In manufacturing, lot-sizing evolution from mass-flow production of abundance to high-variety, low-volume production, ordered-accumulation forms by ordered-entry array, and input/output issues related to traditional GDP are all well-known. The wealth-additive approach, while different, presents a possibility of overtaking the theory of A. Smith.

The so-called accumulated form in this paper can be considered a wealth-additive scheme seen in a world with ordered entry-like ordering and look-ahead policies (Matsui, 1981, 2005) . We previously highlighted the win-win & sharing principles as a wealth-additive approach in 2017 (Matsui, 2018) . This is the win-win situation of the single item in Figure 1 1) (a) income Z (income) = number of people L (time) maximizing wealth, and from Figure 1 2), Z = L as the former Nash equilibrium solution for a middle-income society in lot-sizing of multiple items.

In addition, we know that 3) the formation of vertical plane (sharing) = horizontal plane (balancing) of the OE system is a condition of shared balancing (Matsui, 2018) . Figure 1(c) shows a system (non-independent) that satisfies both (a) and (b) for three or more parties, which is useful for examining operational balance (Matsui, 2018) .

Sharing of balance at QC series(Q<1) busy rate:

income

(revenue)

order

(arrange)

Recently, GDP (efficiency) alone has proven insufficient to measure the richness of life in relation to the SDGs, with attention focused on indicators of “happiness” and “satisfaction,” which were thought to be useless (Nomura Research Institute, 2022) . This kind of index is also based on behavioral science (motivational) knowledge, and the identification of the relationship between motivation for work, waste, and productivity. More recently, our research into the science and modality of artificial bodies has empirically supported this efficiency vs. waste criterion of 0.6 vs. 0.4.

Recently, there has been an interdisciplinary focus on Science ZERO (NHK)’s “Science of Emotions” (May 2022). In a world where the body and mind are connected, “happiness is the maximum value of ‘empathy’ (systematic empathy).” In other words, humans have a simulation link between their brains (external) and bodies (internal) called the “insular cortex” in the prefrontal cortex, which depends on interoceptive sensitivity (IS).

This phenomenon has also recently been attracting attention from a behavioral science perspective. The Nomura Research Institute (NRI), a research organization, has introduced “consumer finance” as a new study of affluence (Matsui, 2020) . This is the degree to which consumers perceive a benefit (“dopamine” reward prediction error, RPE), Figure 2, which is the amount consumers are willing to pay for goods and services minus the actual price. In last year’s survey, the NRI combined GDP and consumer finance to explain and analyze “life satisfaction.”

For this mechanism, we are familiar with look-ahead logics “(error (delay)” minimization) (Matsui, 2005) known from research on conveyor systems (CSPS). The former points out that recent digitalization contributes to life satisfaction, seeking out the correlation between wealth and happiness and just what constitutes DX. With this behavioral science (motivation) approach, we will focus on mitigation issues (angles) such as waste and diversity from an eco-entropy perspective, using traditional inter-industry issues related to GDP as examples.

Note that the effect of mitigation belongs to a linear relation of delay (error) and overflow (lost) of “look-ahead” price (LAP) type (Matsui, 1981) .

The concept of eco-entropy in man-made bodies has already been discussed along with Ternary SW (Matsui, 2023) . For example, the profit formula is as follows.

E C ( input ) + E N ( output ) = E R ( goods ) (1)

The relaxation type in this case is a kind of flow number management formula with the sustainable development value given as SDV. It is expressed from Figure 3 as

E C ( input ) + E N ( output ) = E R ( goods ) + M P ( SDV ) (2)

Here, EN (output) corresponds to the value at the end of the previous period and is considered different from Gross Domestic Product (GDP).

In the wealth-additive approach of the flow number management formula, a mitigation formula is recommended for SDP (MP). As such, since MP > 0 can be assumed, relaxation can generally be expressed using the following formula.

E C + E N < E R + M P ( > 0 ) . (3)

Eco-entropy currently calls for the pursuit of sustainability (lowering) of the individual entropy of man-made bodies. Here, individual entropy is used as an individual value and restraint application, which considers various expressions such as constraint, redundancy, complexity, diversity, and contradiction.

While it serves as a measure of sustainability, schemes that pursue a certain entropy mass (state), particularly eco-entropy, are pursued with a certain marginal utility in Figure 4. Regarding entropy, while the rules for expanding this are generally known, together with restrictions (redundancy/waste), and diversity, entropy enables the individual to flourish, consuming high energy resources such as solar power and fossil fuels. Moreover, in an open system (an environment where heat is exchanged with the outside), this can be lowered by buffers, food load, and the like.

However, in a two-variable system, variables X and Y generally share information T ( X , Y ) > 0 (non-independent), and are expressed as:

H ( X ) + H ( Y ) = H ( X , Y ) + T ( X , Y ) (4)

However, where this is independent, it is expressed as T ( X , Y ) = 0 , H ( X ) + H ( Y ) = H ( X , Y ) (Attneave, 1959) . In section 3.1, this case was considered as X → E C , Y → E N . Note that in traditional cost accounting, this cost and profit are standardized and treated as independent.

Another possible wealth-additive approach that this paper addresses involves eco-entropy 1) versus mitigation of interindustry relations and 2) involving traditional input-output issues, with this section seeking a high-level (macro) approach to GDP vs. SDG. This paper focuses on and provides insights regarding traditional input-output mitigation approaches, especially from the perspective of the latter SDGs.

Figure 5 presents and compares two methods, 1) the buffering criterion and 2) Matsui’s formulation criterion. The former is expressed as endogenous + exogenous = goods, and in this case, production = distribution corresponds to the so-called GDP, which is already practical and can be reduced to the pair map problem. The latter involves geometrically maximizing the area of a square. In the next section, we consider some numerical examples.

Figure 6 shows a numerical example of Figure 5(b). From Figure 6, it is

noteworthy that the axes of monotonically decreasing economy Z and monotonically increasing reliability L intersect, and that heterogeneity, not homogeneity, maximizes richness (dynamic pricing principle). This crossing point SDP is considered to be corresponding to the (sustainable) marginal point (Z = L), SMP, in Figure 6.

In the future, with the wealth-additive approach from Figure 1, an ideal equilibrium point (Z = L) that maximizes (perpendicularly) the product of economy (LAP, Z), and reliability (RPE, L) is anticipated on eco-entropy. This means that the intersection angle δ in Figure 6 should be hetero (diversity) and maximize orthogonality. In addition, although Figure 5 and Figure 6 in this section lack the low-order (microscopic) approach (equivalent to nano), (Figure 5), effective development from Nomura Research Institute (2022) to dynamic 3D integrated design including supply and demand speed system (d, m) is expected.