О принятии решений по вопросам альтернативного проектирования

Голенко-Гинзбург Дмитрий Исаакович

доктор технических наук, профессор кафедры управления и организации производства Университета Бен-Гуриона в Не- геве (г. Беер-Шева, Израиль); e-mail: Этот адрес e-mail защищен от спам-ботов. Чтобы увидеть его, у Вас должен быть включен Java-Script ; Любкин Сергей Михайлович

канд. техн. наук, доцент кафедры проектного и инновационного менеджмента Московского государственного университета экономики, статистики и информатики (Москва, Российская Федерация); e-mail: Этот адрес e-mail защищен от спам-ботов. Чтобы увидеть его, у Вас должен быть включен Java-Script ;

Ницан Свид

преподаватель кафедры управления и организации производства, Ариэльский университет (Ариэль, Израиль), преподаватель кафедры менеджмента факультета общественных наук, Университет Бар-Илан (Рамат-Ган, Израиль); e-mail: Этот адрес e-mail защищен от спам-ботов. Чтобы увидеть его, у Вас должен быть включен Java-Script

Статья получена: 30.04.2015. Рассмотрена: 05.05.2015. Одобрена: 14.05.2015. Опубликовано online: 30.06.2015. © RIOR Аннотация. Одна из основных проблем альтернативного сетевого планирования сводится к определению оптимального варианта разработки рассматриваемой симуляционной программы. В статье предлагаются критерии выбора оптимального варианта для случая однородной альтернативной сети, описанной нами в публикациях [1—3].

Ключевые слова: однородная альтернативная стохастическая сеть, полные и объединенные варианты, оптимальный вариант принятия решений, многовариантная оптимизация, показатель оптимальности.

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optimality criterion, the design decision-maker should direct his efforts to carrying out measures which ensure the most beneficial conditions of executing the determined optimal variant and those ones being close to it.

2. The general approach

The most common situation in practice deals with the case when the quality of variants should be assessed by several parameters (partial criteria) of the simulated process. With the latter in mind consider the following two main formalizations of the regarded problem.

I. Let us be given n different criteria (parameters) I₁,I₂> - >I_n ^t0 assess m alternative variants Вj,BВ_m of a plan to carry out a particular set of activities. Note that each criterion /, may be calculated in the alternative network on the basis of activity estimates comprisingy-th full variants of the simulated program. To calculate values {/,} one may apply the alpha-algorithm outlined in [2].

From the set of possible variants there should be chosen a single one satisfying the following requirements:

• - the chosen variant should meet to the greatest extent all accepted criteria, i.e., it should provide for the extreme value of a metrics which has been defined in a certain way in the criteria space I_bI₂,...,l_n
• — the numerical metrics variation corresponding to the chosen variant should be the minimal one when consecutively applying the criteria in any combination and in a arbitrary order. The latter requirement reflects the need to ensure proper flexibility of the plan, i.e., the least sensitivity of the relative variant’s quality regarding possible amendments of the adopted optimality criteria.

To determine the regarded metrics consider an «-dimension criteria space, while on each axis (assume the i-th axis representing the i-th criterion) indicate the corresponding criterion’s value for the y'-th variant,у = 1,2,...,m, of the design program.

In the thus defined space determine for each variant a point such that each of its coordinates corresponds to the optimal value of every criterion taken apart. It can be well-recognized that this point is nothing but the “ideal” target that the system should seek to achieve while executing a particular full variant. Obviously, variants corresponding to such points exist, in principle, only for plans being characterized by functionally dependent criteria. Introduce therefore the concept of a quasi-optimal plan for which the metrics value delivers an extremum in space I_hI_2>...,I_n. In case of a group of criteria which simultaneously maximize or minimize a certain quality objective, a quasi-optimal plan would correspond to either minimal or maximal distance from the coordinate origin. Besides the point corresponding to optimal criteria values (the “ideal”), each variant is also characterized by sub-optimal values, which turn out the regarded variant to become optimal only in case when planning and control are carried out by a single and pre-determined criterion/*, к = 1,2,...,«. It can be well-recognized that the distance between each pair of sub-optimal points characterizes the variance of the optimized criteria /₇,/₂,in the transition process from delivering the optimal value to one of them to delivering the optimum to another one. Further on, those distances reflect the closeness of the considered variant to its “ideal”. Indeed, when referring to the geometrical interpretation of the considered problem (Fig. 1), we may see how shrinking the distances between sub-optimal points brings the latter closer together to the “ideal”. Besides, the lower the regarded distances are the more probable diminishing the variety of the optimized parameters becomes, if the analyzed dependencies are based on smooth and convex functions. In other words, the lower the pair-wise distances between adjacent sub- optimal points are, the more flexible the considered full program variant becomes (plan B). This flexibility reveals itself in the fact that plan Bj does not change its parameters significantly when amending criteria {/, } in the process of on-line control for a design program to create a complicated system.

Figure 1. Graphical representation of the optimal variant choice

- dy— the sub-optimal value of the i-th

criterion for the y'-th variant on condition that the //-th criterion assumes value a^, ju = 1,2,...,/- 1,/ + 1

• — rjj — the distance from “ideal” Aj to the middle of the segment connecting a pair of sub-optimal points of
• (a^ а type.

VIj ’^w2j y>^uijjy9^unj )

It can be well-recognized that there are altogether n points being the middles of segments connecting sub-optimal criteria values when n > 2, and there is one such point for и = 2. Keeping up to the introduced designations, the coordinates of those points may be determined as

The structure of objective F for the quantitative assessment of they-th variant’s quality in compliance with both above mentioned requirements might be represented then in the following way:

where

and

The quasi-optimal variant to be recommended for the regarded complicated system design program and the one whose implementation should be stimulated by creating the most suitable conditions, would be the one delivering the extreme value to the considered objective, i.e.,

Substitute the relations for the segments middles to determine the distances of the latter from the «ideal» (see (2)):

It can be well-recognized that applying the above outlined method not only enables determining all possible ways of reaching the program’s final target but facilitates also choosing from a set of particular design activities the variant which is the least sensitive to environmental conditions changes. Under these circumstances prediction by means of the alternative network model becomes an active function of the entire process to plan and control design of a new complicated system under conditions of stochastic indeterminacy.

References

• 1. Golenko (Ginzburg) D.I., Livshitz S.E., Kesler S.Sh. Statistical Modeling in R&D Projecting. Leningrad, Leningrad University Press, 1976. (in Russian).
• 2. Golenko-Ginzburg D. Stochastic Network Models in R&D Projecting. Voronezh, Nauchnaya Kniga, 2010. (in Russian).
• 3. Golenko-Ginzburg D., Burkov V, Ben-Yair A. Planning and Controlling Multilevel Man-Machine Organization Systems under Random Disturbances /Ariel University Center of Samaria. Ariel, Elinir Digital Print, 2011.

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