CN103632214A - Maintenance and spare part supply combined optimization method for use in absence of inventory degradation data - Google Patents

Abstract

The invention discloses a maintenance and spare part supply combined optimization method for use in the absence of inventory degradation data. The method comprises the following steps: establishing a random inventory degradation model according to a spare part failure time distribution function; analyzing a series of system maintenance and spare part supply related costs such as desired maintenance cost, desired spare part purchasing cost, desired spare part storage cost and desired spare part shortage loss cost on the basis of the random inventory degradation model; establishing a maintenance and spare part supply combined optimization model at the lowest system maintenance and spare part supply related costs on the basis of the random inventory degradation model; and defining a system predictive maintenance period and the upper and lower limits of the amount to be optimized of a maximum spare part inventory amount according to practical situations, and solving an optimized maintenance and spare part supply relation. As for the situation that a spare part inventory degradation environment exists but sufficient inventory degradation monitoring data are lacked, the method is more consistent with the practical situation than a conventional combined optimization method; meanwhile, the method is also suitable for situations under which inventory degradation does not need to be considered.

Description

Maintenance under stock's degraded data deletion condition and spare part are supplied with combined optimization method

Technical field

The present invention relates to the prediction of the complex engineering system failure and predictive maintenance technology, particularly about a kind of maintenance and spare part under stock's degraded data deletion condition, supply with combined optimization method.

Background technology

The maintenance of system and spare part are inseparable between supplying with, and maintenance is the main source of spare parts consumption, and spare part is the prerequisite that maintenance is carried out.Lacking spare part will affect maintenance and make system cannot recover normal operation.But this does not mean that spare part is The more the better, spare part too much can increase the spare part fund input of enterprise on the one hand, can increase on the other hand corresponding stock management expense.And spare part exists and inevitably degenerates and scrap phenomenon in storage process.The electronic equipment of for example storing on foreign-going ship and components and parts and part mechanical organ, it is for changing in time the operation parts that lost efficacy, to guarantee the normal operation of boats and ships, but due to severe marine environment such as high humidity, high salinity, surges, it is very serious that spare part is scrapped phenomenon, when bringing economic loss, also can affect the reliability of vessel motion.

It is a kind of method that can effectively solve above-mentioned contradiction that maintenance and spare part are supplied with combined optimization method.This combined optimization method according to maintenance or the method that is only optimized according to spare part supply situation, is a kind of global optimum but not the method for local optimum utilizes combined optimization method can obtain the result of more realistic demand than only.But at some in particular cases, for example, for there being Parts Inventory degeneration environment but lack the situation of enough stock's degeneration Monitoring Data, owing to there is no enough data for the deterioration law of Parts Inventory is carried out to modeling, cause combined optimization method can be subject to certain restrictions in the specific implementation.

Summary of the invention

For the problems referred to above, the object of the invention is to supply with for existing maintenance and spare part the situation that lacks Parts Inventory degraded data in combined optimization, provide a kind of maintenance and spare part based on randomicity stock degradation model to supply with combined optimization method.The method can, from the out-of-service time distribution function of single spare part, be set up the randomness Parts Inventory degradation model of describing Parts Inventory deterioration law; Based on randomicity stock degradation model, the minimization system of take maintenance and spare part supply cost are target, further set up maintenance and spare part and supply with combined optimization model; Then by the restriction to some amounts to be optimized, the maintenance that obtains more tallying with the actual situation and spare part are supplied with joint optimization result.

The maintenance and the spare part that the invention provides under a kind of stock's degraded data deletion condition are supplied with combined optimization method, comprise the following steps:

S100, based on spare part out-of-service time distribution function, set up randomicity stock degradation model;

S200, based on randomicity stock degradation model, analytic system maintenance and spare part are supplied with correlative charges, and described expense comprises expectation maintenance cost, expectation spare parts purchasing expense, expectation spare part storage cost and the expectation spare part shortage failure costs of system within a preventative maintenance cycle;

S300, based on randomicity stock degradation model, the minimization system of take maintenance and spare part supply cost are target, set up maintenance and spare part and supply with combined optimization model;

S400, based on maintenance and spare part, supply with the bound of combined optimization model and given amount to be optimized, obtain maintenance and spare part the relation between supply and demand optimum solution, described amount to be optimized comprises predictability maintenance cycle and the spare part maximum inventory of system.

According to embodiments of the invention, above-mentioned steps S100 further comprises:

There is m spare part in part warehouse in the system of setting up departments, the out-of-service time distribution function of each spare part is p (t), it is mp (t) that the distribution of the inefficacy spare part number Y of system in time t is approximately average, variance is the normal distribution of mp (t) (1-p (t)), and the probability density function of Y is g _y(y):

$g_Y\left(y\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\π}}\·\sqrt{m\·p\left(t\right)\·(1-p\left(t\right))}}{e}^{-\frac{{(y-m\·p\left(t\right))}^2}{2m\·p\left(t\right)\·(1-p\left(t\right))}}& ,m>0\\ \mathrm{\δ}\left(y\right)& ,m=0\end{array}\right.$

Wherein, δ (y) is unit impulse function, and

According to embodiments of the invention, above-mentioned steps S200 further comprises:

S210, analytic system inefficacy maintenance frequency:

System in a preventative maintenance period T, the expectation E[X of Failure count X of each operation parts]=M (T), function M (T) carries out iterative computation acquisition when the k=T by following approximate formula:

$M\left(k\right)=\underset{i=0}{\overset{k-1}{\mathrm{\Σ}}}[1+M(k-i-1)]\·{\∫}_i^{i+1}{f}_a\left(t\right)\mathrm{dt},k=\mathrm{1,2},...$

M(0)=0

Corresponding variance Var[X] utilize following approximate formula to calculate acquisition::

$\mathrm{Var}\left[X\right]=D\left(k\right)=M\left(k\right)-M{\left(k\right)}^2+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\left\{\begin{array}{c}M(k-i)[M(i+1)-M\left(i\right)]\\ +M(k-i-1)[M\left(i\right)-M(i-1)]\end{array}\right\}$

Wherein, f _a(t) be the probability density function of operation component failure time, k is discrete magnitude, is positive integer;

Operation part count in system is n, in a preventative maintenance period T, and thrashing maintenance frequency X _nobey expectation for E[X _n]=nM (T), variance is Var[X _n]=nVar[X] normal distribution, and X _nprobability density function be

;

S220, analysis Parts Inventory amount of degradation:

The system spare part original bulk when preventative maintenance period T starts of setting up departments is S _a, spare part out-of-service time distribution function is p (t)=F _b(t)=p, the probability density function of the spare part number Y that lost efficacy in preventative maintenance period T is:

$g_Y\left(y\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\π}}\·\sqrt{S_{a}p(1-p)}}{e}^{-\frac{{(y-S_{a}p)}^2}{2S_{a}p(1-p)}}& ,S_a>0\\ \mathrm{\δ}\left(y\right)& ,S_a=0\end{array}\right.$

Now expect E[Y] be approximately S _ap, i.e. E[Y]=S _ap.

S230, analysis spare part maximum inventory S and spare part original bulk S _abetween relation:

S _a=S-n-E[X _n(T)-X _n(T-τ)]-E[Y(T)-Y(T-τ)]

=S-n-n[M(T)-M(T-τ)]-S _a[p(T)-p(T-τ)]

Wherein, τ is for ordering the delivery time of spare part;

S240, analyze an expectation maintenance cost C in preventative maintenance period T _mfor:

C _M(S _a,T)=c _pr·n+c _cr·E[X _n]

Wherein, c _prthe expense that represents each preventative maintenance, c _crthe expense that represents each correction maintenance;

S250, analyze an expectation spare parts purchasing expense C in preventative maintenance period T _ofor:

C _o(S _a,T)=K+c _sp·(n+E[X _n]+E[Y])

Wherein, K represents disposable buying expenses, c _spthe unit price that represents spare part;

S260, analyze an expectation spare part storage cost C in preventative maintenance period T _hfor:

$C_h(S_a,T)=c_h\·\left[\begin{array}{cc}\underset{0\≤X_n+Y+S_a}{\∫\∫}(S_a-\frac{x_n+Y}{2})\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dyd}{x}_n& \\ +\underset{X_n+Y>S_a}{\∫\∫}\frac{S_a}{2}\·\frac{S_a}{x_n+Y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n& \end{array}\right]$

$=c_h\left[\begin{array}{c}{\∫}_0^{S_a}{\∫}_0^{S_a-x_n}(S_a-\frac{x_n+y}{2})\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\∫}_0^{S_a}{\∫}_{S_a-x_n}^{\∞}\frac{S_a}{2}\·\frac{S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\∫}_{S_a}^{\∞}{\∫}_0^{\∞}\frac{S_a}{2}\·\frac{S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n\end{array}\right]$

Wherein, c _hstorage cost for single spare parts list bit time;

S270, analyze expectation spare part in a preventative maintenance period T shortage failure costs C _sfor:

$C_s(S_a,T)=c_s\·\underset{X_n+Y>S_a}{\∫\∫}\frac{x_n+Y-S_a}{2}\·\frac{x_n+Y-S_a}{x_n+Y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n$

$=c_s\left[\begin{array}{c}{\∫}_0^{S_a}{\∫}_{S_a-x_n}^{\∞}\frac{x_n+y-S_a}{2}\·\frac{x_n+y-S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\∫}_{S_a}^{\∞}{\∫}_0^{\∞}\frac{x_n+y-S_a}{2}\·\frac{x_n+y-S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n\end{array}\right]$

Wherein, c _sshort failure costs for single spare parts list bit time.

According to embodiments of the invention, above-mentioned steps S300 further comprises:

It is target that the minimization system of take maintenance and spare part are supplied with correlative charges, take maximum part warehouse storage S and preventative maintenance period T as amount to be optimized, sets up following Optimized model:

$\begin{array}{cc}\min & C_{2,\∞}(S,T)=C_{2,\∞}(S_a,T)=\frac{C_M(S_a,T)+C_o(S_a,T)+C_h(S_a,T)+C_s(S_a,T)}{T}\\ s.t.& S_a\≥0,T>0\end{array}$

Wherein, S _afor the spare part original bulk of system when a preventative maintenance period T starts, C _mbe an expectation maintenance cost in preventative maintenance period T, C _obe an expectation spare parts purchasing expense in preventative maintenance period T, C _hbe an expectation spare part storage cost in preventative maintenance period T, C _sit is an expectation spare part shortage failure costs in preventative maintenance period T.

According to embodiments of the invention, above-mentioned steps S400 further comprises:

1) give fixed system correlation parameter, described parameter comprises the parameters of computing system maintenance and spare part supply correlative charges, to the fixed system probability density function f of operation component failure time _aand spare part out-of-service time distribution function p (t)=F (t) _b, and calculate the operation parts expectation out-of-service time (t)

2) set bound the discretize amount to be optimized of amount to be optimized:

Bound [the T of preventative maintenance period T is set _min, T _max], and according to interval △ T discretize preventative maintenance period T, obtain discrete time node T _i=T _min+ i △ T, i=0,1,2 ...;

Set the bound [S of spare part maximum inventory S _min, S _max], and according to interval △ S discretize spare part maximum inventory S, obtain discrete stock's node S _j=S _min+ j △ S, j=0,1,2 ...;

3) get i=0;

4) compare discrete time node T _iwith upper bound T _maxif, T _i>T _max, enter step 12), otherwise enter step 5);

5) calculate according to the following formula discrete time node T _icorresponding M (T _i) and D (T _i):

$M\left(T_i\right)=\underset{0}{\overset{T_i-1}{\mathrm{\Σ}}}[1+M(T_i-i-1)]\·{\∫}_i^{i+1}{f}_a\left(t\right)\mathrm{dt}$

M(0)=0

$D\left(T_i\right)=M\left(T_i\right)-M{\left(T_i\right)}^2+\underset{i=1}{\overset{T_i}{\mathrm{\Σ}}}\left\{\begin{array}{c}M(T_i-i)[M(i+1)-M\left(i\right)]\\ +M(T_i-i-1)[M\left(i\right)-M(i-1)]\end{array}\right\}$

6) get j=0;

7) more discrete stock's node S _jif, S _j>S _max, enter step 10), otherwise enter step 8);

8) calculate according to the following formula discrete stock's node S _jthe corresponding initial tank farm stock S of spare part _a,

S _a=S-n-E[X _n(T _i)-X _n(T _i-τ)]-E[Y(T _i)-Y(T _i-τ)]

=S-n-n[M(T _i)-M(T _i-τ)]-S _a[p(T _i)-p(T _i-τ)]

By S _abringing following maintenance and spare part into supplies with combined optimization model and calculates corresponding C _{2, ∞}(S _j, T _i):

$C_{2,\∞}(S_j,T_i)=\frac{C_M(S_a,T_i)+C_o(S_a,T_i)+C_h(S_a,T_i)+C_s(S_a,T_i)}{T}$

Wherein, C _mbe an expectation maintenance cost in preventative maintenance period T, C _obe an expectation spare parts purchasing expense in preventative maintenance period T, C _hbe an expectation spare part storage cost in preventative maintenance period T, C _sbe an expectation spare part shortage failure costs in preventative maintenance period T,

9) get j=j+1, return to step 7);

10) calculate the optimum solution S of spare part maximum inventory S ^{i, *}:

$S^{i,*}=\left\{S_j\right|\underset{S_j}{\min }{C}_{2,\∞}(S_j,T_i)\}$

T now _iit is set-point;

11) get i=i+1, return to step 4);

12) { [S obtaining ^{i, *}, T _i, C _{2, ∞}(S ^{i, *}, T _i)] in set, find out the one group of solution that makes system maintenance and spare part supply with correlative charges minimum and as maintenance and spare part, supply with the optimum results of associating relation:

$(S^{*},T^{*})=\left\{(S^{i,*},T_i)\right|\underset{i}{\min }{C}_{2,\∞}(S^{i,*},T_i)\}$

Wherein, S ^*for spare part maximum inventory optimum results, T ^*for corresponding preventative maintenance cycle optimum results, finish.

According to embodiments of the invention, in above-mentioned steps S400, the lower bound T of described preventative maintenance period T _minvalue and spare part to order delivery time τ relevant, upper bound T _maxvalue relevant with operation parts expectation out-of-service time μ.

Further, T _min=τ, T _max=1.5 μ.

According to embodiments of the invention, in above-mentioned steps S400, the lower bound S of described spare part maximum inventory S _minvalue relevant with the operation part count n of system, upper bound S _maxthe operation part count n of value and system relevant with operation parts expectation out-of-service time μ.

Further, S _min=n, S _max=n+2nM (μ).

Compared with prior art, the present invention brings following beneficial effect:

Combined optimization method provided by the invention can be in actual use, based on existing data, and some relevant prioris that spare part was lost efficacy, the out-of-service time that estimates single spare part distributes, out-of-service time distribution function from single spare part, set up the randomness Parts Inventory degradation model of describing Parts Inventory deterioration law, and this model is incorporated in maintenance and the calculating of spare parts management correlative charges and is gone, thereby the joint optimization result that obtains more tallying with the actual situation, and then provide accurately strong scientific basis for later stage correct decisions.And the present invention is particularly useful for for there being Parts Inventory degeneration environment but lacks the situation of enough stock's degeneration Monitoring Data, and the present invention simultaneously is also applicable to the situation of not considering that stock degenerates.

Other features and advantages of the present invention will be set forth in the following description, and, partly from instructions, become apparent, or understand by implementing the present invention.Object of the present invention and other advantages can be realized and be obtained by specifically noted structure in instructions, claims and accompanying drawing.

Accompanying drawing explanation

Accompanying drawing is used to provide a further understanding of the present invention, and forms a part for instructions,, jointly for explaining the present invention, is not construed as limiting the invention with embodiments of the invention.In the accompanying drawings:

Fig. 1 is the workflow diagram of combined optimization method provided by the invention;

Fig. 2 is the schematic diagram of " spare part is superfluous " situation;

Fig. 3 is the schematic diagram of " spare part shortage " situation;

Fig. 4 is the numerical search algorithm flow chart in the combined optimization method step S400 of embodiment provided by the invention;

Fig. 5 is the level line schematic diagram of the optimum results of embodiment provided by the invention.

Embodiment

Below with reference to drawings and Examples, describe embodiments of the present invention in detail, to the present invention, how application technology means solve technical matters whereby, and the implementation procedure of reaching technique effect can fully understand and implement according to this.It should be noted that, only otherwise form conflict, each embodiment in the present invention and each feature in each embodiment can mutually combine, and formed technical scheme is all within protection scope of the present invention.

In addition, in the step shown in the process flow diagram of accompanying drawing, can in the computer system such as one group of computer executable instructions, carry out, and, although there is shown logical order in flow process, but in some cases, can carry out shown or described step with the order being different from herein.

As shown in Figure 1, be the workflow diagram of combined optimization method provided by the invention.As we know from the figure, the method, from the out-of-service time distribution function of single spare part, is set up the randomicity stock degradation model of describing Parts Inventory degenerate case; Then based on randomicity stock degradation model, analytic system maintenance and spare part are supplied with correlative charges; The minimization system of take maintenance and spare part supply cost are target, set up maintenance and spare part and supply with combined optimization model, the last bound in conjunction with actual conditions initialization system preventative maintenance cycle and spare part maximum inventory amount to be optimized, thus draw maintenance and the spare part supply associating relation more tallying with the actual situation.The method specifically comprises the following steps:

S100, based on spare part out-of-service time distribution function, set up randomicity stock degradation model:

In system, the out-of-service time distribution function of each spare part is p (t), it is Bernoulli Jacob's experiment that the inefficacy of each spare part can be considered as,, for the part warehouse that has m spare part, the inefficacy spare part number Y in moment t obeys binomial distribution B～(m, p (t)).If m is enough large, it is mp (t) that the distribution of Y can be approximately equal to average, and variance is the normal distribution of mp (t) (1-p (t)); If m is zero, Y identically vanishing.Therefore, the probability density function of Y is g _y(y):

$g_Y\left(y\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\π}}\·\sqrt{m\·p\left(t\right)\·(1-p\left(t\right))}}{e}^{-\frac{{(y-m\·p\left(t\right))}^2}{2m\·p\left(t\right)\·(1-p\left(t\right))}}& ,m>0\\ \mathrm{\δ}\left(y\right)& ,m=0\end{array}\right.$

Wherein, δ (y) is unit impulse function, and known

S200, based on randomicity stock degradation model, analytic system maintenance and spare part are supplied with correlative charges, and described expense comprises expectation maintenance cost, expectation spare parts purchasing expense, expectation spare part storage cost and the expectation spare part shortage failure costs of system within a preventative maintenance cycle.This step S200 can be subdivided into following steps:

S210, analytic system inefficacy maintenance frequency:

Conventionally system adopts preventative maintenance strategy in batch, at certain, move after component failure, and to its replacement of losing efficacy (when corresponding spare part exists), and every through after a while, the operation parts in system are all prophylactically replaced.In system after this preventative replacement, can be considered and recover as new, therefore establishing T is System Preventive Maintenance Cycle, also claims the update cycle.The inefficacy replacement process of each operation parts is also renewal process, so expectation E[X of its Failure count X in System Preventive Maintenance Cycle T] namely move the renewal function M (T) of the renewal process of parts, be E[X]=M (T), and function M (T) can utilize following approximate formula iterative computation when k=T to obtain:

$M\left(k\right)=\underset{i=0}{\overset{k-1}{\mathrm{\Σ}}}[1+M(k-i-1)]\·{\∫}_i^{i+1}{f}_a\left(t\right)\mathrm{dt},k=\mathrm{1,2},...$

M(0)=0

Wherein, f _a(t) be the probability density function of operation component failure time, k is discrete magnitude, is positive integer.

Corresponding variance Var[X] can utilize following approximate formula to calculate acquisition:

$\mathrm{Var}\left[X\right]=D\left(k\right)=M\left(k\right)-M{\left(k\right)}^2+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\left\{\begin{array}{c}M(k-i)[M(i+1)-M\left(i\right)]\\ +M(k-i-1)[M\left(i\right)-M(i-1)]\end{array}\right\}$

In the power electronic system of practical application, the quantity n of operation parts is conventionally larger, according to law of great number, and the thrashing maintenance frequency X of system in a preventative maintenance period T _nconventionally obey expectation for E[X _n]=nM (T), variance is Var[X _n]=nVar[X] normal distribution, and X _nprobability density function be

S220, analysis Parts Inventory amount of degradation:

The system of setting up departments includes S when a preventative maintenance period T starts _aindividual separate spare part, spare part original bulk is S _a, the out-of-service time distribution function of these spare parts is F _b(t).The randomicity stock degradation model that integrating step S100 sets up has: m=S _a, p (t)=F _b(t)=p, lost efficacy in the System Preventive Maintenance Cycle T probability density function of spare part number Y of spare part is so:

$g_Y\left(y\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\π}}\·\sqrt{S_{a}p(1-p)}}{e}^{-\frac{{(y-S_{a}p)}^2}{2S_{a}p(1-p)}}& ,S_a>0\\ \mathrm{\δ}\left(y\right)& ,S_a=0\end{array}\right.$

Now expect E[Y] be approximately S _ap, i.e. E[Y]=S _ap.

Relation between S230, analysis spare part maximum inventory and spare part original bulk:

Conventionally system stock adopts cyclic check spare part supply strategy, i.e. τ position iT-τ constantly before each preventative maintenance cycle arrives, i=1,2, ... carry out spare part order, τ is for ordering the delivery time point of spare part, and subscription principle is that spare part quantity is added to maximum inventory S.Therefore within a preventative maintenance cycle; may there are two kinds of situations in the Expenditure Levels of spare part: spare part superfluous (as shown in Figure 2) or spare part shortage (as shown in Figure 3); wherein spare part surplus can cause unnecessary spare part fund input and increase stock management expense; and spare part shortage can make system-down; when serious, can affect system production run, bring economic loss.So spare part maximum inventory S and spare part original bulk S _abetween transformational relation have:

S _a=S-n-E[X _n(T)-X _n(T-τ)]-E[Y(T)-Y(T-τ)]

=S-n-n[M(T)-M(T-τ)]-S _a[p(T)-p(T-τ)]

System maintenance and spare part supply cost that lower surface analysis produces due to operation component failure.The quantity of operation parts of setting up departments in system is n, and system includes S when preventative maintenance period T starts _aindividual separate spare part, in a preventative maintenance period T, required expectation maintenance cost, expectation spare parts purchasing expense, expectation spare part storage cost and the expectation spare part shortage failure costs of system maintenance obtains by step S240～S270 respectively:

Expectation maintenance cost C in S240, a preventative maintenance period T _mfor:

C _M(S _a,T)=c _pr·n+c _cr·E[X _n]=c _pr·n+c _cr·n·M(T)

Wherein, c _prthe expense that represents each preventative maintenance, c _crthe expense that represents each correction maintenance.

Expectation spare parts purchasing expense C in S250, a preventative maintenance period T _ofor:

C _o(S _a,T)=K+c _sp·(n+E[X _n]+E[Y])=K+c _sp[n+nM(T)+S _ap]

Wherein, K represents disposable buying expenses (as freight charges etc.), c _spthe unit price that represents spare part.Can find out, the spare parts purchasing quantity in a preventative maintenance period T is by the demand n of preventative replacement, the demand E[X that lost efficacy and replace _n], and spare part self the loss E[Y that degenerates and to cause] determine together.

Expectation spare part storage cost C in S260, a preventative maintenance period T _hfor:

$C_h(S_a,T)=c_h\·\left[\begin{array}{cc}\underset{0\≤X_n+Y+S_a}{\∫\∫}(S_a-\frac{x_n+Y}{2})\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dyd}{x}_n& \\ +\underset{X_n+Y>S_a}{\∫\∫}\frac{S_a}{2}\·\frac{S_a}{x_n+Y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n& \end{array}\right]$

$=c_h\left[\begin{array}{c}{\∫}_0^{S_a}{\∫}_0^{S_a-x_n}(S_a-\frac{x_n+y}{2})\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\∫}_0^{S_a}{\∫}_{S_a-x_n}^{\∞}\frac{S_a}{2}\·\frac{S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\∫}_{S_a}^{\∞}{\∫}_0^{\∞}\frac{S_a}{2}\·\frac{S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n\end{array}\right]$

Wherein, c _hstorage cost for single spare parts list bit time.

Expectation spare part shortage failure costs C in S270, a preventative maintenance period T _sfor:

$C_s(S_a,T)=c_s\·\underset{X_n+Y>S_a}{\∫\∫}\frac{x_n+Y-S_a}{2}\·\frac{x_n+Y-S_a}{x_n+Y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n$

$=c_s\left[\begin{array}{c}{\∫}_0^{S_a}{\∫}_{S_a-x_n}^{\∞}\frac{x_n+y-S_a}{2}\·\frac{x_n+y-S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\∫}_{S_a}^{\∞}{\∫}_0^{\∞}\frac{x_n+y-S_a}{2}\·\frac{x_n+y-S_a}{x_n+y}\·T\·g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n\end{array}\right]$

Wherein, c _sshort failure costs for single spare parts list bit time.

S300, based on randomicity stock degradation model, set up maintenance and spare part and supply with combined optimization model:

The minimization system overall expenses rate of take is target, take maximum part warehouse storage S and preventative maintenance period T as amount to be optimized, obtains following combined optimization model:

$\begin{array}{cc}\min & C_{2,\∞}(S,T)=C_{2,\∞}(S_a,T)=\frac{C_M(S_a,T)+C_o(S_a,T)+C_h(S_a,T)+C_s(S_a,T)}{T}\\ s.t.& S_a\≥0,T>0\end{array}$

According to step, S250 is known, in the situation that other parameters are definite, and S and S _acorresponding one by one, i.e. S _aor after S determines, correspondingly S or S _acan determine thereupon.Therefore, the C of combined optimization model _{2, ∞}(S, T) is equal to C _{2, ∞}(S _a, T).

Analyze the extreme case of above-mentioned Optimized model:

Work as S _a→ 0 o'clock, can obtain:

$\underset{S_a\→0}{\lim }{C}_{2,\∞}(S_a,T)=\frac{1}{T}\left\{\begin{array}{c}{c}_{\mathrm{pr}}n+c_{\mathrm{cr}}\mathrm{nM}\left(T\right)+K+c_{\mathrm{sp}}[n+\mathrm{nM}\left(T\right)]\\ +c_h[{\∫}_0^{S_a}(S_a-\frac{x_n}{2})\·T\·g_{X_n}\left(x_n\right){\mathrm{dx}}_n+{\∫}_{S_a}^{\∞}\frac{S_a}{2}\·\frac{S_a}{x_n}\·T\·g_{X_n}\left(x_n\right){\mathrm{dx}}_n]\\ +c_s[{\∫}_{S_a}^{\∞}\frac{x_n-S_a}{2}\·\frac{x_n-S_a}{x_n}\·T\·g_{X_n}\left(x_n\right){\mathrm{dx}}_n]\end{array}\right\}$

This formula and 2003

do not considering that with Hudoklin the model of setting up under the prerequisite of Parts Inventory degenerate case is the same, illustrating that Optimized model of the present invention can contain the situation of originally not considering that Parts Inventory is degenerated.

S400, the bound of supplying with combined optimization model and given amount to be optimized based on maintenance and spare part solve maintenance and the spare part the relation between supply and demand of optimization.This step S400 can be subdivided into following steps:

S410, from step S300, the amount to be optimized that preventative maintenance period T and spare part maximum inventory S are optimizing process, arranges the bound of amount to be optimized according to the actual requirements:

S410.1, preventative maintenance period T:

Preventative maintenance period T can be carried out discretize in actual applications.In the present embodiment, first, the lower bound of preventative maintenance period T is set for ordering the delivery time point τ of spare part, the upper bound is the expectation of operation parts out-of-service time μ, i.e. τ≤T≤1.5 μ of 1.5 times; Secondly, in this interval, according to interval △ T, preventative maintenance period T is carried out to discretize, obtain corresponding discrete time node T _i:

S410.2, spare part maximum inventory S:

In the situation that preventative maintenance period T is certain, establish

$P\left(S_a\right)=\frac{\∂}{{\∂S}_a}{C}_{2,\∞}(S_a,T),$

Have

$P\left(0\right)=-\frac{1}{4}{c}_s\mathrm{nM}\left(T\right)\underset{S_a\&RightArrow;0}{\lim }\frac{1}{S_a}+\frac{c_{\mathrm{sp}}{p}_T}{T}-c_s\frac{p}{4(1-p)}\&CenterDot;\mathrm{nM}\left(T\right)-\frac{1}{2}{c}_s=-\&infin;<0$

$P(\&infin;)>c_h\frac{(1+p)}{4p}\underset{S_a\&RightArrow;\&infin;}{\lim }{S}_a+\frac{c_{\mathrm{sp}}{p}_T}{T}+\frac{3}{4}{c}_h-c_h\frac{(1+p)}{4p}\mathrm{nM}\left(T\right)=+\&infin;>0$

In the situation that preventative maintenance period T is certain, always there is optimum spare part original bulk in above-mentioned two formula explanation

by aforementioned spare part maximum inventory S and spare part original bulk S _abetween transformational relation known, S and S _acorresponding one by one, therefore for optimum spare part original bulk

always there is optimum spare part maximum inventory S ^*.Thus, the present invention can consider the optimum solution S to spare part maximum inventory S by enumerative technique ^*carry out numerical search.

In the present embodiment, first, the lower bound that spare part maximum inventory S is set is n, and the upper bound is n+2nM (μ), i.e. n≤S≤n+2nM (μ); Secondly, in this interval, according to interval △ S, spare part maximum inventory S is carried out to discretize, obtain corresponding discrete time node S _i:

S _j=n+j△S，j=0,1,2,...。

S420, by numerical search, obtain maintenance and spare part is supplied with joint optimization result:

As shown in Figure 4, be the numerical search algorithm flow chart that the present invention obtains maintenance and spare part supply joint optimization result.Detailed process is as follows:

1) parameter initialization: give fixed system correlation parameter n, τ, c _pr, c _cr, K, c _sp, c _hand c _svalue, given f _aand F (t) _b, and calculate the operation parts expectation out-of-service time (t)

2) set bound the discretize amount to be optimized of amount to be optimized:

The bound that preventative maintenance period T is set is [τ, 1.5 μ], and according to interval △ T discretize preventative maintenance period T, obtains discrete time node T _i=τ+i △ T, i=0,1,2 ...;

The bound [n, n+2nM (μ)] of spare part maximum inventory S is set, and according to interval △ S discretize spare part maximum inventory S, obtains discrete stock's node S _j=n+j △ S, j=0,1,2 ...;

3) get i=0;

4) compare discrete time node T _iwith its upper bound 1.5 μ, if T _i>1.5 μ, enters step 12), otherwise enters step 5);

5) calculate discrete time node T _icorresponding M (T _i) and D (T _i):

$M\left(T_i\right)=\underset{0}{\overset{T_i-1}{\mathrm{\&Sigma;}}}[1+M(T_i-i-1)]\&CenterDot;{\&Integral;}_i^{i+1}{f}_a\left(t\right)\mathrm{dt}$

M(0)=0

$D\left(T_i\right)=M\left(T_i\right)-M{\left(T_i\right)}^2+\underset{i=1}{\overset{T_i}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}M(T_i-i)[M(i+1)-M\left(i\right)]\\ +M(T_i-i-1)[M\left(i\right)-M(i-1)]\end{array}\right\}$

6) get j=0;

7) more discrete stock's node S _jwith its upper bound n+2nM (μ), if S _j>n+2nM (μ), enters step 10), otherwise enters step 8);

8) calculate according to the following formula discrete stock's node S _jthe corresponding initial tank farm stock S of spare part _a:

S _a=S-n-E[X _n(T _i)-X _n(T _i-τ)]-E[Y(T _i)-Y(T _i-τ)]

=S-n-n[M(T _i)-M(T _i-τ)]-S _a[p(T _i)-p(T _i-τ)]

By S _abringing following maintenance and spare part into supplies with combined optimization model and calculates corresponding C _{2, ∞}(S _j, T _i):

$C_{2,\&infin;}(S_j,T_i)=\frac{C_M(S_a,T_i)+C_o(S_a,T_i)+C_h(S_a,T_i)+C_s(S_a,T_i)}{T}$

9) get j=j+1, return to step 7);

10) calculate the optimum solution of spare part maximum inventory S

t now _iit is set-point;

11) get i=i+1, return to step 4);

12) { [S obtaining ^{i, *}, T _i, C _{2, ∞}(S ^{i, *}, T _i)] in set, find out the one group of solution that makes system maintenance and spare part supply with correlative charges minimum and as maintenance and spare part, supply with the optimum results of associating relation, that is:

$(S^{*},T^{*})=\left\{(S^{i,*},T_i)\right|\underset{i}{\min }{C}_{2,\&infin;}(S^{i,*},T_i)\}$

Finish.

Wherein, S ^*for spare part maximum inventory optimum results, T ^*for corresponding preventative maintenance cycle optimum results.

Above formula represents to work as spare part maximum inventory and the preventative maintenance cycle is corresponding S ^{i, *}and T _itime, system maintenance and spare part are supplied with correlative charges rate C _{2, ∞}(S ^{i, *}, T _i) reach minimum.

The power vehicle arc-extinguish chamber data that Slovenian Railway Bureau announces of take are below object, and specific embodiment of the invention step is described, and the optimum results obtaining.The software platform that this experiment Mathematica9.0 is Optimization Solution carries out emulation and solves.

(1) experimental subjects

Foundation

the Slovenian Railway Bureau data case that and Hudoklin provides, obtains the value of following three class data correlated variabless: the operation number of components n=120 in system; The probability density function of operation component failure time

average μ wherein ₁=44 weeks, standard deviation sigma ₁=12 weeks; Spare part τ=12 week delivery cycle, corresponding unit costs is c _pr=58.2units, c _cr=800.5units, K=20units, c _sp=43units, c _h=0.6units, c _s=5196units; Spare part out-of-service time distribution F _b(t) for obeying average μ ₂=40, standard deviation sigma ₂=15 normal distribution.

(2), based on randomicity stock degradation model, set up maintenance and spare part and supply with combined optimization model, and carry out Optimization Solution.

Concrete condition is as follows:

1) parameter initialization: give fixed system correlation parameter n, τ, c _pr, c _cr, K, c _sp, c _hand c _svalue, given f _aand F (t) _b, and calculate operation parts expectation out-of-service time μ=44 (t);

2) discretize preventative maintenance period T: selected △ T=1, take τ as lower bound, take 1.5 μ=66 as the upper bound;

The maximum part warehouse storage of discretize S: selected △ S=1, take n as lower bound, the n+2nM (μ)=240.988 of take is the upper bound;

3) get i=0;

4) if T _i=τ+i △ T>1.5 μ, enters step 12); Otherwise enter step 5);

5) calculate discrete time node T _icorresponding M (T _i) and D (T _i);

6) get j=0;

7) if S _j>240.988, enters step 10), otherwise enters step 8);

8) calculate according to the following formula discrete stock's node S _jthe corresponding initial tank farm stock S of spare part _a,

By S _abringing maintenance and spare part into supplies with combined optimization model and calculates corresponding C _{2, ∞}(S _j, T _i):

9) get j=j+1, return to step 7);

10) calculate the optimum solution S of spare part maximum inventory S ^{i, *}:

11) get i=i+1, return to step 4);

12) find maintenance and spare part and supply with iptimum relationship: find one group of minimum solution and supply with iptimum relationship as maintenance and spare part $(S^{*},T^{*})=\left\{(S^{i,*},T_i)\right|\underset{i}{\min }{C}_{2,\&infin;}(S^{i,*},T_i)\}$ ; Finish.

The final result of calculation of the present embodiment is (S ^*, T ^*)=(136,22), C _{2, ∞}(S ^*, T ^*)=713.668, as shown in Figure 5, also, when spare part maximum inventory S is 136, corresponding predictability maintenance cycle T is 22 weeks, the standby mode of giving of this maintenance can make overall system scale of charges reach minimum, can reach 713.668units.

Although the disclosed embodiment of the present invention as above, the embodiment that described content just adopts for the ease of understanding the present invention, not in order to limit the present invention.Technician in any the technical field of the invention; do not departing under the prerequisite of the disclosed spirit and scope of the present invention; can do any modification and variation what implement in form and in details; but scope of patent protection of the present invention, still must be as the criterion with the scope that appending claims was defined.

Claims (9)

1. the maintenance under stock's degraded data deletion condition and spare part are supplied with a combined optimization method, comprise the following steps:

S100, based on spare part out-of-service time distribution function, set up randomicity stock degradation model;

S200, based on randomicity stock degradation model, analytic system maintenance and spare part are supplied with correlative charges, and described expense comprises expectation maintenance cost, expectation spare parts purchasing expense, expectation spare part storage cost and the expectation spare part shortage failure costs of system within a preventative maintenance cycle;

S300, based on randomicity stock degradation model, the minimization system of take maintenance and spare part supply cost are target, set up maintenance and spare part and supply with combined optimization model;

S400, based on maintenance and spare part, supply with the bound of combined optimization model and given amount to be optimized, obtain maintenance and spare part the relation between supply and demand optimum solution, described amount to be optimized comprises predictability maintenance cycle and the spare part maximum inventory of system.

2. combined optimization method as claimed in claim 1, is characterized in that, described step S100 further comprises:

There is m spare part in part warehouse in the system of setting up departments, the out-of-service time distribution function of each spare part is p (t), it is mp (t) that the distribution of the inefficacy spare part number Y of system in time t is approximately average, variance is the normal distribution of mp (t) (1-p (t)), and the probability density function of Y is g _y(y):

$g_Y\left(y\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\&pi;}}\&CenterDot;\sqrt{m\&CenterDot;p\left(t\right)\&CenterDot;(1-p\left(t\right))}}{e}^{-\frac{{(y-m\&CenterDot;p\left(t\right))}^2}{2m\&CenterDot;p\left(t\right)\&CenterDot;(1-p\left(t\right))}}& ,m>0\\ \mathrm{\&delta;}\left(y\right)& ,m=0\end{array}\right.$

Wherein, δ (y) is unit impulse function, and

3. combined optimization method as claimed in claim 1, is characterized in that, described step S200 further comprises:

S210, analytic system inefficacy maintenance frequency:

System in a preventative maintenance period T, the expectation E[X of Failure count X of each operation parts]=M (T), function M (k) obtains by following approximate formula iterative computation when the k=T:

$M\left(k\right)=\underset{i=0}{\overset{k-1}{\mathrm{\&Sigma;}}}[1+M(k-i-1)]\&CenterDot;{\&Integral;}_i^{i+1}{f}_a\left(t\right)\mathrm{dt},k=\mathrm{1,2},...$

M(0)=0

Variance Var[X] utilize following approximate formula to calculate acquisition::

$\mathrm{Var}\left[X\right]=D\left(k\right)=M\left(k\right)-M{\left(k\right)}^2+\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}M(k-i)[M(i+1)-M\left(i\right)]\\ +M(k-i-1)[M\left(i\right)-M(i-1)]\end{array}\right\}$

Wherein, f _a(t) be the probability density function of operation component failure time, k is discrete magnitude, is positive integer;

Operation part count in system is n, in a preventative maintenance period T, and thrashing maintenance frequency X _nobey expectation for E[X _n]=nM (T), variance is Var[X _n]=nVar[X] normal distribution, and X _nprobability density function be

;

S220, analysis Parts Inventory amount of degradation:

The system spare part original bulk when preventative maintenance period T starts of setting up departments is S _a, spare part out-of-service time distribution function is p (t)=F _b(t)=p, the probability density function of the spare part number Y that lost efficacy in preventative maintenance period T is:

$g_Y\left(y\right)=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\&pi;}}\&CenterDot;\sqrt{S_{a}p(1-p)}}{e}^{-\frac{{(y-S_{a}p)}^2}{2S_{a}p(1-p)}}& ,S_a>0\\ \mathrm{\&delta;}\left(y\right)& ,S_a=0\end{array}\right.$

E[Y now]=S _ap;

S230, analysis spare part maximum inventory S and spare part original bulk S _abetween relation:

$\begin{array}{c}{S}_a=S-n-E[X_n\left(T\right)-X_n(T-\mathrm{\&tau;})]-E[Y\left(T\right)-Y(T-\mathrm{\&tau;})]\\ =S-n-n[M\left(\tilde{T}\right)-M(\tilde{T}-\mathrm{\&tau;})]-S_a[p\left(T\right)-p(T-\mathrm{\&tau;})]\end{array}$

Wherein, τ is for ordering the delivery time of spare part;

S240, analyze an expectation maintenance cost C in preventative maintenance period T _mfor:

C _M(S _a,T)=c _pr·n+c _cr·E[X _n]

Wherein, c _prthe expense that represents each preventative maintenance, c _crthe expense that represents each correction maintenance;

S250, analyze an expectation spare parts purchasing expense C in preventative maintenance period T _ofor:

C _o(S _a,T)=K+c _sp·(n+E[X _n]+E[Y])

Wherein, K represents disposable buying expenses, c _spthe unit price that represents spare part;

S260, analyze an expectation spare part storage cost C in preventative maintenance period T _hfor:

$C_h(S_a,T)=c_h\&CenterDot;\left[\begin{array}{cc}\underset{0\&le;X_n+Y+S_a}{\&Integral;\&Integral;}(S_a-\frac{x_n+Y}{2})\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dyd}{x}_n& \\ +\underset{X_n+Y>S_a}{\&Integral;\&Integral;}\frac{S_a}{2}\&CenterDot;\frac{S_a}{x_n+Y}\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n& \end{array}\right]$

$=c_h\left[\begin{array}{c}{\&Integral;}_0^{S_a}{\&Integral;}_0^{S_a-x_n}(S_a-\frac{x_n+y}{2})\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\&Integral;}_0^{S_a}{\&Integral;}_{S_a-x_n}^{\&infin;}\frac{S_a}{2}\&CenterDot;\frac{S_a}{x_n+y}\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\&Integral;}_{S_a}^{\&infin;}{\&Integral;}_0^{\&infin;}\frac{S_a}{2}\&CenterDot;\frac{S_a}{x_n+y}\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n\end{array}\right]$

Wherein, c _hstorage cost for single spare parts list bit time;

S270, analyze expectation spare part in a preventative maintenance period T shortage failure costs C _sfor:

$C_s(S_a,T)=c_s\&CenterDot;\underset{X_n+Y>S_a}{\&Integral;\&Integral;}\frac{x_n+Y-S_a}{2}\&CenterDot;\frac{x_n+Y-S_a}{x_n+Y}\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n$

$=c_s\left[\begin{array}{c}{\&Integral;}_0^{S_a}{\&Integral;}_{S_a-x_n}^{\&infin;}\frac{x_n+y-S_a}{2}\&CenterDot;\frac{x_n+y-S_a}{x_n+y}\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right)\mathrm{dy}{\mathrm{dx}}_n\\ +{\&Integral;}_{S_a}^{\&infin;}{\&Integral;}_0^{\&infin;}\frac{x_n+y-S_a}{2}\&CenterDot;\frac{x_n+y-S_a}{x_n+y}\&CenterDot;T\&CenterDot;g_{X_n}\left(x_n\right)g_Y\left(y\right){\mathrm{dydx}}_n\end{array}\right]$

Wherein, c _sshort failure costs for single spare parts list bit time.

4. combined optimization method as claimed in claim 1, is characterized in that, described step S300 further comprises:

It is target that the minimization system of take maintenance and spare part are supplied with correlative charges, take maximum part warehouse storage S and preventative maintenance period T as amount to be optimized, sets up following Optimized model:

$\begin{array}{cc}\min & C_{2,\&infin;}(S,T)=C_{2,\&infin;}(S_a,T)=\frac{C_M(S_a,T)+C_o(S_a,T)+C_h(S_a,T)+C_s(S_a,T)}{T}\\ s.t.& S_a\&GreaterEqual;0,T>0\end{array}$

Wherein, S _afor the spare part original bulk of system when a preventative maintenance period T starts, C _mbe an expectation maintenance cost in preventative maintenance period T, C _obe an expectation spare parts purchasing expense in preventative maintenance period T, C _hbe an expectation spare part storage cost in preventative maintenance period T, C _sit is an expectation spare part shortage failure costs in preventative maintenance period T.

5. as right, will remove the combined optimization method as described in 1, it is characterized in that, described step S400 further comprises:

1) give fixed system correlation parameter, described parameter comprises the parameters of computing system maintenance and spare part supply correlative charges, to the fixed system probability density function f of operation component failure time _aand spare part out-of-service time distribution function p (t)=F (t) _b, and calculate the operation parts expectation out-of-service time (t)

2) set bound the discretize amount to be optimized of amount to be optimized:

Bound [the T of preventative maintenance period T is set _min, T _max], and according to interval △ T discretize preventative maintenance period T, obtain discrete time node T _i=T _min+ i △ T, i=0,1,2 ...;

Set the bound [S of spare part maximum inventory S _min, S _max], and according to interval △ S discretize spare part maximum inventory S, obtain discrete stock's node S _j=S _min+ j △ S, j=0,1,2 ...;

3) get i=0;

4) compare discrete time node T _iwith upper bound T _maxif, T _i>T _max, enter step 12), otherwise enter step 5);

5) calculate according to the following formula discrete time node T _icorresponding M (T _i) and D (T _i):

$M\left(T_i\right)=\underset{0}{\overset{T_i-1}{\mathrm{\&Sigma;}}}[1+M(T_i-i-1)]\&CenterDot;{\&Integral;}_i^{i+1}{f}_a\left(t\right)\mathrm{dt}$

M(0)=0

$D\left(T_i\right)=M\left(T_i\right)-M{\left(T_i\right)}^2+\underset{i=1}{\overset{T_i}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}M(T_i-i)[M(i+1)-M\left(i\right)]\\ +M(T_i-i-1)[M\left(i\right)-M(i-1)]\end{array}\right\}$

6) get j=0;

7) more discrete stock's node S _jif, S _j>S _max, enter step 10), otherwise enter step 8);

8) calculate according to the following formula discrete stock's node S _jthe corresponding initial tank farm stock S of spare part _a,

S _a=S-n-E[X _n(T _i)-X _n(T _i-τ)]-E[Y(T _i)-Y(T _i-τ)]

=S-n-n[M(T _i)-M(T _i-τ)]-S _a[p(T _i)-p(T _i-τ)]

By S _abringing following maintenance and spare part into supplies with combined optimization model and calculates corresponding C _{2, ∞}(S _j, T _i):

$C_{2,\&infin;}(S_j,T_i)=\frac{C_M(S_a,T_i)+C_o(S_a,T_i)+C_h(S_a,T_i)+C_s(S_a,T_i)}{T}$

Wherein, C _mbe an expectation maintenance cost in preventative maintenance period T, C _obe an expectation spare parts purchasing expense in preventative maintenance period T, C _hbe an expectation spare part storage cost in preventative maintenance period T, C _sbe an expectation spare part shortage failure costs in preventative maintenance period T,

9) get j=j+1, return to step 7);

10) calculate the optimum solution S of spare part maximum inventory S ^{i, *}:

$S^{i,*}=\left\{S_j\right|\underset{S_j}{\min }{C}_{2,\&infin;}(S_j,T_i)\}$

T now _iit is set-point;

11) get i=i+1, return to step 4);

12) { [S obtaining ^{i, *}, T _i, C _{2, ∞}(S ^{i, *}, T _i)] in set, find out the one group of solution that makes system maintenance and spare part supply with correlative charges minimum and as maintenance and spare part, supply with the optimum results of associating relation:

$(S^{*},T^{*})=\left\{(S^{i,*},T_i)\right|\underset{i}{\min }{C}_{2,\&infin;}(S^{i,*},T_i)\}$

Wherein, S ^*for spare part maximum inventory optimum results, T ^*for corresponding preventative maintenance cycle optimum results, finish.

6. combined optimization method as claimed in claim 5, is characterized in that:

In described step S400, the lower bound T of described preventative maintenance period T _minvalue and spare part to order delivery time τ relevant, upper bound T _maxvalue relevant with operation parts expectation out-of-service time μ.

7. as right, to remove the combined optimization method as described in 6, it is characterized in that:

T _min=τ，T _max=1.5μ。

8. as right, to remove the combined optimization method as described in 5, it is characterized in that:

In described step S400, the lower bound S of described spare part maximum inventory S _minvalue relevant with the operation part count n of system, upper bound S _maxthe operation part count n of value and system relevant with operation parts expectation out-of-service time μ.

9. as right, to remove the combined optimization method as described in 8, it is characterized in that:

S _min=n，S _max=n+2·n·M(μ)。

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