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Delay reduction
The decomposition of FR-DP113, “Meet customer expected lead
time” and “Mean throughput time reduction,” focuses on identifying
predictable sources of delays and prescribing general solutions
for elimination (see Figure 1). A delay is defined as time
that a part spends in the manufacturing system when it is
not being processed. Throughput time is defined as the total
time that a part spends in the manufacturing system, from
the time it enters as raw material to the time it leaves as
a finished product. A relationship exists between the time
a part spends in the manufacturing system and the total number
of parts in the system. This relationship, known as Little’s
Law (Little, 1961), can be expressed as follows:
L=λ*W (1)
where the variables and their units are the following:
L: Average quantity of parts in the system (i.e. total inventory)
[parts]
λ: Average rate parts enter and leave the system [parts
/ time]
W: Average time spent in system (i.e. throughput time) [time]
This relationship assumes that the manufacturing system is
operating at a steady state, so that the rate parts enter
the system is, on average, equal to the rate at which parts
leave the system. If these rates are not equal, parts will
either accumulate in the system (arrival rate > departure
rate) or the number of parts in the system will go to zero
(arrival rate < departure rate). Little’s Law has been
used to develop quantitative relationships between inventory
and throughput time for the delays mentioned in this decomposition
branch.
The delays identified in the MSDD include: lot delay, process
delay, run size delay, transportation delay, and systematic
operational delays (Figure 1).
Figure 1: Components of delays for throughput time reduction
To illustrate the first four delay requirements, Figure 2
illustrates a basic serial manufacturing line capable of producing
two different types of parts (shown in the figure as cylinders
and rectangles).
Figure 2 Types of delays in serial manufacturing operations
The MSDD has already dealt with uncertainties in the quality
and time variation branches. Thus, the scope of the decomposition
of DP-113 “Mean throughput time reduction” addresses the five
delays that result in increased throughput time. The complete
decomposition relative to delay reduction is shown in Figure
3. This section will provide further details regarding each
type of delay and a formula that can be used to estimate the
amount of delay. A simple, two-operation manufacturing system
will be used to develop examples of the different types of
delays. Assume there are two processing operations (op. 10
and op. 20) necessary, each with a cycle time of two minutes,
with no variability in processing time, reliability, or quality.
It is also assumed that the customer of this system will demand
one part every two minutes. As a result, the amount of inventory
kept in the system must be sufficient to prevent the starvation
of any of the operations. If an operation is idle in this
scenario, demand will go unfulfilled
Figure 3: The MSDD distinguishes five types of delays
FR-T1 “Lot delay”
Lot delay (FR-T1) occurs when parts are transported between
operations in lots (also known as transfer batches) of greater
than one. While one part in the lot is being processed, all
other parts in the lot must wait in storage, either before
or after the operation. For the example system, suppose that
parts are transported from op. 10 to op. 20 in containers
that hold 20 parts each (see Figure 4). Parts are moved only
when a container is full. Thus, the first part completed at
op. 10 and placed into an empty container must wait for the
next 19 parts to be processed before it can be moved to op.
20. The 20th part produced and placed in the container can
be moved to the next operation immediately, but upon arrival
it must wait for the other 19 parts to be processed, assuming
a first-in, first-out processing sequence. Other sequences
(such as last-in, first-out) may be used, but the average
waiting time over all of the parts in a container will be
the same. Neglecting for now the time it takes to transport
a full container from op. 10 to op. 20, we can see that the
total number of parts stored between these operations is one
less than the container size.
Figure
4: Lot delay example
Because transportation time is neglected, part #1 could be
loaded into op. 20 immediately after part #20 is completed
in op. 10. According to Little’s law, the throughput time
added by this transportation lot size is given by:
W = L / λ = 19 parts / 0.5 parts/min. = 38 minutes
Or, more generally,
Lot delay = (Transfer batch size - 1) / Production rate
The means for reducing lot delay is simply to transfer parts
in smaller batches, ideally with a transfer batch size of
one piece (DP-T1). The design matrix at this level shows that
reducing transfer batch size (with the ideal goal being single-piece
flow) can have an impact on the ability to reduce process
delay (FR-T2) and transportation delay (FR-T4), as reducing
the transfer batch size will affect the frequency and quantity
of material handling from one operation to the next.
FR-T2 “Process Delay”
Process delay (FR-T2) results when the arrival rate of parts,
ra, is greater than the service rate, rs
(i.e., the rate at which parts are processed). Unlike the
other four types of delays described in this section, process
delay cannot occur in a steady-state condition. If the average
arrival rate of parts is greater than the average service
rate, the amount of inventory in the system will tend towards
infinity. Assuming that the long-term average arrival rate
is equal to the average service rate, process delay occurs
only during shorter time intervals during which ra
> rs. Essentially, process delay occurs when
parts are processed in excess of demand. The processed parts
must then wait until they are demanded by the customer. Returning
to the two-operation example described earlier, suppose we
look at process delay in the context of operation 20, as shown
in Figure 5 and Figure 6.
Figure 5: Production state at the beginning of a shift
In the previous example, each operation had a cycle time
of two minutes. Now suppose that op. 10’s cycle time has been
decreased to 1.5 min., and that neither operation is ever
starved for parts. Customer demand remains the same at one
part every two minutes, for a total of 240 parts per 8-hour
shift. After 6 hours of operation, op. 10 will have produced
the necessary 240 parts for the shift (6 hrs * 60 min/hr /
1.5 min/part = 240 parts). Op. 20, however, will have only
processed 180 parts (6 hrs * 60 min/hr / 2 min/part = 180
parts), resulting in an increase in in-process inventory of
60 parts. Assuming op. 10 stops producing parts when it has
met demand for the shift, op. 20 will catch up at the end
of the shift, customer demand will be fulfilled, and the amount
of inventory in the system will return to its previous level.
Note that although reducing the cycle time of operation 20
could eliminate the need to run overtime, it would not reduce
the amount of process delay. Instead of waiting before operation
20, the parts would simply have to wait at a point further
downstream in the system. The root cause of process delay
is production ahead of demand, not insufficient capacity.
Figure
6: Production state four hours into the shift
The decomposition prescribes “production designed for takt
time” (DP-T2) as the means to eliminate process delay. Achieving
this condition requires that the pace of customer demand (i.e.,
the takt time) be defined (FR-T21) and that the service rate
and arrival rate of the system be matched to this takt time
(FR’s T-22 and T-23, respectively). The takt time for a system
can be calculated by dividing the total number of available
production hours in a given time interval (e.g., one week)
by the total number of parts demanded during that time. In
calculating takt time, it is important that factors such as
machine downtime, setup time, and worker allowances be considered
in determining how many hours of production can be expected.
Matching the service rate to the takt time requires that the
system have sufficient capacity to meet customer demand. Overproduction
is avoided by ensuring that the arrival of parts at downstream
operations is balanced to takt time (DP-T23). In this way,
operations producing at a pace faster than the takt time will
become starved for incoming materials, and the transfer of
materials from one operation to the next will serve as the
means to pace production.
FR-T3 “Run Size Delay”
Run size delay (FR-T3) occurs when multiple part types are
produced and the sequence of production does not match the
sequence of products demanded by the customer. For example,
suppose that our two-operation system produces two part types,
A and B, and the customer demands 200 of part type A and 40
of type B every day. Assuming that the system runs one shift
per day, five days per week, weekly demand will be 1000 of
part A and 200 of part B. Suppose that, in order to reduce
machine downtime due to changeovers, the system is scheduled
to produce all 1000 type A parts first (requiring 2 min/part
* 1000 parts / 60 min/hour / 8 hours/day = 4.2 days) and then
changeover and produce part type B for the remaining 0.8 days
each week. The result will be that customer demand is met
on a weekly basis. However, excess inventory of each part
type will have to be kept in the system in order to meet the
customer’s daily requirements, as shown in Figure 7. The upwards-sloping
portions of the lines represent times when that product is
being produced. The steep declines represent the daily shipment
of the demanded parts to the customer. On average, an inventory
of about 180 type A parts and 100 type B parts are kept in
the system.
Figure
7: Inventory due to run size delay
To avoid run size delays, production must be matched to customer
demand during each demand interval (DP-T3). The demand interval
is defined here as the period of time between deliveries to
the customer. In the example above, the demand interval is
one day. In practice, the length of the demand interval can
vary significantly. When transportation distances are long
and transportation is expensive, the demand interval might
be a week or longer. When transportation distances are short
and inventory reduction is critical, the demand interval might
be as short as a few hours or less. In order to produce according
to customer demand, demand information must be known in advance
(FR-T31), requiring frequent communication with the downstream
customer, and the manufacturing system must be capable of
producing in sufficiently small run sizes (FR-T32). The ability
to rapidly changeover equipment from one part type to the
next (DP-T33) is critical for achieving this objective. Figure
8 shows how the WIP in the system varies throughout the week
when production in the example system is matched to customer
demand on a daily basis. With this case, inventory is reduced
to an average of 115 of part type A and only 4 of part type
B. Run size delay has, by definition, been eliminated completely.
The inventory that remains in the system is due to process
delay (FR-T2). In this example system, there is a short-term
mismatch between the production and shipment rates (i.e. during
the day parts are produced at a rate of 0.5 parts / minute,
but shipped at a rate of 0 parts / minute).
Figure
8: Reduced inventory – reduced run size delay
FR-T4 “Transportation Delay”
Let us now assume that the time to transport a container
of parts from operation 10 to 20 is non-zero (see Figure 9).
In this case, additional inventory is necessary to prevent
part shortages at op. 20. The transportation delay time (FR-T4)
is defined as the total time from the moment when a full transfer
batch of parts is ready to be transported until these parts
arrive at the downstream operation and are ready for processing.
This time includes the time parts spend waiting to be transported,
the time spent in transit, and any necessary loading and unloading
time. The amount of inventory added to the system due to transportation
time is given by:
Additional inventory =
Transportation time * Production rate
The transportation delay will be equal to the amount of transportation
time. Continuing with the example system and assuming that
it takes 6 minutes to transport parts from operation 10 to
20, the amount of additional inventory will be:
6 minutes * 0.5 parts/min = 3 parts
Figure
9: System state 4 minutes into the transportation time
The manufacturing system design decomposition advocates system
layout design as the means for reducing transportation delays.
By arranging equipment based on product flow (DP-T4) as opposed
to grouping equipment by operation, transportation distance
can be minimized. An alternative means for reducing transportation
delay would be to speed up the means of transportation; however,
this solution is not prescribed by the decomposition, as it
does not address the root cause of the delay: long transportation
distances. Another important factor for reducing transportation
delay is ensuring that transportation resources arrive to
pick up and deliver parts at the proper times. This timing
aspect is covered in the decomposition of FR-T2, “Reduce process
delay.” This information is reflected in the design matrix
by a relationship between DP-T2, “Production designed for
takt time,” and FR-T4, “Reduce transportation delay.”
FR-T5 “Systematic Operational Delays”
Routinely occurring delays caused by interferences among
resources are referred to in the MSDD as systematic operational
delays (FR-T5). The decomposition considers two categories
of resources, production resources (workers and/or automation
involved in the processing of parts) and support resources
(workers and/or equipment supporting this production by supplying
small purchased parts, removing chips from machine tools,
etc.). Delays occur when one resource prevents another from
performing its duties. The delay time is given by:
Systematic operational delay = Duration of interference among
resources
For example, consider a workstation at which an operator
manually performs several assembly tasks, including adding
some screws, washers, etc. to a partially assembled product.
Assuming that the operators have containers of each of these
small purchased parts at their workstations, a support resource
is necessary to periodically replenish the operators’ supply.
If this replenishment requires operators to stop working and
move away from their workstations, an interference has occurred
between a support resource (the material replenisher) and
a production resource (the operator). The part being processed
is delayed by the amount of time it takes the replenisher
to refill the necessary containers. The proposed means for
reducing such delays is the coordination and separation of
the work and access requirements of each resource (DP’s T51-T53).
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