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Ideal Design Process characterization: the impact of preliminary decision-making tools in the consumption of resources and its uncertainty

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Abstract

This study presents a set of definitions and properties that characterize the Ideal Design Process and the resources consumed during this process. As an application of both characterizations, the impact of preliminary decision-making tools in the consumption of resources and its uncertainty is introduced, deriving the conditions that a preliminary decision-making tool needs to satisfy to improve the design process. It is assumed the design process improves when the best design is obtained with a lower consumption of resources (time and money) and with a lower uncertainty, both concepts related to the acquired complexity and the risk. Axiomatic design is studied under this framework, showing evidences that indicate it satisfies this set of properties. Design scenarios where the preliminary decision-making tool deteriorates the design process are also found.

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Abbreviations

AD:

Available design

AO:

Analysis operator

ASO:

Advance synthesis operator

BD:

Best design

BDP:

Best design process

C j :

Set of ADs in the iteration number j

η z :

Relative improvement in variable Z

E :

Expenses

E[X] :

Expected value of variable X

E D :

Design process expenses

E XD :

Design process expenses for configuration X

E DF :

Design process fixed expenses

E XDF :

Design process fixed expenses for configuration X

E DV :

Design process variable expenses

E XDV :

Design process variable expenses consumed by operator X per unit of time

E P :

Non-design expenses

FO:

Filter operator

IDP:

Ideal Design Process

IDP-R:

Replicated Ideal Design Process

J :

Number of iterations

K :

Number of ADs satisfying FO conditions

λ :

The best design

M :

Total number of ADs satisfying FO conditions

μ j :

Solution selected by SO in the step number j

N :

Total number of Ads

NI:

Net income

Ψ k :

kth solution that satisfies FO conditions

R :

Revenues

R&D :

Research and development

SA:

Synthesis analysis configuration

SFA:

Synthesis filter analysis configuration

SO:

Synthesis operator

T :

Time

T D :

Design process time

T XD :

Time required by the operator X per iteration or by the configuration X for the design process

UDP:

Utopic design process

Var[X]:

Variance of variable X

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Authors and Affiliations

  1. Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros, 3, 28040, Madrid, Spain

    Oscar Lara-Rapp & Efrén M. Benavides

Authors
  1. Oscar Lara-Rapp
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  2. Efrén M. Benavides
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Corresponding author

Correspondence to Efrén M. Benavides.

Appendices

Appendix 1: Projected income statement

The next points are a summary of the basic aspects of a projected income statement as per the International Accounting Standards Board (2010). All of them should be referred to the life cycle of the product. More information about the projected income statement can be found in Pinson (2007).

  • Operating section

    • Revenue (+) Cash inflows or growing of assets.

    • Expenses (−) Cash outflows, use of assets or increment of liabilities.

      • Cost of goods sold (COGS) Cost of the units sold and produced. Production related costs.

      • Selling, general and administrative expenses Non-production related costs.

        • Selling expenses Expenses needed in order to sell the product (salaries of salesmen, deliveries, advertising, trips…).

        • General and administrative expenses Expenses needed in order to manage the business (executives’ salaries, insurances, office rents…).

    • Depreciation/amortization (−) Allocation of the costs of tangible (depreciation) or intangible (amortization) assets.

    • Research and development expenses (−) Expenses related to R&D activities.

  • Non-operating section

    • Other revenues or gains (+) Revenues that come from the product’s activities that are not the main ones (e.g., income from patents, goodwill). It also includes profits that are either unusual or infrequent (e.g., profit from fixed assets sale)

    • Other expenses or losses (−) Expenses that come from the product’s activities that are not the main ones

    • Finance costs (−) Costs of borrowing.

    • Income tax expense (−) Taxes to be paid.

  • Net income The result of all the previous statements, adding the ones indicated with (+) and subtracting the ones indicated with (−)

Appendix 2: SA uniform distribution

The probability of finishing the design process in the step j (event C) is the same as the probability of selecting the BD in the step j (event A) conditioned by the probability of not selecting the BD in the j − 1 first solutions chosen by SO (event B).

$$P(C) = P(B)P(A)$$
(47)

Event A Initially there are N ADs that can be picked up by SO. It is unknown in what order they are going to be selected, however the design process will be finished only once the BD is selected. In the iteration number j, the size of the set of all the ADs is |C j | = N − j + 1, so the probability of selecting the BD in the iteration number j is P(A) = 1/(N − j + 1).

Event B The j − 1 solutions that have been selected before the BD is selected in the j iteration drives to the following number of possible combinations of selecting j − 1 solutions among N − 1:

$$r = \left( {\begin{array}{*{20}c} {N - 1} \\ {j - 1} \\ \end{array} } \right)$$
(48)

However, the possibilities of selecting j − 1 solutions are:

$$s = \left( {\begin{array}{*{20}c} N \\ {j - 1} \\ \end{array} } \right)$$
(49)

Putting together both results we get that the probability of the event B is:

$$P\left( B \right) = r/s = \frac{{\left( {\begin{array}{*{20}c} {N - 1} \\ {j - 1} \\ \end{array} } \right)}}{{\left( {\begin{array}{*{20}c} N \\ {j - 1} \\ \end{array} } \right)}}$$
(50)

Event C Using the results for events A and B:

$$P\left( {J = j} \right) = P\left( C \right) = P\left( B \right)P\left( A \right) = \frac{{\left( {\begin{array}{*{20}c} {N - 1} \\ {j - 1} \\ \end{array} } \right)}}{{\left( {\begin{array}{*{20}c} N \\ {j - 1} \\ \end{array} } \right)}}\frac{1}{N - j + 1} = \frac{1}{N}$$
(51)

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Lara-Rapp, O., Benavides, E.M. Ideal Design Process characterization: the impact of preliminary decision-making tools in the consumption of resources and its uncertainty. Res Eng Design 26, 97–119 (2015). https://doi.org/10.1007/s00163-015-0188-x

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