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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).
David S. Cochran, PhD.
Phone: (617-901-2108)
©2007-2009