Buffer Capacity
Read this article. The researchers studied buffer capacity and the effects of holding on to extra buffer inventory. Do you agree or disagree with the concluding analysis and why?
Profit results
While TR and ABL results are relevant in isolation for some firms with a concern for either maximising revenue or minimising inventory costs, most firms are more interested in finding a balance between revenue and costs via a profit function. For this reason, studying the effect of buffer allocation patterns on the combined performance of TR and ABL provides a deeper insight into the implications of unbalanced buffer allocation.
Consequently, the profit function (), defined in Eq. (3),
was used to study the combined performance of TR and ABL, as it takes
into consideration inventory holding costs and buffer capacity
investment/maintenance costs while generating revenue via the production
rate. Therefore, the best pattern for different values of
and
will be the pattern which sufficiently increases TR, outweighing the
costs of ABL and BC.
where is the profit resulting from the buffer allocation pattern attaining the maximum TR,
is the maximum TR per scenario,
is the ABL resulting from the BP that reached maximum TR, BC is the average buffer capacity for a particular experimental scenario;
is the profit obtained from the BP with minimum ABL,
is the minimum ABL per scenario, and
is the TR generated from using the BP which resulted in the minimum ABL.
Since the term is equal for both sides of the equation when
is equal among experiments; then,
This means that when for a particular manufacturing environment,
has a higher
than
because the system is better off minimising holding costs, as they are too high to overcome with higher TR; whereas when
will result in higher
than
because inventory holding costs are not as penalising. For example, an
shown in Fig. 4a for
and
, means that if
has a higher
than
since
; whereas if
has a lower
than
since
Fig. 4 and
values for all experimental scenarios
where is the
reached for a
while applying
and
is the
reached for a
using
for a specific scenario.
Therefore,
It is worth noting that all variables in Eqs. (6) and (7) consider experimental scenarios with equal values of and
. Moreover,
was selected as the pattern considered for these equations because the BP with minimum experimental ABL produces the highest
when
.
Thus, lower values for a given set of
and
values represent higher penalties for investing in higher buffer capacity, while higher
values depict lower profit penalties with high
values. Similarly to
, a higher value of
than
for a given line configuration suggests that it is more profitable not to invest in higher buffer capacity, i.e. stay at
; whereas a lower value of
than
means that it is profitable to invest in the additional 4 buffer spaces, i.e. a
. For instance, an
shown in Fig. 4b for
and
, means that a buffer investment/maintenance cost of
results in a decision of staying with
as
; whereas if
, then
is more profitable than
since
Results from Fig. 4a show that higher values of resulted in higher values of
, which suggests that patterns that increase TR are more relevant for longer lines than for shorter lines; whereas patterns that reduce ABL produce better overall results for shorter lines in terms of
. Furthermore, higher values of
and lower values of
(shorter MTTF and MTTR) result in higher values for
, suggesting that higher machine reliability results in a reduced impact of inventory holding costs.
Further analysis of Fig. 4 a shows that scenarios with smaller buffer capacity have lower values of
, suggesting that profit in these scenarios is highly penalised by ABL and that a pattern that reduces ABL produces higher
for most inventory holding costs values. The opposite is true for scenarios with
, since
is less penalised by
as
(the pattern producing the maximum TR) results in a higher
even for higher values of
. This suggests that the extra TR produced by the extra ABL (resulting from higher BC capacity) allows for
to be more relevant when
. An
indicates that the corresponding scenario, e.g.
and
, produces the highest profit by selecting the buffer allocation pattern that reduces
, irrespective of the value of
.
The only exception to this general behaviour occurs in scenarios with reliable merging lines
, or with
and
, since
is higher for scenarios with
than for experiments with
. This might be due to the fact that the added
produced by higher BC capacity does not result in a sufficiently additional TR to overcome the inventory holding costs. Therefore, for reliable lines with
is more relevant than
with respect to
.
Results regarding (see Fig. 4b ) suggest that higher values of
(longer MTTF and MTTR) produce a higher investment/maintenance penalty (lower
values) for systems with higher buffer capacities, which means that the additional throughput produced by the added buffer capacity is more cost-effective for shorter MTTF and MTTR than for longer ones. Similarly, systems with
were less penalised in terms of profit by higher buffer capacities than systems with
, suggesting that the extra throughput produced by the increased buffer capacity is more cost-effective when reliability is
than when reliability equals
.
An exception to this observation occurred for the reliable merging lines results, as values for reliable lines were lower than for experiments with
and
with
, suggesting that even with low buffer capacity investment/maintenance costs, small buffer capacities will be better in terms of profit performance for reliable lines than larger buffer capacities. This result might be caused by the fact that the relative difference between the throughput generated by lines with small and big buffers is smaller for reliable lines than for unreliable ones. For instance, considering
and a balanced
, the increase in
between a line with
and a line with
, considering
and
, is
; whereas for a reliable line with
, the relative increase in TR between a line with
and a line with
is only
(see Table 4 in the "Appendix").
Finally, to investigate the relationship between and
values in terms of the profit function for different buffer capacity investments levels, Fig. 5 shows a comparison of the suface plots of
between merging lines with
(in blue) and merging lines with
(in orange) for various values of
and
, taking
as an example.
Fig. 5 function surface plots for
(blue) and
(orange) for different values of
and
considering experiments with
and
, and
(colour figure online)
Figure 5 shows similar results than those for Fig. 4b by suggesting that highly unreliable scenarios with longer MTTF and MTTR (e.g. Fig. 5c) scenario are more sensitive to higher costs than moderately unreliable scenarios with shorter MTTR and MTTR (see, e.g. Fig. 5d). Thus, a bigger buffer capacity () is only more profitable than a smaller buffer capacity (
) when very low costs (both
and
) are present and when lower unreliability exists. Again, a reliable system is the exception, as a smaller buffer capacity is almost always more profitable in reliable scenarios (see Fig. 5g: the blue surface (
) is "above" the orange surface (
) for most of the values of
and
).
Note that results pertaining to merging lines with and
are not shown as they are very similar to the ones presented in Fig. 5 and follow the same general pattern as in Fig. 4, i.e. the profit in longer lines is less penalised by inventory-related costs than for shorter lines. Furthermore, in order to reach the highest possible
values for Fig. 5, the best pattern for the corresponding
values was considered. That is, for values lower than
,
was used in the calculation of
, whereas for values higher or equal to
,
was considered.