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5ТЕХНИЧЕСКИЕ НАУКИ
MATHEMATICAL MODELS FOR THE MATERIAL SUPPLY MANAGEMENT BASED ON THE INTEGRATED LOGISTICS SUPPORT APPROACH
Nguyen Thanh Duong,
Le Quy Don Technical University Hanoi, Vietnam Nguyen Trung Kien, Nguyen Phu Vinh Le Quy Don Technical University Hanoi, Vietnam DOI: 10.31618/nas.2413-5291.2021.1.69.457
ABSTRACT
Integrated Logistics Support (ILS) is disciplined and unified management including activities in product life cycle management to create a product maintenance system (MS) to support the product throughout its intended life cycle at an acceptable cost. Along with information models combining product descriptions such as breakdowns, fault trees and methods of restorations, etc., mathematical models considered effective tools to get optimal results are proposed. The paper will present mathematical models, which play important roles in assessing and estimating material demand (spare parts), for the material supply management. These models are applied, in different levels of the ILS system, to the direct calculation of the material demands for scheduled and unscheduled maintenance
Keywords: spare parts demand, unscheduled maintenance, scheduled maintenance, mathematical models.
Introduction
Integrated Logistics Support (ILS) is disciplined approach that influences the product design and develops the Support Solution to optimize supportability and Through Life Finance; it delivers the Initial Support Package and ensures continued optimization of the Support Solution in light of product modifications and changes in operational use and requirements [5, p.3]. Practically, ILS activities create a product maintenance system (MS) which can be considered as a multi-level system with the organizational hierarchy (e.g. operational level, intermediate level, depot level, etc.) and material supply management hierarchy (e.g. stock for operational level, intermediate level; stock for a specific location, city, region. etc.). The ILS purpose is minimizing product life cycle cost meanwhile still achieving a high level of availability. To this end, the general task is to seek solutions to the issues such as how many organizational levels are needed, what and where to do the work, which restoration methods are employed, etc. These levels, methods, and scopes of work all require material supply planning which involves the following decisions:
- assessment of the spare parts and material demand for scheduled and unscheduled maintenance for a certain period of operation;
- estimation of the nomenclature and volume of spare parts/ materials for the initial period of operation;
- determination of the nomenclature and volume of spare parts and materials for the current periods of operation in accordance with the accepted structure of the maintenance system;
- description of delivery procedures and sources of items;
- recommendation on storage and transport capacities with their distribution at maintenance levels;
- recommendation on the use of various methods for the identification of items.
This paper aims to analyze and apply mathematical models to material supply management which helps to reach ILS system goals: higher level of availability and less cost.
THE PROPOSED MODELS
A. Notation
First, the following notations are adopted herein:
xy - mean operating time per year, in units of measurement of elapsed time.
N - number of final products.
Tini - duration of initial maintenance period, months.
Tlife - time limit (intended life cycle time of the final product), years.
Z - the total number of product logistic breakdown (PLB) elements (including parts located in different zones or performing different functions in one system) where parts of the same type are used.
B. Calculation of spare parts (material) demand for scheduled and unscheduled maintenance
Spare parts and material demand for scheduled maintenance is calculated on the basis of the maintenance plan describing maintenance work and conditions which the final product performs under.
Spare parts and material demand for unscheduled maintenance is determined on the basis of the probability of failures in the period of operation. It is expected that the number of unscheduled removals in the time T is equal to the number of confirmed failures in this period.
M1 and M2 allow estimating spare parts demand for unscheduled maintenance with an acceptable accuracy. M3 is recommended for a multi-level material support management system for unscheduled maintenance. M4 is for scheduled maintenance.
In multi-level systems such calculations should be performed for each maintenance system level, accounting for the scope of maintenance work
performed at this level and the methods chosen for failed parts restoration.
1) M1. Calculation of the spare parts/material demand for unscheduled maintenance without risk considerations
The number of unscheduled removals per year is formulated based on the notation mentioned above as follows:
A,un-rem =N.Ty ■Yfj=1xi-nij (1)
The following formulas can be used (the nearest estimation of the spare parts demand for unscheduled larger integer is taken as a result) to obtain a rough removals (without any stock).
un—ini * un—rem
1 un—ini 1 u
Tl
12
r-M~> orders ^^un—rem—n _^^un—rem T i
T
^^ un—rem—r _^^ un—rem -*- i
12
overhaul
12
rr* del
^^ un—min _^^ un—rem i
1 = i " 12
(2)
Where:
A""-""- initial stock volume of i-th PLB elements for unscheduled removals.
Aiun-rem-n - stock volume of repairable PLB elements for unscheduled removals.
Aiun-rem-r - stock volume of non-repairable PLB elements for unscheduled removals.
Am-mm- minimum stock level of i-th PLB elements for unscheduled removals.
2) M2. Calculation of spare parts demand for unscheduled maintenance with the risk level
considerations (risk of the lack of necessary spare parts):
The calculation of the number of spare parts for unscheduled maintenance in a certain period of time is based on an estimate of the number of failures probability (1, 2, 3,..,b) for this period [1, 2]. Supposing that the failure flow is the simplest (Poisson), the probability P(b) of failures of the i-th product for the T period is calculated by the formula:
ub
Where: ^ - the average number of failures for a period of time T (months) is calculated as:
The accumulative probability of 0 to b failures for a given period is determined by the formula:
,k
V = N-nij-Ai--If (3)
YX=oP(b) = Y,bk=0^e-» (4)
The acceptable risk level of the lack of the required spare parts at the time when they are needed is set by the product designer for each type of PLB element and is defined during the Logistics Support Analysis (LSA) process. This level depends on the
permissible operating time with such a failure. Designate the acceptable risk level for the j-th type of PLB elements as Rj, the required number of spare parts can be found by solving the following inequality for b:
1-Ri<Tli=o^e-» (5)
The decision of this inequality allows obtaining stock for normal exploitation (Aiun-rem-n, A1un-rem-r) and the volume of the initial stock (a™-1"1), the volume of the minimum stock level (A1''n-m'n) with the given level
of risk Rj by placing T '"', T?rders, T,overhaul and T,del in (3) as T.
3) M3. Calculation of spare parts demand for unscheduled maintenance, based on the predefined availability level of spare parts system
The approach is based on the calculation of spare parts system availability level [3,4]. The availability level of spare parts system may be expressed as the probability of the fact that in the given moment all spare parts requirements are satisfied. It can be applicable for various inventory management models:
- for continuous replenishment, when order to replenish the stock is generated just right after replacement (usage of stock);
- for periodical replenishment, when orders to replenish are generated after given time interval;
- for level-based replenishment, when orders are generated, when stock level decreases and reaches the predefined level.
For "continuous replenishment inventory model" the following formula for calculation of spare parts system availability level is used [4]:
kr" = 1
(mW
(Ailnl+1)!Zkl=
¡Aiini+1(miXiTi)k
(6)
1
k!
where:
m, - number of i-th parts in exploitation T— average time of order fulfillment, i.e. mean time of new part delivery (for non-repairable) or time of repair/overhaul (for repairable parts)
where T n i - is a periodicity of replenishment of i-th part.
Aiini - initial stock volume. For "periodical replenishment inventory model" the following formula is used [4]:
(7)
For "level based inventory model" and for conditions where threshold stock level A,min is less than initial stock Aiini, i.e. when 2At min+2 <A,ini the following formula is used [4] :
K sps = 1 yAjlnl(1 - y] (mhTnj)k -m¡x¡Tni) K = mtXtTniyi=0 (1 yk=0 k! e l)
^ min
K^ = 1--^-_ (8)
m,n ini minmii. i
(rnthTi) 1 1 1
It is important to point out, in all three cases considered above the task boils down to the calculation of Aiini for desired value of Ksps.
4) M4. Calculation of the spare parts demand for scheduled maintenance
The number of scheduled product removals during the product life time can be determined by the below formula:
Í rj, life _ \
A, sch-rem = N . yZ R()UND ( ? ) (9)
J 1 \Ti prt-life-limit I
where ROUND is the result of rounding to the Similarly, the number of scheduled product
nearest integer. substitutions in the initial material support management
period is:
A
sch-rem-ini
1
N -Yn^ROUND
i =1
rjiini
--T -—1
12 " rp prt-life-limit
V y
(10)
The total number of part removals for the initial material support management period is calculated as the sum of such removals for scheduled and unscheduled maintenance.
The total number of part removals during product life time is the sum of scheduled and unscheduled removals:
S — A .sch-rem +
Ai S =Ai
Au
(11)
The overhaul duration is approximately the same as the delivery time of the new part and is equal to 3 months.
The calculation by the formula (9) gives 40 units for the scheduled maintenance for the entire fleet for a given period of time. The volume of the initial stock, calculated by the formula (10) gives 0 (based on rounding). The volume of the stock for unscheduled maintenance for a given risk level (0.1) will be 4 units for the entire fleet.
The non-repairable valve 0K-10A is operated by 'on-condition maintenance' method. The calculated spare parts demand for unscheduled maintenance (calculated by the formula (1)) is 13 units. The initial stock for 12 months is 2 units. The minimum stock level is 1 unit.
Filter 8D2.966.017 is operated by the "time-limit maintenance method'. According to formula (9), 300 units are required for the scheduled maintenance for the entire fleet; 19 units will be required for the fleet for the initial exploitation period (formula (10)). The demand for unscheduled maintenance for 15 years for the whole fleet will be 174 units. The minimum stock level, calculated on the basis of delivery time, will be 7 units.
The magnet crane HA-74M is operated by "on-condition maintenance method'. The spare parts demand for unscheduled maintenance for the fleet for 15 years is 9 units. The initial stock for a period of 12 months is 2 units. Delivery lot (3-month delivery time, 12-month periodicity) is 2 units. The minimum stock level, based on the delivery time of the new product, is 1 unit.
Table 1
Source data for calculating the spare parts^ demand
Name Maintenanc e method MTB F The possibilit y of flight with failure Numbe r on board Assigne d time limit, hours Maintainabilit y Deliver y time, months 0ver-haul, month s
Gear pump HM-39M By timelimit 4650 No 2 12000 Yes - 3
Accumulato r NA-01 On-condition 20000 No 3 30000 Yes - 12
Non-return valve OK-10A On-condition 94700 Yes 4 30000 No 3 -
Filter 8^2.966.01 7 By timelimit 3450 No 2 2000 No 3 -
Micron filter ®r-11EH By timelimit 780 No 2 2000 No 3 -
Magnet crane rA-74M On-condition 72900 Yes 2 30000 No 3 -
C. An empirical application
There are 10 helicopters with an average annual flight time of 2,000 hours. The period of initial exploitation is 12 months. The average time between orders is also 12 months. The spare parts demand is calculated for a period of 15 years.
The parts of the aircraft hydraulic system, whose characteristics are given in Table 1, can be considered as an application of the calculation of the spare parts demand for scheduled and unscheduled maintenance.
The source data for the elements are given:
- maintenance method;
- mean time between failures (MTBF);
- the possibility of using aircrafts as intended in case of element failure;
- the number of elements of this type in the hydraulic system;
- assigned time-limit (for elements operated by time-limit maintenance method);
- the possibility of maintenance (yes or no) and its duration;
- average delivery time.
Application of the models for calculation can be summarized in Table 2.
The calculation gives the following results (Table 3):
"Gear pump" is operated by the "time-limit maintenance method' and should be replaced every 12,000 hours (Table 1). The pump is a repairable part.
Table 3
Table 2
Formulas for calculating scheduled/unscheduled removals and the amount of initial reserve
The number of removals The initial stock volume Stock volume during normal exploitation Minimum stock level
Non-repairable parts Repairable parts
Unscheduled removals
A un-rem A un-rem-ini A un-rem-n A .un-rem-r A .un-min
Out-of-repair products Calculated by the formula (1), T = Tlfe (aircraft life time) Calculated by the formula (5), T = Tni (initial exploitation period) in formula (3) Calculated by the formula (5), T = T order (average time between orders) in formula (3) Calculated by the formula (5), T = T^el (delivery duration) in formula (3)
Repairable products Calculated by the formula (5), T = T°verhaul (overhaul duration) in formula (3)
Scheduled removals
A .sch-rem A .sch-rem-ini
Repairable and out-of-repair products Calculated by the formula (9) t = Tllfe (aircraft life time) Calculated by the formula (10), T = Tmi (initial exploitation period)
The spare parts demand and calculated material support management
Name Scheduled removals Unscheduled removals Acceptable risk level Working reserve Min. reserve level Initial reserve
Gear pump Hffl-39M 40 - 0,1 4 - 0
Accumulator NA-01 - - 0,1 5 - -
Non-return valve 0K-10A - 13 0,1 2 1 2
Filter 8^2.966.017 300 174 0,02 19 7 19
Micron filter ®T-11EH 300 770 0,02 67 21 67
Magnet crane TA-74M - 9 0,1 2 1 2
III. Conclusion and further research Integrated Logistics Support, an advanced approach to dealing with systems' cost and level of availability, manages to synthesize MS. Maintenance system, in turn, require spare parts/material supplying planning to achieve ILS goals. The paper has proposed mathematical models, which can be applied in different levels of ILS systems, for calculating spare parts/material supply for scheduled and unscheduled maintenance with and without considering the risk of lacking the required spare parts, and based on the availability level of the spare parts system. For scheduled maintenance (e.g. time limit maintenance method), consideration of the risk is not necessary because the time when there is a need for specific spare parts is known. By contrast, it is crucial to examine the risk of lacking the required spare parts for unscheduled maintenance (e.g. on-condition maintenance). Besides, in the real world, there is always an acceptable availability level of spare parts systems. Therefore,
defining an availability level of a spare part system in advance for calculating the number of spare parts for initial period and stock is a feasible approach to both reducing cost and maintaining a level of system availability.
The choice of the parameters of an inventory system (spare part system) such as the number of layers, inventory models for scheduled and unscheduled maintenance, size of stock etc., may be considered as the general optimization task, where optimization criteria are cost and the availability level of products. This task will be formalized and solved in the next stage of the research.
ACKNOWLEDGMENTS
This work is financially supported by the National program KC-4.0.
Literature:
1. "Reliability, Spares and Other Considerations"// Ed Welch, Available:
http://www.slideshare.net/EdWelch/reliability-spares-and-other-considerations. Accessed May, 2, 2019.
2. "Technologies of integrated logistic support for machine building products"// Sudov E.V., Levin A.I., Petrov A.V., Chubarova E.V., Moscow: Publishing house "InformBurou", 2006, pp. 232.
3. "Methods of organisation of calculations and optimisation of spare parts stock for complex technical
systems"// Shura-Bura A.E., Topolsky M.V.. Moscow: Znanie, pp.114, , 1981.
4. "Estimation of reliability of systems, using spare parts"// Cherkesov G.N. SPb.: BHV Peterburg, pp. 480, 2012.
5. Def-Stan 00-600// UK Ministry of Defense, 2011.
УДК 614.8
СРЕДСТВО ПРОТИВОПОЖАРНОЙ ПРОПАГАНДЫ
Мельников Сергей Михайлович
Преподаватель кафедры тактики и аварийно-спасательных работ Дальневосточной пожарно-спасательной академии -филиала Санкт-Петербургского университета ГПС МЧС России,
Владивосток, Россия Хабиров Тимур Ринатович Старший преподаватель кафедры тактики и аварийно-спасательных работ Дальневосточной пожарно-спасательной академии -филиала Санкт-Петербургского университета ГПС МЧС России,
Владивосток, Россия
A MEANS OF FIRE PREVENTION PROPAGANDA
Sergey M. Melnikov
Lecturer Far East Fire Rescue Academy -a branch of the St. Petersburg University of State Fire Service of EMERCOM of Russia Timur R. Khabirov Senior Lecturer Far East Fire Rescue Academy -a branch of the St. Petersburg University of State Fire Service of EMERCOM of Russia
АННОТАЦИЯ
Социальные сети в современном мире являются неотъемлемой частью нашей жизни. В настоящее время все большую популярность набирает профилактика пожаров в различных социальных сетях, где сотрудники системы МЧС России занимаются непосредственной противопожарной пропагандой. Целью исследования данной темы является доказательство того, что размещение информации по профилактике является эффективным средством по борьбе с образованием новых случаев непредвиденных пожаров. В статье показаны результаты проведенного анкетирования среди различных слоёв населения на предмет влияния социальных сетей в сфере противопожарной пропаганды. Данное исследование способно составить более полную картину такого социального явления, как восприятие гражданами профилактических мероприятий, связанных с пожарами, а его результаты будут интересны не только тем, кто связан с службой в МЧС России, а также тем, кто является активным пользователем различных социальных сетей.
ANNOTATION
Social networks in the modern world are an integral part of our life. Currently, fire prevention is gaining more and more popularity in various social networks, where employees of the EMERCOM of Russia are engaged in direct fire prevention propaganda. The purpose of the study of this topic is to prove that the placement of information on prevention is an effective means to combat the formation of new cases of unforeseen fires. The article shows the results of a survey conducted among various segments of the population on the influence of social networks in the field of fire prevention propaganda. This study is able to form a more complete picture of such a social phenomenon as the perception of citizens of preventive measures related to fires, and its results will be interesting not only to those who are connected with the service in the Ministry of Emergency Situations of Russia, but also to those who are active users of various social networks.
Ключевые слова: социальные сети, МЧС России, профилактика пожаров, противопожарная пропаганда.
Keywords: social networks, EMERCOM of Russia, fire prevention, fire prevention propaganda.
В современном мире достаточно непросто найти человека, который бы не был знаком с понятием «социальные сети». В теории, такая сеть
является способом сближения людей на единой Интернет-платформе, которая позволяет любому пользователю делиться информацией, а также
