign required machine hours to the facility.

2. Units in which loading and scheduling is to be expressed.

3. Effective capacity of the work center.

4. Demand pattern and extent of flexibility to be provided for rush orders.

5. Overlapping of operations.

6. Individual job schedules.

 Scheduling Manufacturing Operations
• Scheduling tasks are largely a function of the volume of system output.
• High-volume systems require approaches substantially different from those
required by job shops, and project scheduling requires still different approaches.

JAN FEB MAR APR MAY JUN

Build A

A Done
• High-volume
Build B
• Intermediate-volume
B Done
• Low-volume
Build C
• Service operations C Done
On time!
Build D

Ship
 High-volume systems

• High-volume systems are characterized by standardized equipment and activities

that provide identical or highly similar operations on customers or products as they
pass through the system.
• The goal is to obtain a smooth rate of flow of goods or customers through the
system in order to get a high utilization of labor and equipment.
• High-volume systems, where jobs follow the same sequence, are often referred to as
flow systems; scheduling in these systems is referred to as flow-shop scheduling,
although flow-shop scheduling also can be used in medium-volume systems.
• Examples of high-volume products include autos, smartphones, radios and
televisions, office supplies, toys, and appliances.
• A major aspect in the design of flow systems is line balancing, which concerns
allocating the required tasks to workstations so that they satisfy technical
(sequencing) constraints and are balanced with respect to equal work times among
stations.
• Highly balanced systems result in the maximum utilization of equipment and
personnel as well as the highest possible rate of output.
High-Volume Success Factors
High-volume systems usually require automated or specialized equipment for
processing and handling.

The following factors often determine the success of such a system:

• Process and product design

• Preventive maintenance
• Rapid repair when a breakdown occurs
• Optimal product mixes
• Minimization of quality problems
• Reliability and timing of supplies
Intermediate-Volume Systems

• Intermediate-volume system outputs fall between the standardized type of output

of the high volume systems and the made-to-order output of job shops.
• Intermediate-volume systems typically produce standard outputs.
• The products may be for stock rather than for special order.
• Volume of output is not large enough to justify continuous production. Instead, it is
more economical to process these items intermittently.
• Intermediate-volume work centers periodically shift from one job to another.
• In contrast to a job shop, the run (batch) sizes are relatively large.
Intermediate-Volume Systems
The three main issues faced in intermediate volume system scheduling are:

1. Run size: It refers to the production capacity of the manufacturing unit in a single
run. In intermediate volume system the run size need not be too large or too
small.
2. Sequencing: It is related to determination of both, the order in which the
processing of jobs is done at various work centers and the order in which
processing of jobs is done at individual workstations (within the work centers).
Operations managers look for a sequence that results in minimizing the costs of
the process and job completion time.
3. Timing: It refers to the time required to meet the order. It is usually low in the
case of intermediate volume systems.
Intermediate-Volume Systems
• Sometimes, the issue of run size can be determined by using economic
run size model of inventory management. The run size that would
minimize setup and inventory costs is
• Economic run size:

2DS p
Q0 
H p u
p – production rate
u – usage rate

Q = Order quantity in units

H = Holding (carrying) cost per unit per year
D = Demand, usually in units per year
S = Ordering cost per order or setup cost
• Another approach frequently used is to base production on a master schedule
developed from customer orders and forecasts of demand.
• Companies engaged in assembly operations would then use an MRP approach
to determine the quantity and projected timing of jobs for components.
• The manager would then compare projected requirements with projected
capacity and develop a feasible schedule from that information.
SCHEDULING IN LOW-VOLUME SYSTEMS

• Products are made to order, and orders usually differ considerably in

terms of processing requirements, materials needed, processing time,
and processing sequence and setups.

• Because of these circumstances, job-shop scheduling is usually fairly

complex.

• This is compounded by the impossibility of establishing firm schedules

prior to receiving the actual job orders.

• Two basic issues of Job-shop scheduling:

o Loading. How to distribute the workload among work centers?

o Sequencing. what job processing sequence to use?

 Loading
• A load means the quantity of work, and allocating the quantity of work to the
processes necessary to manufacture each item is called loading.
• Loading refers to the assignment of jobs to processing (work) centers. Loading
decisions involve assigning specific jobs to work centers and to various machines
in the work centers.
• In cases where a job can be processed only by a specific center, loading presents
little difficulty.
• However, problems arise when two or more jobs are to be processed and there
are a number of work centers capable of performing the required work. Different
facilities take different time to complete the job, and facilities have different
production capacity.
• In such cases, the operations manager needs some way of assigning jobs to the
centers.
• Managers often seek an arrangement that will minimize processing and setup
costs, minimize idle time among work centers, or minimize job completion time,
depending on the situation.
 Approaches of loading:
Infinite loading
• Infinite loading assigns jobs to work
centers without considering the
capacity of the work center.
• This can lead to overloads in some
time periods and underloads in
others.
• The priority sequencing rules use
infinite loading.

• One possible result of infinite loading is the formation of queues in some (or all)
work centers. That requires a second step to correct the imbalance.

• Among the possible responses are shifting work to other periods or other centers,
working overtime, or contracting out a portion of the work.
Finite loading
• Finite loading projects actual job starting and stopping times at each work center,
taking into account the capacities of each work center and the processing times of
jobs, so that capacity is not exceeded.

• One output of finite loading is a detailed projection of hours each work center will
operate.

• Schedules based on finite loading may have to be updated often, perhaps daily, due to
processing delays at work centers and the addition of new jobs or cancellation of
current jobs.

• Finite loading may reflect a fixed upper limit on capacity. For example, a manufacturer
might have one specialized machine that it operates around the clock. Thus, it is
operated at the upper limit of its capacity, so finite loading would be called for.
Shop Loading Methods

• Loading charts
• Index Method
• Assignment problem (Hungarian method )
Gantt Charts.

Visual aids called Gantt charts are used for a variety of purposes related to loading
and scheduling.
They derive their name from Henry Gantt, who pioneered the use of charts for
industrial scheduling in the early 1900s.
Gantt charts can be used in a number of different ways,
Figure shows scheduling classrooms for a university
• The purpose of Gantt charts is to organize and visually display the actual or intended
use of resources in a time framework.

• In most cases, a time scale is represented horizontally, and resources to be

scheduled are listed vertically. The use and idle times of resources are reflected in
the chart.

• Managers may use the charts for trial-and-error schedule development to get an
idea of what different arrangements would involve.

• There are a number of different types of Gantt charts.

• Two of the most commonly used are the load chart and the schedule chart.
A load chart depicts the loading and idle times for a group of machines or a list of
departments.

Figure illustrates a typical load chart.

This chart indicates that work center 3 is completely loaded for the entire week,
center 4 will be available from Tuesday to Friday, and the other two centers have idle
time scattered throughout the week.
• A manager often uses a schedule chart to monitor the progress of jobs.
• The vertical axis on this type of Gantt chart shows the orders or jobs in progress, and
the horizontal axis shows time.
• The chart indicates which jobs are on schedule and which are behind or ahead.
• A typical schedule chart is illustrated in Figure.
• The chart indicates that approval and the ordering of trees and shrubs was on
schedule. The site preparation was a bit behind schedule.
• The trees were received earlier than expected, and planting is ahead of schedule.
• However, the shrubs have not yet been received.
Index Method

• It is a heuristic method of loading.

• Time is assumed as criterion.

• Indices are calculated for different processing time (same job done in
different work centers).

• Processing time of different machines are divided by the lowest processing

time.

• The lowest index jobs are then assigned to the work centers, keeping in view
the limitations of the capacities of the centers.

• The next lowest job are then assigned to the work centers (without
exceeding capacity constraints).
 work centre
Job 1 2 3 4
Days Days Days Days
A 10 9 8 12
B 3 4 5 2
C 25 20 14 16
D 7 9 10 9
E 18 14 16 25
No of days
avilable 20 20 20 20
 work centre
Job 1 2 3 4
Days Index Days Index Days Index Days Index
A 10 1.25 9 1.13 8 1.00 12 1.50
B 3 4 5 2
C 25 20 14 16
D 7 9 10 9
E 18 14 16 25
No of days
avilable 20 20 20 20
Days
assigned
 work centre
Job 1 2 3 4
Days Index Days Index Days Index Days Index
A 10 1.25 9 1.13 8 1.00 12 1.50
B 3 1.50 4 2.00 5 2.50 2 1.00
C 25 1.79 20 1.43 14 1.00 16 1.14
D 7 1.00 9 1.29 10 1.43 9 1.29
E 18 1.29 14 1.00 16 1.14 25 1.79
No of days
avilable 20 20 20 20
Days
assigned
 work centre
Job 1 2 3 4
Days Index Days Index Days Index Days Index
A 10 1.25 9 1.13 8 1.00 12 1.50
B 3 1.50 4 2.00 5 2.50 2 1.00
C 25 1.79 20 1.43 14 1.00 16 1.14
D 7 1.00 9 1.29 10 1.43 9 1.29
E 18 1.29 14 1.00 16 1.14 25 1.79
No of days
avilable 20 20 20 20
Days
assigned 7 14 8 16
 Assignment Method
• The assignment method involves assigning tasks or jobs to resources.

• Examples include assigning jobs to machines, contracts to bidders, people to

projects, etc.

• The idea is to obtain an optimum matching of tasks and resources. Commonly used
criteria include costs, profits, efficiency, and performance

• The objective is most often to minimize total costs or time required to perform the
tasks at hand.

• Only one job (or worker) is assigned to one machine (or project).

• If there are to be n matches, there are n! different possibilities.

• One approach is to investigate each match and select the one with the lowest cost.
However, if there are 12 jobs, there would be 479 million different matches!

• A much simpler approach is to use a procedure called the Hungarian method to

identify the lowest-cost solution.
 Hungarian method

• Each job, must be assigned to only one worker.

• It is also assumed that every worker is capable of handling every job.
• The costs or values associated with each assignment combination are known and
fixed (i.e., not subject to variation).
• The number of rows and columns must be the same.
• Each assignment problem uses a table. The numbers in the table will be the costs or
times associated with each particular assignment.
• Build a table of costs or time associated with particular assignments

TYPESETTER
JOB A B C
R-34 $11 $14 $ 6
S-66 $ 8 $10 $11
T-50 $ 9 $12 $ 7
 Assignment Method (Hungarian method)
1. Subtract the smallest number in each row from every number in the row. This is
called a row reduction. Enter the results in a new table.
2. Subtract the smallest number in each column of the new table from every number.
3. Test whether an optimum assignment can be made. You do this by determining the
minimum number of lines (horizontal or vertical) needed to cross out (cover) all
zeros. If the number of lines equals the number of rows, an optimum assignment is
possible. In that case, go to step 6. Otherwise go on to step 4.
4. If the number of lines is less than the number of rows, modify the table in this way:
a) Subtract the smallest uncovered number from every uncovered number in the
table.
b) Add the smallest uncovered number to the numbers at intersections of cross-
out lines.
c) Numbers crossed out but not at intersections of cross-out lines carry over to the
next table.
5. Repeat steps 3 and 4 until an optimal table is obtained.
6. Make the assignments. Begin with rows or columns with only one zero. Match items
that have zeros, using only one match for each row and each column. Eliminate
both the row and the column after the match.
 Assignment Example
Typesetter
A B C
Job
R-34 $11 $14 $ 6
S-66 $ 8 $10 $11
T-50 $ 9 $12 $ 7

Step 1a - Rows Step 1b - Columns

Typesetter Typesetter
A B C A B C
Job Job
R-34 $ 5 $ 8 $ 0 R-34 $ 5 $ 6 $ 0
S-66 $ 0 $ 2 $ 3 S-66 $ 0 $ 0 $ 3
T-50 $ 2 $ 5 $ 0 T-50 $ 2 $ 3 $ 0
 Assignment Example
The smallest uncovered number is 2
Step 2 - Lines so this is subtracted from all other
uncovered numbers and added to
Typesetter numbers at the intersection of lines
A B C
Job
R-34 $ 5 $ 6 $ 0
S-66 $ 0 $ 0 $ 3
T-50 $ 2 $ 3 $ 0 Step 3 - Subtraction

Typesetter
Smallest uncovered number A B C
Because only two lines are Job
needed to cover all the zeros, the R-34 $ 3 $ 4 $ 0
solution is not optimal
S-66 $ 0 $ 0 $ 5
T-50 $ 0 $ 1 $ 0
 Assignment Example
Step 2 - Lines Start by assigning R-34 to worker C as
this is the only possible assignment for
worker C.
Typesetter
A B C Job T-50 must go to
Job worker A as worker C is already
assigned. This leaves S-66 for worker
R-34 $ 3 $ 4 $ 0 B.
S-66 $ 0 $ 0 $ 5
T-50 $ 0 $ 1 $ 0 Step 4 - Assignments

Typesetter
Because three lines are needed,
the solution is optimal and A B C
assignments can be made Job
R-34 $ 3 $ 4 $ 0
S-66 $ 0 $ 0 $ 5
T-50 $ 0 $ 1 $ 0
 Assignment Example

Typesetter Typesetter
A B C A B C
Job Job
R-34 $11 $14 $ 6 R-34 $ 3 $ 4 $ 0
S-66 $ 8 $10 $11 S-66 $ 0 $ 0 $ 5
T-50 $ 9 $12 $ 7 T-50 $ 0 $ 1 $ 0

From the original cost table

Minimum cost = $6 + $10 + $9 = $25
TABLE 16.1
A typical assignment problem showing job times for each job/ worker combination
Hungarian Method Example

Step 1: Select the smallest value in each row.

Subtract this value from each value in that row

Step 2: Do the same for the columns that do not

have any zero value.
Hungarian Method Example

If not finished, continue

with other columns.
Hungarian Method Example
Step 3: Assignments are made at zero values.
• Therefore, we assign job 1 to machine 1; job 2 to
machine 3, and job 3 to machine 2.
• Total cost is 5+12+13 = 30.
• It is not always possible to obtain a feasible
assignment as in here.
• Hungarian Method Maximization Problem
• Some assignment problems entail maximizing profit, effectiveness, or payoff of an
assignment of people to tasks or of jobs to machines.
• An equivalent minimization problem can be obtained by converting every number in
the table to an opportunity loss.
• To convert a maximizing problem to an equivalent minimization problem, we create a
minimizing table by subtracting every number in the original payoff table from the
largest single number in that table.
• We then proceed to step 1 of the four-step assignment method.
• Minimizing the opportunity loss produces the same assignment solution as the
original maximization problem.