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doi: 10.24411/2409-5419-2018-10191
THE OPTIMIZING METHOD OF REPAIRING ALLOCATION FOR ARMING SAMPLES AND MILITARY EQUIPMENT TO CARRY OUT RESOURCESREGENERATIVE REPAIRING ACCORDING TO THE TECHNICAL CONDITION
ROMAN V. DOPIRA1 DMITRY YU. BREZHNEV2 DMITRY V. YAGOLNIKOV3 VADIM B. SHAROGLAZOV4
Information about authors:
PhD, Full Professor, Senior Research Officer of the Military academy of aerospace defense of Military Space Academy, Tver, Russia, rvdopira@yandex.ru
2PhD, Doctoral Candidate of the Military academy of aerospace defense, Tver, Russia, dimanbreg@mail.ru
3PhD, Lecture at the Department of tactics and arming radio engineering forces of the Military academy of aerospace defense, Tver, Russia, yagolnikov_dv@mail.ru
lecturer at the Department of the organization of operation and technical providing arms of military and special equipment of the Military Space Academy, St Petersburg, Russia, sh.vadim.b@yandex.ru
ABSTRACT
The lag in new arming samples and military equipment production due to lag of their wear makes the resourcesregenerative repairing according to technical condition more necessary that provide technical preparedness level maintenance and required equipment margin. The key aspect of resourcesregenerative repairing according to technical condition realization is the need for military equipment repairing and repairing authorities' possibilities reconciliation procedure. The planning of repairing becomes more difficult for the planning of arming and military equipment replacement, so this task requires mathematical solution methods. The peculiarity in solving this task is the fact that there are objects with different repair size and repairing possibilities among all the objects of this kind both in stationary and army conditions and repairing authorities are mobile and stationary subdivisions with different productive capabilities. The task is to find out how to distribute military equipment samples between repairing authorities so that the costs would be minimal at a certain planning point. In formalized shape this is a combinatorial optimization task in mathematical optimization area which is characterized as generalized assignment problem with additional conditions and is NP-complete. The algorithm of distribution is based on solution of the Boolean linear programming task using the Hungarian method with repair facility's queuing recalculation. The task decomposition in several private subtasks that are accomplished in a chain is suggested to reduce the tusk dimension. Such a method allows us to get an optimal plan of resourcesregenerative repairing according to technical condition realization with minimal costs and on time. The programming task realization and the suggested algorithm will allow getting an instrument of Event Management in resource replacement to a variable degree that will provide repairing authorities management.
KEYWORDS: arming and military equipment of air defense; repairing according to technical condition; equipment management; Boolean linear programming, Hungarian method.
For citation: Dopira R.V., Brezhnev D.Yu., Yagolnikov D.V., Sharoglazov V.B. The optimizing method of repairing allocation for arming samples and military equipment to carry out resourcesregenerative repairing according to the technical condition. H&ES Research. 2018. Vol. 10. No. 6. Pp. 94-99. doi: 10.24411/2409-5419-2018-10191
Army equipping with modern military equipment samples requires considerable financial allocations. The country's budget capacity makes us search for solutions that allow arming and military equipment maintenance, technical condition and military equipment life margin. At the same time it is rather difficult nowadays to reach the desired level of new military equipment in short time period considering industrial capacity and country's budget allocation limits. Especially concerning high-tech arming samples which include air defense system and radar stations that are operational with air defense troops. That's why we need a complex approach in the condition of defense allocations that allows finding a sensible compromise between industrial capacity for new military samples delivery and troops and service organizations' capacity to maintain available equipment according to resource margin included.
The military equipment management is one of the most important management operation system functions and includes several tasks, the main of them are:
1) planning, order and organization of military equipment delivery as part of State arming program and State defense order;
2) planning, organization and control of the resource rate put into action in military equipment in all kinds of storage included;
3) planning, organization and control of resources regenerative repairing realization;
4) organization of working military equipment life extension with operating time close or equal to the appointed resource before resources regenerative repairing realization (retirement).
In this article, we consider one of the solutions to the third task — planning, organization and control of resources regenerative repairing realization.
To solve this task in military equipment repairing system that is a subsystem of technical service and repairing system a regenerative system of air defense military resource was organized and works now.
A regenerative system of air defense military resource is multilevel and is a body of interrelated performers, facilities and documentation used for resources regenerative repairing realization.
The structure of the regenerative system of air defense military resource allows operation management authorities to plan and to organize different variants of resources regeneration differing in resources regenerative level, repairing location, enlisted performers, facilities and documentation:
1. Variants with complete and close to complete arming and military equipment resources regeneration performing capital resources regenerative repairing (with or without modernization) in stationary institutions in-house using their funds, operational documentation, construction repair documentation for capital repair realization, engineering construction documentation while carrying out modernization and defense in-
dustry bulletins. Stationary institutions are industrial establishments (institutions-developers and institutions- manufacturers of arming and military equipment) and defense-industrial sector repairing institutions for short.
2. Variants with partial military equipment resources regeneration performing repairing according to technical condition:
- in stationary institutions in-house using funds of operational documentation institutions, repair documentation and defense industry bulletins;
- in military equipment operation places using force-account mobile repairing teams ability of stationary institutions, circulating and reserve funds of institutions or force-account operational staff and repairing institutions ability with or without mobile repairing teams ability of stationary institutions using military equipment, means of stationary and mobile workshop repair in military units, operational documentation, repair documentation and defense industry bulletins.
All the resources regenerative repairs are planned and can be performed both according to age repair and technical condition.
Note that the lag in new arming samples and military equipment production due to lag of their wear makes the resources regenerative repairing according to technical condition more necessary, especially applied to the military equipment samples that have already been routinely capitally repaired. The idea of resources regenerative repairing according to technical condition is to perform repairing service that are directed to technical samples work capability repair and partial resource replacement according to factual technical condition of resource elements [1]. We understand a resource element here as an element of military equipment sample the nonremovable defect of which generally determines the sample limiting state and its lifetime generally determines military equipment sample lifetime. The military equipment sample has several resource elements, as a rule, every of them limits its lifetime on the whole.
One of the resources regenerative repairing realization key problems is the matching procedure of need for repairing military samples after technical diagnosis and repairing authorities' capability. At the same time repair planning becomes more difficult for necessity to perform both army repairs (in military equipment operation places using force-account mobile repairing teams' ability of stationary institutions from repairing authorities) and depot repair connected with military equipment relocation to the places of repair realization in stationary conditions. High dimension of event planning task involves mathematical methods of decision-making for resources regenerative repairing according to technical condition organization [2].
Now we will formulate the task solution specification of the military equipment optimal distribution between repair authorities while repair planning.
Let the range of repair authorities be R, each of which includes several mobile repairing teams B and one stationary repair section for military equipment samples repairing in depot conditions.
Let according to results of technical diagnosis determine the list of the samples N which have resource elements in a damage wear condition. At the same time we know the damaged resource elements nomenclature of every «-sample and the elements number of every nomenclature ¡1. Note that the range of resource elements nomenclatures ¥ includes subset of such resource elements F, repair of which is possible only in depot conditions F œ ¥. Other elements of set ¥ make the subset E = ¥\F and can be repaired both in depot and army conditions.
Thus the set of military equipment samples N that needs repairing is represented by subsets N (the samples are repaired only in depot conditions) h N2 (the samples are repaired both in depot and army conditions): Nx œ N, N2 œ N, N2= N\Nv
The task is to search for such a variant of military samples distribution between repairing authorities and mobile repairing teams whereby we have minimal costs connected with repair realization at this planning stage.
In a formalized shape we can perform the task of optimal military samples distribution this way: there is a set of repair samples N so that N = N fW2. At the same time Nl={nm}, N2={nk}, where nm—complex of set N elements, nk—complex of set N2 elements; there is the set of repairing channels Q = {q1, q2, ...q., ... q}, at the same time the capacity of the set |Q| can be determined by
1 = * = £ Br + R,
(1)
where Br — the quantity of mobile repairing teams in r-th repairing authorities.
We need to distribute samples set N between repair channels Q so that the whole cost of repairing C be minimal
C (X ) = Z Ê [ V„q ]-— mm,
n=1 q=1
to certain constraints
N \Q\
Шх t !< "
nq nq J I
n=l q=l
N _
Z xnq = 1 v? = 1
(2)
(3)
(4)
where X = x I _ _ — a sought-for matrix of functions
II "q\\n=1,N; q =l,s
for military equipment repair realization by repairing authorities the elements of which are determined in the form of Boolean variables:
J1, nominating n - th sample q-th repair canal "q 10, otherwise
cq — repair cost of «-th military sample in q-th repair channel considering logistic operations connected with relocation of samples or mobile repairing teams; Tq — time spending for repair realization of «-th military sample in q-th repair channel considering logistic operations connected with relocation of samples or mobile repairing teams; Tp—duration of planning period.
The limit (3) provides with repair carrying-out within the directive time and means that one repairing channel can be designated to repair a number of military equipment samples during a certain planning period Tp = [0, T] considering relocation time (of samples or mobile repairing teams) and repairing time. The limit (4) means that the repairing of each «-th military sample can be performed only by one q-th repair channel.
Thus, the formulated task is formalized and is in mathematical form: the desired function and its corresponding limits are discovered.
In a formalized shape the task is the problem of combinatorial optimization in mathematical optimization area. We can also characterize it as a generalized assignment problem with additional limits. It is NP-complete [3] and to solve such tasks specific algorithms based on combinatorics, graphs, etc are worked out [4,5].
We can solve formulated task using exact methods, such as branch and bound method [6-9] or Hungarian method [10-12].
In case of using branch and bound method before the start of branching and tree traversal assessment we recommend to perform branching levels presorting considering limit (3) [13]. Branching levels presorting is especially necessary for high task dimension as it helps to reduce level exhaustion. Nevertheless, one of the branch and bound method disadvantages is high computational complexity and computational burden [14] as one should keep in mind the results of prior level tops assessment while traversing the tree.
The algorithm of Hungarian method allows solving the task in polynomial time [15].
We can convert the task (1-5) into Boolean linear programming task using the Hungarian method for its solution.
In this case the main difficulty in working out the algorithm of its solution is connected with the presence of repairing specification subsets in the range of samples N and the range of repair channels Q which limit the usage of linear programming algorithms and also limits (3) and (5) where repairing queue size is specified in each repairing channel in planning time.
Thereby the task decomposition in several private sub-tasks that are accomplished in a chain is suggested to reduce the tusk dimension.
At the first stage, we consider elements of N set the repairing necessity of which is defined by resource elements
r=1
n=1
damage wear of nomenclature F. At this stage, we solve the task of sample distribution between repairing authorities in the following sequence:
Step 1. Input data about allocated samples and repairing channels of stationary type (of sets N and R).
Step 2. Formation of matrix input data \cn
and
"qlln=1, Nl;q =1,R
sized N xR that match cost and duration of re-
t _ _
II "qlln=1, N1;q=1, R
pairing between samples and stationary-typed repair channels.
Step 3. The set-up of initial position allocation cycle-counter (iterations) (n = 1) and preparing data for the first military samples distribution between stationary-typed repair channels.
Step 4. Solving of the Boolean linear programming task (2)-(6) using Hungarian method [6].
Step 5.Testing conditions in which the quantity of distributed military samples corresponds the quantity of repair channels:
if N1 = K, then we found the solution, go to step 12;
if N < K, then the solution isn't found, find the quantity of free channels (R(n+1) = R-Rdis(n)) for their further distribution at the second stage and go to step 12;
if N > K, then military samples queue is formed, test condition (3) and if it works go to the next step. If it doesn't work the rest of the samples are to be repaired at the next planning stage.
Step 6. Choose one allocation for every repair channel for derived solution.
Step 7. Exclude the derived set of military samples allocations from the input set and form a new set of samples for further distribution iteration (Nj(n+1)= N^Nfii)).
Step 8. Correction of matrix sizes ||cnJ| and ||tmJ for further distribution iteration. Thereby exclude lines from matrix according to step 7 and columns if condition 3 doesn't work for corresponding repair channels.
Step 9. Recalculate repair time of each sample for each repair channel in matrix |xnJ| adding military samples repair time distributed to these repair channels during current iteration.
Step 10. Go to further iteration (n = n + 1).
Step 11. Go to step 4.
Step 12. Stop calculating. Form the final variant of samples distribution plan between stationary repair channels.
At the second stage we consider elements of N2 set the repairing necessity of which is defined by resource elements damage wear of nomenclature E and elements of Q set, the list of which is formed according to results of the first stage.
Military samples distribution sequence is analogic to the first stage sequence with refinements in some steps.
At the first step the quantity of set Q elements is defined according to
In this case we form the list of repair channels which include not only mobile repairing teams but also stationary repair authorities from samples that aren't used for repairing of N2 set. At the second step we form matrix input data
\\cm\\ — — and x„
II "qlln=1,N2;q =1,S
sized N2 x S. Note that while
S = Z Br + R
(6)
nq \\n=1,N2;q=1,S
forming this matrix in cells corresponding to samples repairing in stationary repair channels we should indicate cost of this repairing and repair time considering military equipment delivery duration to the repair location. Knowing in advance that repair cost in stationary conditions is much more expensive and a longer time than army repair, the algorithm will automatically give assignments to stationary repair channels in case of mobile repairing teams deficit at the bottom of priority.
The rest of the steps are accomplished analogically.
At the third stage we unite derived assignments and form a free repair plan.
Thus the introduced method of task solution allows us to get an optimal plan of resources regenerative repairing according to technical condition realization with minimal costs and on time.
The programming task realization and the suggested algorithm will allow getting an instrument of Event Management in resource replacement to a variable degree (depending on factual condition of resource elements) that will provide mobile repairing teams and stationary industrial repair authorities management.
The suggested method considerably reduce the time of repair planning problem solution and can be used in automatical system of technical troops maintenance management.
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МЕТОД ОПТИМИЗАЦИИ РАСПРЕДЕЛЕНИЯ ОБРАЗЦОВ ВООРУЖЕНИЯ И ВОЕННОЙ ТЕХНИКИ ПО РЕМОНТНЫМ ОРГАНАМ ДЛЯ ПРОВЕДЕНИЯ РЕСУРСОВОССТАНАВЛИВАЮЩИХ РЕМОНТОВ ПО ТЕХНИЧЕСКОМУ СОСТОЯНИЮ
ДОПИРА Роман Викторович,
г. Тверь, Россия, rvdopira@yandex.ru
БРЕЖНЕВ Дмитрий Юрьевич,
г. Тверь, Россия, dimanbreg@mail.ru
КЛЮЧЕВЫЕ СЛОВА: вооружения и военной техники противовоздушной обороны; ремонт по техническому состоянию; управление ресурсом техники; линейное булево программирование; венгерский метод.
ЯГОЛЬНИКОВ Дмитрий Владимирович,
г. Тверь, Россия, yagolnikov_dv@mail.ru
ШАРОГЛАЗОВ Вадим Борисович,
г. Санкт-Петербург, Россия, sh.vadim.b@yandex.ru
АННОТАЦИЯ
Отставание темпов производства новых образцов вооружения и военной техники от темпов их старения обусловливают необходимость более широкого применения ресурсовос-станавливающих ремонтов по техническому состоянию, обеспечивающих поддержание уровня технической готовности и требуемый запас ресурса техники. Ключевым вопросом проведения ресурсовосстанавливающих ремонтов по техническому состоянию является процедура согласования потребностей в ремонте образцов вооружения и военной техники с
возможностями ремонтных органов. Планирование ремонта осложняется большой размерностью задачи планирования мероприятий по восполнению ресурса вооружения и военной техники и требует применения математических методов её решения. Особенностью решения задачи является наличие в составе множества распределяемых объектов ремонта образцов с различным объемом ремонта и возможностью его проведения, как в стационарных, так и в войсковых условиях, а ремонтные органы представлены подразделениями
в мобильном и стационарном вариантах с различными производственными возможностями. Задача заключается в поиске варианта распределения образцов вооружения и военной техники между ремонтными органами, при котором обеспечиваются минимальные экономические затраты, связанные с проведением их ремонта на заданном интервале планирования. В формализованном виде задача представляет собой задачу комбинаторной оптимизации в области математической оптимизации,характеризуется какобобщеннаязадачаоназначениях с дополнительными условиями и является NP-полной задачей. В основу алгоритма распределения образцов вооружения между ремонтными органами положено решение задачи линейного булевого программирования с применением венгерского метода, дополненного процедурой пересчета длины очереди на ремонтных предприятиях. Для снижения размерности решаемой задачи предложено провести ее декомпозицию на ряд частных подзадач, выполняемых в определенной последовательности. Представленный метод решения задачи распределения образцов вооружения и военной техники позволяет получить оптимальный план проведения ресурсовос-
станавливающих ремонтов по техническому состоянию при минимуме затрат на их проведения в требуемые сроки. Программная реализация данной задачи с использованием предложенного алгоритма позволит получить инструмент управления мероприятиями по восполнению ресурса различной степени, обеспечивающий рациональное использование ремонтных органов.
СВЕДЕНИЯ ОБ АВТОРАХ:
Допира Р.В., д.т.н., профессор, старший научный сотрудник Военной академии воздушно-космической обороны имени Маршала Советского Союза Г.К. Жукова;
Брежнев Д.Ю., к.т.н., докторант Военной академии воздушно-космической обороны имени маршала Советского Союза Г.К. Жукова; Ягольников Д.В., к.т.н., преподаватель кафедры тактики и вооружения РТВ Военной академии воздушно-космической обороны имени маршала Советского Союза Г.К. Жукова; Шароглазов В.Б., преподаватель кафедры организации эксплуатации и технического обеспечения ВВСТ Военно-космической академии имени А. Ф. Можайского.
Для цитирования: Допира Р.В., Брежнев Д.Ю., Ягольников Д.В., Шароглазов В.Б. Метод оптимизации распределения образцов вооружения и военной техники по ремонтным органам для проведения ресурсовосстанавливающих ремонтов по техническому состоянию// Наукоемкие технологии в космических исследованиях Земли. 2018. Т. 10. № 6. С. 94-99. doi: 10.24411/2409-5419-2018-10191 (Англ.)
