Línea de Ensamble para una Mezcla de Productos.

A) Descripción de la Tarea.

El caso que se anexa describe y ejemplifica un procedimiento para balancear una

línea de ensamble que produce una mezcla de tres productos de una misma

familia.

Para este ejercicio tomaremos el resultado del balanceo que viene desarrollado

en el ejemplo, en el cual resulta un balanceo con 5 estaciones.

Consideraciones.

1) Cada una de las estaciones estará a cargo de un operario, el operario será

asignado como un recurso para las operaciones que le corresponden a su

estación.

2) Correrás 30 réplicas de 40 horas cada una.

3) El sistema será completamente “push”. Para modelarlo generarás

solamente 1 “arrival” de 1 sola entidad, pero al terminar la primera

operación duplicarás la entidad que se procesó con el bloque “separate” y

la opción “duplicate original”. La entidad original sigue su ruta de

proceso, la entidad duplicada se introducirá de regreso a la primera

operación, simulando así una nueva llegada de insumo de manera

constante.

4) Antes de ingresar a la primera operación será necesario asignar de manera

aleatoria el tipo de producto de que se trata, de acuerdo a la proporción

de productos en la demanda.

5) Como se muestra en el texto, los tiempos reales de proceso dependen del

tipo de producto que se esté ensamblando. Debes familiarizarte con

algunos bloques, por ejemplo el bloque “assign” para poder modelar esta

situación. Elige libremente la lógica de modelación que te funcione.

Lo importante es que los tiempos de las operaciones se modifiquen de

manera dinámica de acuerdo al tipo de producto de que se trate.

6) Los tiempos de operación son constantes en todas las operaciones, es

decir, una vez que se sabe el tipo de producto, el tiempo de ejecución de

cada una de las operaciones se considerará constante. La única

variabilidad que se está introduciendo es la causada por la mezcla

aleatoria de productos.

7) Analiza la capacidad productiva del sistema y otras variables que

consideres relevantes. Compara con el desempeño esperado del sistema.

B) Efecto de la variabilidad en los tiempos de operación.

En este ejercicio utilizarás el modelo del ejercicio “A” pero haciéndolo más

realista al introducir variabilidad moderada en los tiempos de las operaciones.

Todos los tiempos aleatorios se modelarán como variables aleatorias uniformes,

continuas, con media igual a los tiempos que vienen originalmente en el caso,

pero variando aleatoriamente en los rangos que se especifican en la siguiente

tabla.

Operación Rango (seg.)

A ± 3

B ± 0

C ± 2

D ± 2

E ± 2

F ± 4

G ± 2

H ± 2

I ± 1

J ± 4

Por ejemplo, para el producto “Basic” el tiempo para la operación A será

uniforme en el rango de 9 a 15 segundos, mientras que para el producto “Luxury”

dicho tiempo será uniformemente distribuido en el rango de 12 a 18 segundos.

Cuando una operación no es requerida para un producto, el tiempo será 0 fijo,

sin considerar los rangos.

Realiza 30 corridas de 40 horas de operación cada una. Analiza el rendimiento

de la línea comparándolo con el rendimiento de la línea en el caso A.

Sugiere al menos 2 estrategias para mejorar el desempeño de ésta línea.

Assembly Line Balancing:

Mixed- and multi-model lines

Background

You will have previously studied methods of balancing assembly lines where only a single model is

produced. The strength of such a line is that the work elements can be assigned to stations in

such a way as to maximize efficiency, which peaks at a particular rate of output.

The weaknesses of a single-model line are that it becomes inefficient when demand falls or rises,

and that it is only efficient when producing the model for which it was designed. If market

demand changes so that other products are required, other products need to be produced.This

can be done by installing separate, dedicated lines for other products, but this is only economic

when the additional lines themselves are running efficiently in fulfillment of greater demand. It’s

not a solution for “flat” overall demand with varying product mix.

Two solutions to this problem of fluctuating demand have been used in the past:multi-

model lines and mixed-model lines.Each has its own strengths and weaknesses.

Multi-model lines

This approach treats the assembly line as a reconfigurable resource, which produces different

models in batches one after the other.Before producing a batch, the line’s equipment (people,

tools, material supply) is set up to suit the model or variant required.This process takes time.The

batch of products is then produced according to schedule.

The benefit of a multi-model line is that once set up for a particular model it is as efficient as a

conventional line.The drawback is that setting-up takes time, which means lost production and

inefficiency.

The problems for the planner of a multi-model line are:

1. How to balance the line for each product separately?This is straightforward enough, since it’s a

function of technological feasibility followed by application of a standard balancing method (see

Helgeson & Birnie[1] or Moodie & Young[2]).

2. How to sequence the batches to minimize changeover losses? It is often the case that changeovers

from one to another will take less time than the reverse change.

This second problem is not discussed further here: it is a standard sequencing problem which the

reader will find dealt with in most texts on Operations Management.

Mixed-model lines

The mixed-model approach is a more realistic one in the modern world, given the rise of

software-configurable flexible manufacturing equipment.The basic premise is that multiple

products are handled by each workstation without stops to change over between them.This

permits a random launch sequence so that products can be made in the order and mix that the

market demands.

Although this sounds like a salesman’s dream, one difficulty is that the work content at each

workstation may differ from model to model.Another, which follows from this, is that the idle

time at each station varies from time to time depending on the sequence of models along the

line.

The problems for the planner of a multi-model lines are again twofold:

1. How to balance the line when different products have different work content?

2. How to determine the optimum launch sequence which minimizes losses?

The second problem is an Operations Management issue which, again, the keen student can

research from OM texts.What we’ll deal with here is the DESIGN (Balancing) of a mixed-model

line.

Balancing a Mixed-Model line

Although the problem may appear daunting, the solution method is quite straightforward.There’s

just one overriding caveat: it must be technologically feasible to produce the different models

on the same line.Thus, it’s reasonable to try to mix production of, say, 10 different models of

video recorder, or 15 different TV’s on the same line, but it’s not realistic to make tractors and

aircraft on the same line! Really, we should talk about different VARIANTS of the same product,

rather than completely different PRODUCTS.

There are several ways of going about this, but here’s and adaptation of Helgeson and Birnie’s

procedure that is conceptually simple and easy to apply.The outline procedure for solving the

problem is this:

1. Get together the process and technological data for the range of product, i.e. operation times

and precedences (what must follow what if the product is to go together)

2. Get demand data on what volume of each product is required and at what rate. This may be

available as absolute variant volumes, or may be as aggregate volume plus product mix

data.

3. Use this information to produce a table of composite process times.The table should contain, for

each operation, a process time weighted by the proportion of products using that operation.Thus,

an operation taking 10 minutes that occurs on only 35% of the total demand becomes 3½ minutes.

4. Calculate the cycle time and minimum number of stations required.

5. Construct a precedence diagram for the composite product, showing which operations depend

on others, taking account of all the variants to be produced.

6.Determine the positional weight (PW) of each operation, as you would for a normal

balancing exercise.Use the weighted times for determining PWs.

7.Assign operations to stations, having regard to PWs, precedence and remaining time at

the workstation.Depending on the objectives and constraints, you may have to repeat

this final step several times, seeking to minimise the number of workstations, maximise

throughput or to maximise efficiency.

As you can see, it all comes down to creating a fictitious “composite product” which doesn’t

really exist but which has the characteristics of all of the range, then applying the standard LB

technique.

Let’s do an example. Thanks go to Vonderembse & White[3] for their inspiration.

Example

Background information

A flexible assembly line is to be set up to package a range of hospital medical kits.All the kits use

the same basic elements, but there is variation.The “standard” product contains one set of

components, the “basic” kit has a smaller set, while the “luxury” version contains the same items

as the standard kit but in greater quantity plus a couple of additional items.

The operational and product mix data for the three variants is given in Table 1.

Time (seconds)

Op Description

Standard

(50%

sales)

Basic

(30%

sales)

Luxury

(20%

sales)

Preceding

Task(s)

A Unfold & place box 15 12 15 -

B Insert water bottle 9 9 9 A

C Insert drinking

glasses 7 4 10 A

D Insert bedpan 7 0 7 A

(not Basic)

E Insert divider(s) 7 7 9 B, C, D

F

Fold dressing

gown

& insert in box

18 18 24 E

G Insert tissues 6 0 9 E

(not Basic)

H Insert plasters 7 7 10 E

I Place lid 10 10 10 F, G, H

J Shrink-wrap box 21 21 28 I

Total times 107 88 131

Table 1 – Operational and product mix data for the three products

An aggregate output of 6,000 units is required from an effective working week of 40 hours.

Solution

First, let’s determine the process times for the “composite” product, multiplying the actual

process time for each element by the proportion of demand for that element.

Table 2 on the next page shows the result.Each of the first three columns shows the basic

operation time, and in bold the result when this is multiplied by the demand proportion.The

final column shows the sum of these weighted times – the “composite operation time” –

which is the effective time for this operation.

In this model, operation times are in seconds and working sessions are in hours and weeks.You

need to be sure you are consistent in your use of units, using multipliers as appropriate.

Basic Time (seconds)

Op

Standard

(50%

sales)

Basic

(30%

sales)

Luxury

(20%

sales)

Composite

time

(Sum of

weighted

op times)

A 15 7.5 12 3.6 15 3.0 14.1

B 9 4.5 9 2.7 9 1.8 9.0

C 7 3.5 4 1.2 10 2.0 6.7

D 7 3.5 0 7 1.4 4.9

E 7 3.5 7 2.1 9 1.8 7.4

F 18 9.0 18 5.4 24 4.8 19.2

G 6 3.0 0 9 1.8 4.8

H 7 3.5 7 2.1 10 2.0 7.6

I 10 5.0 10 3.0 10 2.0 10.0

J 21 10.5 21 6.3 28 5.6 22.4

10753.5 8826.4 13126.2 106.1

Table 2 - Composite operation times

Next, let’s determine the minimum number of workstations needed.

Target cycle time = (Available hours/wk x 3600) / (Wkly output)= 40 x 3600 / 6000

= 24 seconds

Ideal number of workstations= Composite work content / Cycle time

= 106.1 / 24

= 4.42

We can’t have 0.42 of a station, so the minimum number of stations is 5 (five).

Next, let’s draw a precedence diagram.

Figure 1 - Precedence diagram for assembly of the Medical Kit

Note that in this case there are no operations unique to a single variant.If there

were, they would be handled just like any other op.The diagram is consistent

with the final column of Table 1.

Now, let’s determine the positional weights of each operation.The PW of an operation is the sum

of the process times for ALL the operations which depend on it, plus its own process

time.In Figure 1, all operations depend on Operation A.In the case of a mixed-model line, the

PWs are calculated from the composite times established earlier.The PW of Op A here is

thus 106.1.Table 3 shows the PWs for all the other ops, ranked in descending order.Note how

the PW changes when parallel operations (B, C, D and F, G, H), are involved.

PW rank Operation Positional Weight Comment

1 A 106.1 First op – all others depend

on it

2 B 80.4 B, C, D are independent

E & later ops depend on each 3 D 76.3

4 C 78.1

5 E 71.4 Sum of all following op times

6 F 51.6 F, G, H are independent

I & Jdepend on each 7 H 40.0

8 G 37.2

9 I 32.4 F, G and H must all precede I

10 J 22.4 Last op, soPW = Op time

Table 3 - Ranked Positional Weights of Operations

Now we can assign operations to stations in the normal manner.The heuristic procedure is:

1.At Station I, consider all “eligible” operations (i.e. those for which there are no precedent

operations).If there is more than one, select that with the highest PW.

2.Continue attempting to assign operations to Station I until no more eligible operations exist or

will fit into the remaining time.Record idle time, if any.

3.Move to Station II.Repeat the attempts to assign eligible operations, in descending order of PW,

until there is no eligible operation that will fit.Note that eligibility/precedence always comes

before PW; PW is used to break ties.

4.Repeat until all operations have been assigned, even if it means creating more than the

theoretical minimum number of stations.

5.Finally, calculate the Balance Delay Ratio (= 100-efficiency) from the available working time

and the total idle time.

Table 4 shows the procedure step-by-step, while Table 5 shows the results.

Eligible

operation(s)

Selected

operation(s)

Composite

Operation

Time (sec)

Assigned

to Station

Cumulative

Assigned

Time (sec)

Idle Time

(sec)

A

B, C, D

A

B

14.1

9.0

I

I

14.1

23.1

0.9

C, D

C

E

D

C

E

4.9

6.7

7.4

II

II

II

4.9

11.6

19.0

5.0

F, G, H

G, H

F (largest

PW)

G

(H won’t fit)

19.2

4.8

III

III

19.2

24.0

0

H

I

H

I

7.6

10.0

IV

IV

7.6

17.6

6.4

J J 22.4 V 22.4 1.6

Table 4 – Step-by-step application of the heuristic to determine work

assignments

Station Assigned

Operations

Idle Time

I A, B 0.9

II D, C, E 5.0

III F, G 0

IV H, I 6.4

V J 1.6

Total

Idle Time

13.9

Table 5 – Summary of Station Assignments

To calculate the Balance Delay Ratio, recall that the cycle time was 24 seconds.Thus:

Total available working time on line= Cycle time x Number of stations

= 24 x 5

= 120 seconds

Balance Delay Ratio=Total Idle Time x 100

Available time on line

=1390

120

=11.6%

Conclusion

We have determined a balance for the desired product mix at the target level of output. The

remaining problem is one of sales - only if the product mix is close to 50:30:20 will efficiency be

maintained. Should sales of “luxury” kits rise, the line will not cope, while if sales of “basic” kits

rise, idle time will increase.

[1] W B Helgeson & D P Birnie, “Assembly Line Balancing using the Ranked Positional Weight Technique”, Journal of

Industrial Engineering, Vol 12, No 6, Nov-Dec 1961

[2] Moodie and Young, cited in W Bolton, “Production Planning and Control”, Longman, 1994.

[3] M A Vonderembse & G P White, “Operations Management – Concepts, Methods and Strategies”, West 1996