Che materia stai cercando?



Cells are formed after defining the minimum similarity coefficients amongst the couples of machines

(machine groups). Of course I can define a threshold under which I decide to not accept similarities (e.g.:

0.75, so I’ve found three groups of machines).

But which one is the best method? Under a computational perspective this two methods are the same, ROC

repeats the same procedure, so the results will always be the same, similarity coefficient is strictly related to

our choices (because of the threshold I fix), so ROC can be considered as the most robust.

Virtual cellular manufacturing

Virtual Manufacturing Cells (VMC) are an alternative to traditional manufacturing cells, with the purpose to

be more responsive with production mix variability.

In Virtual Cellular Manufacturing the machines that belong to a cell are not physically located together, but

are identified as a group only by the Production Planning and Control system. Of course groups are formed

on the basis of forecasts and may change from period to period, because virtual cells can achieve the benefits

of repetitive processes without the issues related to a layout rearrangement, so I can manage product mix

variability easily (this won’t avoid problems regarding alternative routings because we want to maintain

separated routing, like in a traditional cell!). Other things may change: of course material handling is not so

efficient as in the traditional situation, and I have no more team working.


Each transfer line consists of a series of machines, integrated by a rigid device for handling parts and a

common control system, where a single type of product (or a limited number of product types within the

same family) flows, resulting in a routing through the machines. Items are moved individually or in small lots,

since there is no need to carry handling lots to optimize the transport system (as opposed to JS and MC). The

movement of item can take place in a synchronous manner at regular intervals, or asynchronously in case

the line is provided with buffers between a station and the other. Machines are generally arranged in line,

but an alternative might be the circle layout. This configuration is adopted for production of high precision.

In this case, the number of station is very low due to the boundaries of the circle’s dimension. Moreover, it

might be extremely hard to have inter-operational buffers or to add a station to increase the system’s

capacity. One of the most important step in designing a transfer system concerns the counterbalance, which

is the allocation of operation to the different stations in the system. The cycle time cannot exceed the

processing time of the slowest station (bottleneck). To reduce the time cycle it is important to balance

operation time and try to make it equal in each station in order to increase the production potentiality. In a

multiproduct transfer the production takes place in lots since the system cannot manage a simultaneous

production of different items. Each lot’s change requires stopping the production and making a setup. The

stopping time depends on machines’ flexibility and the number of similarities between products. A product

type is visiting the machines according to the technological sequence required by the product type. There’s

a rigid interconnection between the machines. It is an integrated system, in fact we have a material handling

system integrated in every machine, and the material handling is parallel to the parts flows. Automation is

really important in this system also because the aim of this system is to achieve a great productivity.

This is the case of very small products (e.g. electronic components).

In the previous systems we talked about intermitted production management: every time a machine is visited

by different lots of different products; here I prepare the line for the production of a specific product (e.g.

for two weeks I have to manufacture the same product), and this production may last for weeks without

stops. We talk of “production campaign” in this case.

Transfer lines can be considered:

intermittent asynchronous transfer lines: I am working with machines that may have different speeds

- or may require different production time, so I have to provide a buffer between them. Transport

system activates when some products have ended the operation on one machine, but then these

work in progress may have to wait,

intermittent synchronous transfer lines: the material handling synchronizes movements between

- one station and the following one because every Δt material handling system moves pieces from a

station to following one. When pieces are moved from station1 to station2, material handling moves

also pieces from station3 to station4, so I have a simultaneous movement.

It may happen to have not used machines because we have more machines than required due to a “multi-

model production” (e.g. I may have a line dedicated to two products –that of course are similar- A and B.

when I’m producing A, some machines may not be required because A doesn’t require to do that specific


Transfer line can be:

multi model: we have different products entering the system (of course when I change the product

- to manufacture I have to do a set up!),

mixed model: we have different products entering the system but set up is never required in this

- case, because the system can proceed the different products indifferently,

single model: a dedicated transfer line.


In general terms we can find general features that characterize this system:

► The production flow is serial, products must visit machines in the same sequence, at most skipping

some machines

► The transfer line is usually a highly automated manufacturing system (related to the rotary table we

may have problems regarding dimensions),

► The demand of products should be high and stable so I utilize all the machines along the transfer line

for some years and I’ll be able to repay the investments made. Of course high automation is related

to high fixed cost (also for installation)

► The line must be balanced

Line balancing.

When we allocate operations, we have to decide which station has to do a particular task. Of course, one

station may do more than one task.

The first case is not balanced because I have different working times. In the first case there’s a bottle neck

constituted by the first station, that has a higher working time compared to the others.

The second and the third cases are perfectly balanced, because every station has the same working time!

The difference between these two cases comes from the different number of stations: less stations lead to

less costs of installation and less space occupied!

Production capacity: number of work pieces that can be produced by transfer line in a given time unit

(generally an hour).

Cycle time: max(working time) + time for transportation (sometimes negligible).

Production capacity = time unit / cycle time of course I have to use homogeneous measures (e.g.: 60[min/h]

/ 4[min/piece] = 15[pieces/h]).

Ex: Total time for the operations = 12’ coming from

t = 4’, t = 1’, t = 1’, t = 1’, t = 2’, t = 3’


of course I’m able to balance a line only if I can distribute tasks on different stations in the right way

(maintaining the right sequence!)!

In this case I can’t have a perfect balanced line: A B,C,D E,F

4’ 3’ 5’


Simple production management: transfer line is a series of machine, by definition, which are visiting according

to a specified sequence (depending on the technological requirements of a product), so we don’t have any

alternative routings, and the management it’s simple because it doesn’t require any decision making. When

we have a product we have only to decide the length of the production campaign. According to the Magee

Boodman’s method we can identify the optimum number of campaigns (respect to costs of setup and

inventory primarly) that have to be produced in the year, so we can calculate the best batches size as BS =


D /N (annual demand of j / optimum number). Of course if we have more than one product to manufacture

j opt

(multi-model case) we have also to decide the best batches sequence (basing on the setup time, because

some setup times can depend also on the sequence):

Production management Single-model Multi-model

Batch sizing X X

Batch sequencing X

High machine utilization: the line is supposed to work every time there’s a production campaign, and the

demand of the product is high and stable. This stability in the production mix makes the problem of balancing


Low space occupied: this is a compact system, so the space occupation comes from the stations and the

material handling systems installed (if I have a synchronous transfer line, in other case I have also to provide

a space for the buffer).

These strengths lead us to have:

Low WIP,

Low lead-time (also considering variability) because of the absence of queues in the synchronous, but I have

also low LT in the asynchronous transfer line.

Low need for workforce: there are few tasks that are auxiliary, because basically this is an automatic system,

Qualitative characteristics of products are stable: there is only one technological routing, and I have quick


Weaknesses: 

Low flexibility: mix flexibility we are basing the sequences of the operations (and of course also the layout

and the order in which machines are installed) according to the specific technological routing required by the

products. Each line can manufacture only few products (in the same family).

Product flexibility is low because I don’t have alternative routings, so, if I want to produce pre-series, I have

to stop the normal production.

Expansion flexibility (deals with the introduction of new capacity or new technological capabilities in the

system) low due to space problems.

Variation in volumes (volume flexibility) can be a concern both if the volumes are increasing or decreasing,

High investment needed: being an automated system we have a lot of fix costs to bear,

Long time required to start new productions: change from a product type for the one the line was dedicated

to another one, and this means that I have also to change the technological routing,

High risk of obsolescence: the facility lifetime is strictly bound with the product lifetime, so if the product

becomes obsolete, also the line will be obsolete (not the machine, because we can use them for other


Significant impact of failures: if only one machine (or other devices) has broken down, the entire line will

have to stop until that machine is totally repaired. Buffers can protect us for a while, or I can think of installing

more parallel machines (e.g.: two machines are needed but I decide to install three machines, so, if one of

them has failed, I have another machine to manufacture my production), but, of course, this will arise more


Rough design of a synchronous transfer line (single-model):

1. Define the technological routing and operations of the product

2. Identify all the machine types that are needed and balance the line. I have to make a distinction

between: Specialized dedicated machines General purpose machines

#operations Low High

Speed High Low

performance These machines are useful to fulfill a These machines are useful to fulfill a

strategy focused on efficiency strategy focused on flexibility

3. Calculate the theoretical production capacity:

TPC= 3600 / CT [p/h]


CT = cycle time of the line [seconds/piece]

Of course if we rebalance the line we may have a different TPC because I may have a different cycle


4. Calculate the actual production capacity

APC = TPC * A * (1 – SR) [p/h]


A = line availability (0 < A ≤ 1). Availability can be defined as a percentage of time coming from

this calculus: A = uptime / (plant uptime + downtime)

SR = scrap rate (0 < SR ≤ 1)

We don’t have HC because these lines are highly automated.

5. Compare the actual production capacity and the demand. If necessary, modify the line as it follows:

a. go back to step 2 rebalancing the line,

b. add new machines,

c. increase the availability,

d. put in parallel more machines so I can create different routings on which I can produce

different parts. In this case I have to split the time of production of one machine type on the

different products (type) I can produce in parallel on this machine! (e.g.: if two products are

produced in parallel on a machine type that consumes 7’, I have a cycle time of 7’/2


Rough design of a synchronous transfer line (multi-model):


Pieces are manufactured in batches (batch A, batch B, batch C and so on); changing production from

- one batch to another requires a setup,

Setup times do not depend on the production (batch) sequence or we assume that we’ve already

- found the optimal sequence.

1. Identify the production mix

2. Define the technological routing and operations of the products (in the production mix)

3. Identify all the machine types that are needed and balance the line (for each product)

4. Calculate the cycle time for each product j

CT = max {TL } [seconds/piece]

j h jh


TL = unit working time of product j at workstation h [seconds/piece]


5. Calculate the whole time to produce a batch of product j

T = CT * H + CT * (Q -1)+ STT [seconds/batch]

j j j j j


H = number of workstations in the line

Qj = batch quantity of product j [pieces/batch]

STT = setup time related to a batch of product j [seconds/batch]



6. Calculate the time needed for a set of batches (within a production campaign)


T = ∑ Tj [seconds/batches]


N = number of batches (one batch per product j in the campaign)

7. Calculate the average theoretical production capacity


TPC = 3600 * ∑ Qj / T [p/h]

8. Calculate the actual production capacity

APC = TPC * A * (1 – SR) [p/h]


A = line availability (0 < A ≤ 1)

SR = scrap rate (0 < SR ≤ 1)

9. Compare the actual production capacity and the demand. If necessary, modify the line and go back

to step 3 and intervene in one of the following:

 Reduce scrap ratio

 Reduce breakdowns’ frequency

 Decrease the time required to restore the functioning of the station after a fault

 Modify the configuration of the transfer, by choosing different machines and/or increasing

the number of machines in series and/or adding machines in parallel in some stations.

Obviously, it need to balance workload again.


We analyze this problem under the workers’ perspective.

In manufacturing systems, a worker is usually required to attend two or more machines (similar or different

machine types) running concurrently, being the system configured as a job shop or others. Machine

interference occurs when the worker is requested a task while being already busy in another task, that can

be expected (regular) or not (i.e. attending another machine, unloading other pieces from another machines,

do some maintenance, and so on. Ex: we may have a material out of the tolerance limits, and it blocks the

machine, so the operator has to remove it!)

The measure of this problem is the interference time (i.e. the time the other machines have to wait until the

worker has completed his current task).


 How many operators do we need to attend machines? We need to decide the assignment of workers

on machines/workstations/…!

 Where are the bottlenecks (the resources that are limiting capacity): machines or operators? Waiting

means that we’re losing production capacity: if workers are doing other tasks is the machine that is

waiting, but we consider the machines as a bottleneck, due to their high cost, so, in this case, is the

operator that is waiting for the machine. In conclusion we have to find a good balance between

workers and machines in order to limit the interference time.

To solve the problems above we have to:

 analyze machines’ and workers’ operating cycles;

 evaluate the impact of the interference times on the machines’ capacity (i.e. the required capacity

to meet the demand).

When studying the machine interference, it is worth devising the utilization of both workers and machines

during their operating cycles.

This can be obtained by adopting simple graphical methods, e.g. a Gantt chart (that is showing us, using bars

and lines, the scheduling of the machines. A bar’s length is representative of the real time consumed by an


If I suppose that the time when the worker is required (a single red bar) is 2, and the time when the worker

is not required (a single yellow box) is 10, I have a window of 10 in which the operator can working on other

machines. In conclusion, a single operator, according to this example, can work on 12/2=6 machines! In this

example the utilization rate of the worker is 50%.

Of course there could be differences between a machine and another! 2 may be considered as an average.

In this case, the worker is required to attend the machine in order to load/unload work-pieces and to fix

minor problems.

The total interference time is the sum of all the interference times on the three machines.

The utilization rate of the worker, in this case, is high (66% = (red+blue lines) / total production time).

1.33 is the average time loss per machine (sum of green lines / number of machines).

The Gantt method is really useful for a qualitative reasoning (it provides a rough analysis of the current

scenario), but an analytical method is required in order to better solve the problem!

Performance evaluation – state space method

It’s an approximated method, and it can be easily performed on Excel.

It is based on the following general assumptions:

 the state of the system depends on the state reached by its machines;

o the state of the system as function of the state of its machines, because a machine issues a

service request, the workers deliver the service (because they’re able to perform that task);

 each machine is working independently of the others;

o independent events/states for each machine (“a worker is required or not required to attend

the machine”). In reality there are some dependences because the scheduling is done looking

at all the machines;

the method can be used to provide a rough estimate of the expected interference time (we have to highlight

“expected” because we have to consider that we are not in a deterministic environment, but we’re dealing

with probabilities – stochastic environment) (it is focused on the operators).

The system is modeled through a state space table, where:

each machine is assigned its own state indicator;

- the system is assigned its own state indicator.


I can calculate the probability of having only k service requests coming from n machines using the formula


n= number of machines

k= service requests coming from the machines

machine’s states system’s states


the total amount of cases can be evaluated using: #possible states .

Of course I may have interferences only when more than one machine is working.

In other words, I have to sum the

rows and multiply the columns

We apply this statistic method to our table considering for all the cases the probability that that specific case

may happen.


1. Model the state space table of the system (s )


2. Model the correspondent table of probabilities (p )


3. Evaluate the probability of each state of the system

Worst case

The second request stands between a and b (where b is the maximum length). The second request will

happen within the interval with the same probability (so it’s uniform) so I have to do (a+b)/2 having no other


4. Evaluate the expected interference time due to each state



Yi = interference time occurring at the state of the system i

5. Calculate the expected interference time due to all states

6. Calculate the production capacity of the system

7. Calculate the utilization rate of workers and machines

it is difficult to evaluate the impact of the interference times on the machines’ capacity!


In manufacturing systems, the occurrence of failures leads to performance losses at each machine

and, subsequently, at system level; the impact of failures can be different depending on the

configuration of the system.

The system availability can be evaluated by analyzing the configuration of the system, based on the

availability of each single machine (e.g. if we’re considering a rotary table, a failure in one of the machines

leads to a stop in the entire system. In a flexible system if one of the machines stops, the pieces will constantly

flow in the system).

The impact of failures at a system level depends on:

routing flexibility (depends on the system configuration),

- buffer capacity (of course is limited, so we can absorb this kind of problems only within a defined

- range – it does not depend on the system configuration but on our choices),

machine capacity (I can decide to buy more machines than the required one. It’s my choice, it doesn’t

- depend on the system configuration). t

failure repairing time

machine is not functioning, so it is not available for production (downtime).


- How many machines do we need to meet demand?

- What happens if a machine breaks down?

- What is the impact of a failure on the production capacity of the system?


- to analyze the function carried out by the machines for the production capacity of the whole


- to evaluate the impact of unavailability of the machines on the availability/unavailability of

the manufacturing system, thus on the whole production capacity (in order to meet the


When studying the impact of a failure on the production capacity, it is worth devising the

configuration of the system in order to analyze how much the production flow is affected.

Ex: M2, M3 and M4 are put in parallel because they’re

We have 6 machines along a line with some buffer between them. second one (we’re using

used to manufacture different products. The station with the maximum working time is the

parallelization here because if we had not do this we would probably have a bottleneck!).

In this case we’re working at a reduced rate, but the production capacity is not zero!

In this second case all the products have to pass through the first station! Now I have to consider the buffers: M1 has

stopped, but we have some material (in the buffers) that can flow through the line.

If the buffer capacity is low, we can neglect it (and the production capacity will be reduced to zero immediately or after

some time – it depends on when the buffer stops to provide materials), but if we have enough buffer size we’re repairing

M1 and there are still materials in the buffer (we’re not losing capacity!). immediately

total reduction of


capacity after some time

buffer capacity immediately

partial reduction

of capacity after some time

When we are in a job shop things are different because we have high routing flexibility.

State space method.

Based on the following general assumptions:

- the state of the system depends on the state reached by its machines;

the state of the system as function of the state of its machines;

- each machine is working / degrading independently of the others;

independent events/states for each machine (“a machine is failing independently of the


the method can be used to provide a rough estimate of the expected system availability &

production capacity. n= number of machines in the system

k= number of machines that have been failed

writing this conclusions we have to consider the system configuration

and the buffer we’re dealing with (this is a generic case).

And the procedure follows the same steps for the interference time.

We have to highlight that in this case we are interested in calculating the time losses due to machines’

failures, and we don’t base our probabilities on the workers’ requested time.

Yi depends on the system configuration. We have to find the bottleneck in order to determine it.

Ex: if we have M2, M3 and M4 parallelized, and the working time assigned to them is 90, the production

capacity of the system is 1/90 and each machine has 3/90.

We have to consider that uptime and downtime are repeated in a infinite time. So we can calculate the

probability of a failure as: average downtime divided by the average uptime plus the average downtime and

the opposite for the probability of no failures.

So the availability is the probability that we are available in uptime p(s =1) with s parameter of Bernoulli.

j j

One other difference between the state space method of the interference time and this one is that the tasks

requested to the workers require a short time to be performed, in this case the downtime can absorb long

time (hours!) instead and have to be estimated from data collected in the past.

The availability depends on many factors, such as:

- technological characteristics of product types (as materials to be manufactured on given

machine types),

- number of machines and their state (dependent on their characteristics as reliability and


ability to schedule preventive maintenance It is difficult to evaluate the impact of unavailability of

the machines on the availability/unavailability, thus the production capacity (i.e. to meet the demand),

of the manufacturing system.



A process plant is formed by a series of production equipment used to make non-reversible

chemical-physical transformation of materials through a fixed technological routing. We start from

the technological requirements (so the technological parameters are important) of the products to

build up plants. The structure of the plant usually reproduce exactly this sequence and it is fixed.

We have a flow of materials constrained to a single routing or that can have some (few) options.

Plants are design to operate:

- A continuous flow production process: where there is no waiting time along the process. As a

consequence, there a not stock-holding points within the process (only stocks for raw materials and

finished products).

- Batch production process, instead, is characterized by the presence of intermediate buffers

Usually the raw materials (inputs of our system) come from nature or from reverse logistic (e.g.:

steel that was a piece of junk or a scrap and now has to be re manufactured).

The process industry is producing some raw materials that will be an input for the manufacturing

industry (usually we do not come out with the final product).

To summarize,

Plants are designed to operate:

A continuous flow production process: the transformation comes from a continuous

- movement and transformation of materials. In this case we don’t have storages along the

process (of course we have one for raw materials and final products); or

A batch production process: In this case, we have storage points and buffers (tanks, silos,

- etc.) because the parts have sometimes to stop.

This industry is typical related to the commodity production.

The production flow is serial (continuous transformation), analytical (continuous with different products)

or synthetic (discontinuous transformation).


Continuous sequence of process stages; a very common example is the transformation of vegetable

fibers into paper.


The continuous transformation with different products can be exemplified by the petroleum

industry. We have crude oil entering the refinery plant and we can come up with different final

products (of course we will also have scraps). Continuous sequence of process stages that share

some raw materials in their compositions and parts of the process


Cement industry starts with more than one material: limestone and marl, which are two typical raw

materials that we need to extract and process and then join together. Several raw materials that

come into one product.

In general,

Process plants are highly automated:

relevance of technological parameters of the production process (temperatures, pressures, …);


- significant investment in sensors, equipment control, etc.;

- control often automated with supervisory intervention: the control system is very important

since technological parameters have to respect some constraints. The variability of conditions

of the process is one of the main problems; so the systems of measurement and control are of

great importance. These systems allow responding in real time to perturbations, so as to

maintain as stable as possible the conditions of the process; so as to maintain on the one hand

the constancy of the quality level of the FP and on the other, the maximum efficiency of


The control logic can be summarized by the following scheme:

According to some logic present in the process model, we decide to act on the production process and the

process variables (e.g.: we decide to change the temperate we can have a decision to mix the production and

environmental temperature). All these actions are affecting the production process and are aimed to obtain

a stable production. Process control is important for this reason.

Process plants general features: because it’s already been decided when the plant was built. E.g.:

a. Simple production logistics

pipelines are integrated in the plant,

b. Simple production management (decisions only referred to sizing and sequences of the


c. High plant utilization and equipment efficiency is necessary in order to reach the economy

scales (we also want to split high fixed costs). We also want to avoid failures because

malfunctions could be dangerous due to the high temperatures and other working conditions.

We want to do few set ups in order to maintain the conditions stable,

d. Low need for workforce. The workforce is normally required for the control activities - they

don’t have to measure (we usually have sensors), but only to supervise, for maintenance and

maybe transportation (truck drivers as an instance),

e. Qualitative characteristics of products are stable (when process conditions are kept stable. We

have to control the production conditions also during the dynamics. In other words we have

to control the production conditions also when the conditions should have reached their

regime values, because they can vary)

f. Low flexibility. More in detail:

o mix flexibility: few product types (or only one product),

o expansion flexibility: the plant structure is fixed, so I would have to stop the plant (but I want

to reach scale economy!) and rearrange it,

o volume flexibility: in continuous productions we’re already producing 24/24 hours, but also

the volume in terms of physical structure can be a constraint.

g. High investment needed: very high for continuous production process plants and quite high for batch

process plants,

h. High risk of obsolescence: we build a plant in order to manufacture a product, so the life time of the

plant is strictly bounded to the product lifetime,

i. Significant impact of failures: in a line in which we have a continuous flow, a stop would terrible

because I would have to stop all the production. Of course in the case of batch production process I

would have buffers to absorb little failures,

j. Importance of variations in process conditions.

Rough design of a process plant (continuous flow).

1. Define the production flows according to the technological routing required for the product,

2. Identify all the production equipment types that are needed and the bottleneck,

3. Define the theoretical production capacity:

TPC [ton/hour] - or other similar units, i.e. [kg/hours],

1. Calculate the actual production capacity:

APC = TPC * A * (1 SR) [ton/hour]

where A ≤ 1)

A = line availability (0 <

SR = scrap rate (0 SR < 1) (varying according to the process conditions kept in the


2. Compare the actual production capacity and the demand. If necessary, modify the line and go

back to step 2. If we can’t meet the demand we have to make changes (i.d. we have to duplicate

plants, so we will have two plants with the same structure in this case energy costs are


Rough design of a process plant (batch).


- Production in batches (batch A, batch B, batch C and so on);

- Setup times are required and do not depend on the production (batch) sequence.

1. Identify the production mix,

2. Define the production flows according to the technological routing required for the products

(in the production mix),

3. Identify all the production equipment types that are needed,

4. Calculate yearly workload and number of hours available for each type of production

equipment i,

5. Calculate the number of production equipment of type i necessary to produce the production


6. Yearly workload NH for production equipment i:


In this case n is not high: we have few product types to manufacture!

Input can’t be expressed in min/piece, because the environment is different. So, as input, we

have production capacity = flow rate.

We’re not producing continuously like the case of continuous flow (24h/24, 7d/7), but now

we’re dealing with intermittent production, so we have also to consider set ups, that are really

relevant (in this case they can be also expressed in hours/setup, not in minutes/setup, as it was

for job shop case).

Availability is related to logistic.

HC is not relevant in this environment, so we’re not considering it in this formula,

7. Number of hours available for each type of production equipment i:

AH (s) = WH (s) * SE

i i


WH (s) =yearly working time available (depending on the number of shifts per day)


SE = scheduling efficiency (0 < SE ≤ 1),

8. Number of production equipment of type i necessary to produce the production mix:

Number of shifts is related to flexibility.

In continuous flow we don’t have to make this decision because we operate 24h/24, 7d/7, so

it’s like considering 3 shifts per day mandatorily.


The worker is the relevant resource.

Every assembly system has the characteristic to put together pieces that were previously


We may have different assembly systems:

Fixed position assembly:

The fixed position assembly system generally uses a table on which the pieces to be joint together

are put. The product that has to be assembled is not moving (single site) so materials, equipment

and tools are brought to the site. In this case we will target high flexibility and variety of products.

The repetitiveness is low because I’m doing so many different tasks on this product. The assembly

line can be easily compared to a transfer line and is focused on efficiency. On each station we

always do only a part of the assembly (always the same operations on different pieces of the same

product type), so the repetitiveness of the process is high. On an assembly line we have high

production volumes, so the cycle time is short. This solution is widespread in the manual assembly

of two kind of products:

- Parts with relevant weight and encumbrance, to be produced in low volumes in order to reduce the

inconvenience of transporting.

- Simple products, made of few components, to produce in medium volumes. Operations are

allocated to few operators, rather than investing in a line that obligates to subdivide the cycle

between different resources and stations, dedicated to the execution of limited number of


Shared characteristics: high dimension and weight. Handling efficiency is low. Moving the products

will lead us to have some problems and low efficiency, so moving the components would be better.

Another driver that will make us choose the fixed position assembly is the fragility of the product:

we don’t want to move fragile products because we don’t want to have scraps.

The third driver is related to the skills owned by the workers. In this case we have to consider that the

workers have to manage a wide range of competences. Of course they have to be trained, but the

ability to manage so different skills depend also on their attitude. High skilled workers also permit

us to have products of great quality.

We have to consider another driver: the low complexity of the products. If we have simple products

to be assembled we will also have few components, so having a lot of stations would be useless and

we will use a single assembly station.

How is the single site organized? we have assigned some space to the

worker. We also need space allocated to

the stocks of the components required.

Each position also requires some tools in

order to assemble parts and components

(e.g. screwdrivers).

Workplaces are organized according

to ergonomic principles, so the

worker can do his work comfortably

(comfortable actions) and with the

less fatigue possible so he will work

at his best and can reach high levels

of efficiency.

Everything need to be designed

according to our product, so also this

layout may change.


- High flexibility (for every dimension): we want to support a wide range of products so we will

have different products running at the same time (mix flexibility); we may also customize our

products or innovate (product flexibility),

because we don’t need specialized machines but only some tool. Of course

- Low investment,

we probably have to duplicate them on the different sites, but tools’ cost is usually low (unless

they’re specialized, so in this case probably we won’t duplicate it in different sites, but then

we would have interferences. We have a trade off!),

- Job enlargement, enrichment and rotation for the employee, the workers have to manage a

wide range of competences because they are required to do different tasks, but they are also

required to fix minor problems. Rotation is related to the fact that from time to time workers

are requested to do different portions (that are always very wide) of the assembly process.

- Rapid launch of new production, the system if flexible from the physical POV


- Potentials for intertwining of material flows, the product is fixed, and on different stations we

may have different products to be assembled, so we have to manage the components in input

well. This complexity is growing with the number of station and the range of products to be


- High WIP, remember that CT in this case is high (production is slow). When we finish the

assembly the product may stay there for some time. Of course we synchronize production

with logistics, but logistics are not continuously passing by; so in that space we will have

some finished products and some products with high cycle time,

- Large space requirement,

- Labor training might be difficult and time-consuming, especially when the assembly is

complex, because we’re paying their qualification; so the

- High cost for workforce advantages we have

from the workforce require some additional costs.

Rough design of a fixed position assembly.

Number of single sites /stations.

The number of stations Nj for the product j can be calculated as follows:

N = PC * T

j j j

where: We’re considering the yearly

PC = requested production capacity for product j [pieces/h].

j demand of the product j but we also consider some losses (HC and SR -in reality, more

than the scrap rate we should talk about re-work rate)

T = time required in order to complete the assembly process on a piece of product j [h/piece]


Assembly line

Each assembly line consists of a series of stations where the product is progressively assembled.

Here we don’t have problems regarding the tools duplication. The movement of the pieces to be

assembled is made through a rigid system, so the sequence amongst station is always the same. Each

station is assigned to a worker (or more than one) that performs operations on a repetitive basis.

Regarding the personnel we can think of Adam Smith and the division of labor: we reduce the

assembly process in small tasks and each of them (or few tasks) is assigned to a worker that has to

repeat it over and over in order to reach efficiency (because the worker learns it very fast).

Repetitiveness is really high and we can come up to alienation. In this case a worker only knows his

own task, he doesn’t know anything about what happens before and after his station.


- Rationalization of material flows, the BOM permits us to know the exact number of

components (for each level) required to come out with the final product. Using the bom we

can also divide the operations that have to be done on each station according to the different

levels we have, in order to have a rationalized material flow (i.e. the first station puts together

the parts of the second level, the second station puts together the parts of the first level,

optimizing the flow),

- Low WIP, CT is short and we have a continuous movement, so parts and products are always

moved from a station to the following one,

- Limited space requirement, if I do a lot of setups (related to material handling movements)

we will have low space dedicated to stocks,

- Labor training might be easy, elementary operations

- Low cost for workforce. Repetitive operations, so skills are not required.


- Low flexibility, rigid by definition, as it involves dedicating a subsystem to a family of similar

products, for which the line has been developed and designed; varying product family

components or the quantity may not work.

- Long time required to start new productions, reconfiguring a line is not simple and requires

some time because we have to arrange and balance the line again. Of course if the product

differs a lot from the previous ones (especially in terms of bom), we would also have to change

and re-arrange equipments and components,

- Repetitive work, few operations lasting few minutes, decreasing performance and satisfaction

- Line balancing might be difficult depending on the complexity of the products.

Depending on the material handling system and how it works, we may have:

- paced lines (intermittent synchronous assemble line):

Material handling system moves every some fixed time. The operator has a time windows to

conclude its operations (no buffers between stations) and all products are moved simultaneously

from one station to the next. We have 2 different situations:

o Machine paced lines. The movement of pieces is paced by a timer and given by the cycle time

of the line: every some time the conveyor moves.

Strength CT and PC are perfectly controlled

The big difference compared to transfer lines is that here we’re dealing with workers, so we

can face some variability in the working time.

Weakness probability of no completion (at the line stations) and problems of unfinished

pieces. No guarantees that the operator has completed its operations on the piece.

How to solve the problem?

- increasing the cycle time (but reducing the production capacity)

- increase the number of stations (but increasing the costs of installation, the space occupied,

number of workers…)

o Operator paced lines. The movement of pieces is paced by the operators: the material

handling system moves only after all operators have given their approval.

Strength No problem of unfinished pieces

Weaknesses CT is variable and it is determined by the slowest operator. Consequent

difficulty in controlling the production capacity.

In this case, it is important to lever on an individual motivation through incentives and

reward, in order to decrease the possibility of delays.

- un-paced lines (intermittent asynchronous assemble line): 


1.No problem of unfinished


2.CT can be exceeded, but

only occasionally. This won’t

cause problems because we

have buffers, but if they are

not well dimensioned we can

have starvation (the buffer is


empty and the 2 machines

stops) or we reach their

maximum capacity so we


have blockages (the 1

machine can work no more).

Weakness CT and PC are not perfectly controlled.

- continuous flow line: the material handling system moves at a constant speed and operators

follow the piece on which they have to perform the assembly tasks (or they move with it on a

platform). Of course we can choose different configuration of the line (floor, overhead

or also conveyor belt) in dependence of our product’s characteristics.


The products are fixed on the conveyor at a given distance D, and the conveyor is moving at

a given speed. Low speed enables the worker to work on the single unit while “following” it

in a delimited space. In this case cycle time comes from: CT= D/S with D distance and S

speed the distance is fixed, so we have to determine the right speed. Of course we have to

consider two possible cases:

 

low speed of the conveyor is related to low distance between pieces so we

have workers working really close one to each other and we may have

problems of physical interference!

 

high speed of the conveyor is related to high distance between pieces so the

length of the line will be greater.

The length of the conveyor depends on the distance between a pieces and the following one.

If we have L = D we are in the case of intermittent assembly line.

If we have L > D we can also write: that means that we have more time to do

and conclude the operations than the cycle time of the line. Reasoning at the extreme, if we

have L >> D all the work pieces will be completed (we have reduced the probability of

complexion), but this also imply that the workstation (considered as the space in which the

worker can do his operations) is very long, so we have high space occupied for that particular

operation and high WIP because we will have a piece on the line and another one (at least) in

the extra space of the line that can be considered as a buffer.


Case 1: operators can’t stop the line.

Strength CT and PC are perfectly controlled (because we know that CT=D/S),

Weakness Probability of no completion (at the line stations) and problems of

unfinished pieces.

Case 2: operators can stop the line

Strength No problem of unfinished pieces,

Weakness CT and PC are not perfectly controlled (of course if the worker stops the

line for some bugs or other problems the CT will be longer, but then the line will

continue working at its nominal conditions).

Design of an assembly line.

We want to define the number of stations and the allocations of operations to each worker. The first

step is as usual the identification of product mix, in terms of quantity, and types of products to be

realized. The second step regards the precedence constraints between operations and the balancing


1. Definition of the balancing constraints;

2. Evaluation of the time of each assembly operation;

3. Calculation of the cycle time;

4. Assembly line balancing (ALB). We have two possible approaches:

a. I type CT is constant so also the production capacity is fixed ,

b. II type number of stations is fixed;

5. Assembly process:

The nodes are the operations, and the

rows express the precedences. So we do

each operation according to the order

shown by the precedences.

We can also show precedences using the Hoffman matrix.

In every cell we will have h = 1 if i precedes j, 0 otherwise. This tools is helpful because it permits


us to reach some kind of automation in performing this evaluations.

Then, it is necessary to evaluate the time of each assembly operation that are less easy to


We have 3 methods to obtain these data:

1) Work sampling: we simply observe the operations and chronometer them.

 Pros: easy to perform (no competences required) and reliable,

 Cons: requires long time to collect data that can be usefully apply to the


2) MTM (motion time measurement): a method based on the assumption that, based

on an archive with elementary operation data (based on custom parameters as

weight lifted or angle or rotation or length of movements), it is possible to compose

any complex movement (or operation) and calculate the average duration and

standard deviation. Nowadays this method is performed by computer.

 Pros: it’s very specific and precise,

 Cons: it requires the tool.

3) Standard times collected from the past operations. The new products can reuse this

standard times because they may share some similarities in the operations required.

 Pros: quickly, no time consuming,

 Cons: it requires a long set of past data.

Balancing constraints:

They can be:

- Cycle time, cannot be higher than the production capacity we want to reach.

- Precedence relationships among operations, linked to problem of physical access to the

various components.

- Incompatibility between operations that cannot be assigned to the same station, due to

space constraints, but also because of safety issues (e.g. flammable materials, …),

- Opportunity or necessity to assign some operations to the same station, for example we

may have a specialized tool, so we can save cost of duplication if we put all the operations

that require that specific tool in the same station,

- Constraints related to space, due to the volume of the components or equipments, but we

have also constraints related to the number of station (remember that we’re in an assembly


- Constraints related to workers. If we allocate some tasks to the same worker, of course he

has to have some skills, that have to be adequate to the task that he has to perform.


a. Technical objectives.

-Minimizing the number of stations, given the cycle time,

-Minimizing the cycle time, given the number of stations (exactly the opposite of the first

one: here we want to achieve the maximum production capacity according to this number

of stations),

-Minimizing the total idle time (related to the utilization rate). If we have more stations we

have to consider all of them. The best situation is having IT = 0 in each station, in order to

achieve the maximum utilization rate of the operators. The following formula simply shows

the total idle time considering all the stations:

∑ N

IT = n * CT - t

i=1 i


n = number of stations

CT = cycle time

N = number of assembly operations

t = time to perform operation i (i.e. unit working time)


UR = ∑t /CT so we can modify the numerator (allocating a lower number of tasks


to the station) or the denominator in order to reach 1.

-Minimizing the probability of no completion

 in a machine-paced line, or

 in a continuous flow line, in case the operator can’t stop the line.

We want to have a certain IT (>0) because in this case we don’t utilize fully the operators

but we’ll have some spare time in order to face problems or other issues. So in this case

we will not achieve the best cycle time.

-Minimizing the probability that the times of operations in one or more stations exceeds CT

 in an operator-paced line, or

 in a continuous flow line, in case the operator can stop the line

b. Economical objectives.

- Minimizing the total expected cost (TEC)


Min( line cost (equipment cost +

operators cost)

expected cost of unfinished

operations (i.e. tasks)

Of course we have to consider that each scenario is related to a different cost, so we

have to multiply each scenario for its probability of occurrence, and then sum them all

because scenarios are all mutually exclusive!

Equipment costs are related to the cost of facilities installed (it is a capital expenditures),

so (as it was in the job shop) we have to consider also the coefficient that expresses the

lifetime of the facility.

In order to compare these two costs we have to divide LC with the volume, because

E_CUT is a cost per unit.

Performance indicators:

Balance Efficiency: E = T / (K * CT) = K / K**


K is the minimum number of stations

(K* is the minimum number of stations with a fixed alpha)

K** is the actual number of stations

Balance Delay: D = (K ** ∙ CT – T) / (K ** ∙ CT) = 1 - E

the numerator is the idle time we have.


The utilization rate of an operator is defined as follows

t = mean time of task i


S = set of tasks assigned to the operator

CT = cycle time

For each operator, the following constraint has to be verified:

UR ≤ α; α is the maximum value of the utilization rate (0 < α ≤ 1). We set alpha because we don’t always want

to have 1 as UR because we may need some spare time in order to fix minor problems! (but of course we

want UR =1. It is alpha the threshold).

Steps of line balancing:

1. Draw the precedence graph (assembly graph);

2. Calculate the total tasks’ time T (sum of all tasks’ times). It can be defined as total assembly work

content or, equivalently, total assembly time;

3. Calculate the cycle time CT

CT = available time / demand

Where available time – AH = WH * A (a coefficient that represents the unavailability of the operators

or their absence – absenteeism as an instance).

4. Calculate the minimum number of stations K*= T/(CT * α). K is not the absolute minimum, but it’s

the minimum according to the α we’ve chosen (α is a threshold).

5. Assign tasks to stations, respecting the constraints (CT, precedence relationships, UR < α, etc.). Of

course if the constraints are not respected, we go back and re-do the assignment. If there is more

than one task available to be assigned, use a rule to prioritize tasks as:

a) Prioritize tasks in order of longest task time

b) Prioritize tasks in order of the largest number of following tasks

If there is any task that requires more than the defined CT use parallel stations.

NB: ideally speaking we want to obtain K*, but in reality saturate α is very difficult, so we will usually

obtain K**. K** > K* > K.

Line balancing - Positional Weight Heuristic


This task selection is simple and thereby made in order to reduce the complexity of the problem.

A task is prioritized by the cumulative assembly time associated with the task itself and its successors:

PW(i) = t + ∑ t w in S(i)

i w w where:

S(i) successor tasks to task i, so this solution affect all the following.

We’re looking for a solution that fits well locally, so it can happen that from a global perspective this is not

the best one. Of course the optimal condition is reaching the minimum number of station possible K** =

K* = K (this calculation can be considered as a synthetic benchmark of our choices).

Data we need: mean times, precedences.


1. Task ordering:

for all tasks i, compute the positional weight PW(i), then

rank tasks by decreasing PW,

2. task assignment: for ranked tasks, assign task i to the first feasible station (obey the precedence

relationships; do not exceed cycle time; obey other constraints).

Ex: CT = 70

Let’s consider the minimization of number of stations the main objective, so α = 1. Of course may consider other

values for alpha, but then the calculation for K will be different.

K = T/ CT 202/70 = 2,89 ≈ 3 We start assigning task to

the first station basing on

the ranking (we follow a

decreasing order), so we

assign tasks: a, d, b, c, g.

Every time we add a task

to the station we have to

remove its time to the

cycle time of 70 (adjusted

by the cumulated

reductions we’ve

computed so far).

We stop at g because the

time remaining after g is

only of 3 secs (idle time),

that are too few to add

another task to the current


And so on…

Of course the CT=70 might not be always respected.

Probability of no completion.

In this flowchart we don’t consider UR ≤ α as a threshold anymore! (the steps showed before at page 42 have

to be followed anyway).

For each task the following constraint has to be satisfied:

P ≤ P*

k where:

P = probability of no-completion of task k (probability that I cannot complete the task k that

k has be assigned to this station)

P* = maximum probability of no-completion.

Of course in this case I need to know also the standard deviation for each operation (not only the mean time

related to them) because we’re dealing no more with deterministic values.


1. Calculate the remaining time (idle time) related to task k:


CT = cycle time

t = mean time of task i (time required to perform task i)


S = set of tasks assigned to the operator (task k included)

2. Calculate the variable associated to the remaining time. We’re dealing with probabilities, so the

variable follows a specific distribution – the typical distribution taken is the Gaussians:


σ = standard deviation of the time required to perform task i

i ∑ ∑ ∑


3 volte




3.32 MB


+1 anno fa

Corso di laurea: Corso di laurea in ingegneria gestionale
Università: Bologna - Unibo
A.A.: 2016-2017

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher gianfranco.pannia di informazioni apprese con la frequenza delle lezioni di Industrial Technologies e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Bologna - Unibo o del prof Macchi Marco.

Acquista con carta o conto PayPal

Scarica il file tutte le volte che vuoi

Paga con un conto PayPal per usufruire della garanzia Soddisfatto o rimborsato

Ti è piaciuto questo appunto? Valutalo!

Altri appunti di Corso di laurea in ingegneria gestionale

Lezioni, Valorizzazione delle risorse primarie e secondarie M
Logistica industriale T-AB - Appunti prima parte
Impianti industriali (2' modulo)
Sistemi informativi T-1 - progetto