Department of Logistics and Supply Chain Management, School of Economics and Management, Chang’an University, Xi’an, China

- *Corresponding Author:
- Syed Abdul Rehman Khan

Department of Logistics and Supply Chain

Management, School of Economics and

Management, Chang’an University, Xi’an, China

**Tel:**+862584949

**E-mail:**sarehman_csc[email protected]

**Received date:** August 01, 2017; **Accepted date:** September 10, 2017; **Published date:** September 20, 2017

**Citation: **Khan SAR, Zhang Y (2017) In the JIT System: Effects of Processing Time and Set-up Time Glob Environ Health Saf. Vol. 1
No. 1:7

The presence of variance, processing time and setup time reductions can have “detrimental” effects on the WIP (world in process) inventory in both pull systems and push systems. In this context, we point out that the merits of such a warning for Just in Time manufacturing systems are questionable. If we deal setup time as PERT network, it is very complex to accept claim that waiting queues can grow without bound when setup time minimized. In addition, we show that the amount of setup cut and the level of variance can determine whether waiting time grows or not. This result may help in planning a viable setup minimization project and we use example to show that, even when the variances are not minimized proportionately, the expected waiting time does not necessarily increase.

Supply chain management; Just in time; Setup time; Processing time; Reduction waste

In last couple of decades, JIT (Just in Time) systems frequently use in manufacturing industries to reduce the waste and increase the efficiency of overall systems. JIT system is not use only for reduction of waste but also use for the increase the efficiency and total quality of manufacturing processes. According to the Khan et al. there are several barriers faces during implementation of JIT system and mostly times companies are unable to respond or have limited capability to mitigate risks occurs during the implementation of JIT systems [1]. As per the research of Sarkar and Zangwill, [2] a stochastic cyclic manufacturing system where a machine processes n products in term one through n, and carry on this cycle every time.

In the research of Takagi, waiting line model over system of polling, represents, a two item, product producing example: that reduction in setup times and reduction in processing time individually can upturn waiting time, however, work-in-process (via Law of Little) [3]. The existence of variation (variability) in processing times and set-up times are attributed for like a result of counterintuitive. For the system of the JIT (Just in Time) manufacturing, these results, findings are true for both approaches pull and push. In fact, some results, applications and interpretation are remains incomplete and somewhat mistaken, if we fail to perceive the following.

First of all, as per the little’s law, the conversion of waiting into number of units (physical) waiting in the system are known to be applicable in a push type system or conventional type system. In few system, manufacturing is planned in advance and then items are going through the machine centre(s) and then there physical queues are formed. Conversely, in a system of JIT of Pull the items, products cannot go themselves. In fact the demand occurs (for example: Kanban cards, multikaban systems etc.) according to the [4]. The system of Kanban might have to wait, but it might not be interpreted as a physical work-in-process buildup [4]. But that is such system’s novelty (Kanban system do not wait very long, however rational the system of JIT use “brute forces” like as lights to stop coming goods and thus break away from the cycle (continuous time). That happened when an unusually high level of variation exists, for example: breakdown of machines, etc. reasons of such systems shocks are then inspected to escape recurrence. However, no Work-in-Process (physical) build-up is possible, at least not because of above mentioned reasons).

Secondly, they assume in term to define their paradoxical results.

Var(d)-K_{j}(d_{j})^{aj} (1)

for positive constants K_{j}, and they obtain:

W_{i}=(1-p_{i})/2[d/(1-p)+hi_{j}XSIX{1+Var(S_{j})/S)j_{2}+(1-p)K_{j}(d_{j})ai/X_{j}S_{j}d}] (2)

Where j=1

where the setup time and unit processing time for product, i are
assumed to be iid random variables with means d_{i} and Ss, and
variances Var(d_{i}) and Var(S_{i}), respectively. Also, p_{i}=X_{i}S_{i} where X_{i} is
the Poisson process parameter, p=E _{i}1-p_{i} and d=E _{i}1-d_{i}.

They then speculate that "clearly, if a_{j}<1, then W can increase
without any bound”. We hope to debate that a_{j} cannot be in
negative, i.e., reduction time in set-up does not increase variance
of setup time. In the light of real world recommendations of
Shingo examining in the JIT system [5], reduction of setup is
actually accomplished through breaking down an original set of
sequential activities into two main subsets of parallel activities
external and internal setup. Although internal activities are those,
which will be finished even machine is stopped, but external
setup activities are not same like internal, these activities can
be finished when the machine is in running operation. If setup
is analysed like PERT network, then the critical path variances of
a new reduced setup containing fewer activities provided and
those actions and activities are independent must be smaller
as compare to the variance of the original setup. In specific
situations, by (1) and (2), then Cannot grow without bounds with
decreasing d_{j}.

In addition, let rdj be the new setup reduced time with 0<r<1.
By treading r as a decision variable, setup reduction team can
manage and control, and definitely influence, the effect of setup
reduction time on waiting time. It is very clear that the waiting
time W_{i} will increase if,

(1)

To validate this in the case of 0<a_{j}<1, for S-Z example, let we
replace their original variance of product 2 with Var

(d_{2})=2305(d_{2})0.5. So, for d_{2}=3, Var(d_{2})(Unchanged)

~3992 (unchanged). So W_{1}=441, W_{2}=363

Now suppose that one product setup, d_{2} is being targeted to be
cut by 10%, 50%, 70%, and 100% (i.e., r=0.9, 0.5, 0.3, and 0). From
condition (3), 14i will increase for a 10% or a 50% cut, and will
decrease for a 70% or a 100% cut. The new waiting times will
be W_{1}=444.9, 444.6, 415.4, and 1.125; W_{2}=363.1, 366.3, 365.9,
341.9, and 1.125, respectively, for 10%, 50%, 70% and 100% cuts.
Waiting times first grew and then went down as we increased
the amount of cut. Furthermore, an upper bound can be found
by setting first derivative of Wi with respect to di to zero and
solving for di, and plugging it into Wi. In this example, maximum
W_{1}=449.48, maximum W_{2}=369.97, and both occur at d_{2}=2.025,
i.e., at a cut of 32.67%. Furthermore, at a 55% cut (or, r=0.45)
or beyond, both W_{1} and W_{2} drop below their respective original
values of 441 and 363. A setup reduction management team
could find this "good" r from condition (3), and use it for their
planning purposes. Such criticality of choice of r value has not
been stressed in earlier research.

When setup times for all products are cut by 100%, Var(d_{j})=0 and
d_{j}=0 V_{j}. In this case, however, the use of equation (2), we believe,
will erroneously result in an infinite Wi. This is evident since by
taking the limit of Var(d_{j})->0 and d_{j}-O0V_{j}, Takagi (1986, p. 82) has
shown that the explicit form of Equation (2).

For n=2 (see S-Z 1991, Eq. 2.2.8, p. 447) reduces to:

W_{1}= X_{1}E(S)/2(1-P_{1})+(X_{i}P_{2}E(S_{2}) + 2(1-P)2 E(S_{2}))/2(1-P_{2})(1-P_{1}-P_{2})
(1-P_{1}-P_{2}+2p1P_{2})

W_{2}= X_{2}E(S_{2})/2(1-P_{2})+(X_{2}p_{2}E(S_{2}) + X(1-p_{2})2E(S_{2}))/2(1-P_{2})(1-P_{i}-P_{2}+2p_{1}P_{2}) (4)

Equation (4) comparison with Equation (2.2.8) [6] discloses that
W_{i} is not just minimized in (4) but also is finite [7,8].

Lastly, it is important pointing out that Sarkar and Zangwill [2]
used an extraordinary high Var(d_{2})=3992, i.e., a 63.2 is standard
deviation and a C.V of 63.2/3=2106%. After that, attribute the
results of paradoxical to the presence of variance in processing
time and set-up time distribution. However, this might not be
right for all levels of variance. Such as; keeping everything else
same in their example, if we only replace the setup time of
product 2 by:

d_{2}=10/9 with prob 9/10

d_{2}=2 with prob 1/10

with d_{2}=1.2 and Var(d_{2})=0.0711, the results are just the opposite.
With processing times, S_{i}=S_{2}=1/50, we find that W_{1}=1.815 and
W2=1.812; with a faster processing time, S_{i}=1/100 (while keeping
S_{2} fixed at 1/50), W14=1.799 and W_{2}=1.704. Both expected
waiting times decreased. When setup time d_{1} was reduced by 5%
and 50%, W_{1}=1.759 and 142=1.757, and W_{1}=1.258 and W_{2}=1.254,
respectively. Both decreased from their original values of 1.815
and 1.812, respectively. These results show that at a low level of
variance, cutting setup or processing time does not necessarily
increase waiting time.

In the mentioned, example vis-à-vis the Sarkar and Zangwill [2] claim (however reducing average processing time or set-up time) “if variances will not minimize proportionately arrivals will wait longer” the variance was, certainly, fixed. Although in our example does not fault their result of paradoxical, it does, since, determine a research need for characterization of variances ranges or processes for which reduction setup does not or does imply work in process reduction.

- Khan SAR, Dong Q (2015) Case of civic company: The implementation of enterprise resource planning. International Business Research 8: 11.
- Sarkar D, Zangwill WI (1991) Variance Effects in Cyclic Production System. Management Sci 37: 444-453.
- Takagi H (1986) Analysis of Polling System. MIT Press, Cambridge, MA, USA.
- Suzaki K (1987) The Manufacturing Challenge. The Free Press, New York, USA.
- Shingo SA (1985) Revolution in Manufacture: The SMED System. Productivity Inc., Stanford.
- Inman RA, Mehra S (1991) Just In Time (JIT). Applications for Service Environments.
- Conway RW, Maxwell WM, Miller LW (1967) Theory of Scheduling. Addison-Wesley.
- Cooper RB (1970) Queues Served in Cyclic Order: Waiting Times. The Bell System Technical J 49: 399-413.

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