Our global world is under the variety of individual bodies on the division of work. This paper would consider the invisible body-balancing network and economics by a medium approach. This medium approach originated from the Newsboy problem, and would be attained by the invisible hand of market (demand) speed at Chameleon’s criteria. First, our new treatment and condition to balancing are given. Next, a few trial cases are discussed and verified at the series type.
There are a variety of individual bodies on the division of work. This paper would consider the invisible body- balancing network and economics by a medium approach. This medium approach originated from a Newsboy problem [
The traditional balancing problem originates from Ford system, and is essential to the economy of mass production (economics) in the automobile industry [
The related domain is called the line balancing in Industrial Engineering (IE), and is based on the principle of system balancing in the assembly industry, including service types [
In the Toyota system [
We here consider the medium approach to the efficiency vs. muda (loss) problem in the stochastic system balancing, based on the medium inventory that originates from the Newsboy in Operations Research (OR). This paper would be prepared to apply this approach to the SCM/GDP system in the country-like region toward the near future.
Modern society is being formed by the worldwide division of work as we move towards globalization. Since 1776, there is the problem of invisible hand by Smith [
Generally, the body-centered network (SCM/GDP) might be able to be invisibly balanced and cooperated by the demand speed (God hand) and cloud computing [
As an example, let us consider the two- or three-center model consisting of sales, assembly and fabrication centers [
Thus, each unit-optimization in profit gives the total optimization in sum under non-cooperation, and the point (balancing) occurs at near middle lead-time (reliability). This class is called the integral optimization, and might be governed by the Ellipse map and strategy in Matsui [
Our profit is corresponded to the marginal profit/value in Accounting/GDP, and it is similar to the medium criterion in [
The stochastic balancing problem is a class of the Conveyor-Serviced Production Station (CSPS) and its networks [
In the body balancing system, the definition of stochastic balancing is here as follows: A stabling phenomenon of transient, bottlenecked vs. balanced, state of the object system. The balanced solution by this stochastic balancing becomes quasi-optimal.
Recently, the medium approach to the body-balancing system is outlined to SCM type in
The medium criterion,
Now, the Newsvendor’s condition [
where
Then, the balancing goal is given by the following objective function:
where
An optimal condition (balancing) is assumed from the classical inequality and Matsui’s equation
In (3),
Two principles on the medium balancing are here presented and considered. At first, the
in the respective body of entity
Now, the following condition is considered under the demand speed (cycle time),
and the demand speed,
On d-balancing, the following relation is obtained from (6):
Especially, for Poisson service, the optimal condition is
where
These relations are outlined in
and the balancing principle is
from (9) and the classic inequality.
On the lower level, the entity
Now, the following notations are introduced in each
where
For each
From (11), the second balancing principle is obtained as follows:
where the second and third terms of right hand are corresponded to the coordinating of the moving marginal inventory,
The equation (11) is similar to that of progressive control in [
The usual conveyor systems are the two types of the stations with or without stopper. These systems are treated in [
A cost approach to the delay and idleness is seen in [
The Newsboy method to this case [
where the right hand consists of the objective of -th station:
in which
Then, the optimal condition is obtained by a differenciation method in the followings:
The cycle time,
For example, let us
Now, let us apply the simulator of SALPS soft [
Another verification is considered by
total cost | |||||
---|---|---|---|---|---|
1.0 | 469.5706 | 0.8773 | 0.6608 | 0.8541 | 4.146 |
1.1 | 91.20302 | 0.7790 | 0.6818 | 0.7973 | 3.816 |
1.2 | 85.43137 | 0.6692 | 0.6804 | 0.7200 | 3.408 |
1.3 | 84.78923 (SALPS) | 0.5591 | 0.6604 | 0.6324 | 2.970 |
1.4 | 84.88829 (optimal) | 0.4561 | 0.6260 | 0.5423 | 2.536 |
1.5 | 85.45898 | 0.3645 | 0.5813 | 0.4557 | 2.130 |
1.6 | 86.13179 | 0.2862 | 0.5300 | 0.3761 | 1.765 |
Next, let us consider the two-stage supply chain (SCM) of a franchise type in
In the case, the outflow is uncontrollable, and the system is only controllable by inflow.
For this case, the balancing problem is the minimization of the total inventory between suppliers. That is,
The objective (16) is here available in replace of (2).
For this case, the
From
It is them noted that any bottleneck phenomena would be doubtful in July, September and April.
This result would show the effectiveness of medium balancing method, and the hypothesis (3) is ascertained.
This paper summarizes a recent approach (possibility) to the medium (Chameleon’s) balancing from conveyor system toward SCM/GDP-economic system. First, the body-balancing problem was briefly outlined. Next, the unified economics treatment to the physical balancing problem was presented.
Finally, an optimal condition of balancing was pointed out and verified at the view of Matsui’s equation and Chameleon’s criteria. The materials would give a shortcut way to the traditional balancing method, for example, much more than the 2-stage method [
By the further study, the GDP balancing of the country would become probably possible on the base of pro-
month | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|
7000 | 5595 | 7874 | 6632 | 5624 | 8782 | |
M-inventory | 58 (0.4) | 907 (0.5) | 1010 (0.6) | 2314 (0.7) | 1418 (0.5) | 897 (0.5) |
N-inventory | 278 (0.4) | 9(0) | 2057(0.5) | 1542 (0.4) | 1607 (0.4) | 866 (0.4) |
outflow | 7723 | 7318 | 14356 | 18485 | 9122 | 15245 |
inflow | 1059 | 2640 | 9549 | 15710 | 6522 | 8227 |
inventory | 336 | 916 | 3067 | 3857 | 3025 | 1763 |
balance | 78,178 | 84,974 | 54,502 | 47241 | 58,050 | 61,907 |
stock out | 0 | 0 | 0 | 0 | 0 | 0 |
month | 12 | 1 | 2 | 3 | 4 | 5 |
6104 | 10636 | 5856 | 13343 | 12626 | 7510 | |
M-inventory | 1851 (0.5) | 254 (0.5) | 2577 (0.5) | 91 (0.3) | 2307 (0.1) | 2837 (0.5) |
N-inventory | 1490 (0.4) | 1233 (0.4) | 883 (0.4) | 96 (0.4) | 1386 (0.4) | 2207 (0.5) |
outflow | 11,201 | 19,609 | 13,748 | 23,422 | 13,055 | 9904 |
inflow | 8438 | 10460 | 11,352 | 10,266 | 4122 | 6911 |
inventory | 3341 | 1487 | 3460 | 187 | 3693 | 4517 |
balance | 23,779 | 75,988 | 35,552 | 126,559 | 83,958 | 29,870 |
stock out | 0 | 0 | 0 | 0 | 0 | 0 |
gressive and autonomous control of marginal profit/value in GDP networks. This foundation may be derived by changing from the invisible hand to visibility of demand-to-supply speed.