<>2021 Mathematical modeling of May Day cup A topic
<> Vaccine production issues
Novel coronavirus pneumonia rages the world , It has brought profound disasters to the world . Countries have developed new coronavirus vaccines to control the epidemic . It is assumed that vaccine production needs to go through CJ1 Station ,CJ2 Station ,CJ3 Station and
CJ4 Station, etc 4 Process flow . Each process can be treated at one time 100 Dose vaccine , this 100 The vaccine is put into a processing box and sent to the equipment at the station for treatment . and , Only according to CJ1-CJ2-CJ3-CJ4 The order of 4 After all stations have been processed , To complete production . To prevent confusion in vaccine packaging , Regulations of the production department of a vaccine production company , Each station cannot produce different types of vaccines at the same time , Vaccine production is not allowed to jump the queue , That is, once the production sequence of each type of vaccine arranged in the first station is determined, it must remain unchanged , And after the former type of vaccine leaves a station , The latter type of vaccine can enter this station .
existing YM1-YM10 etc. 10 Two different types of vaccines need to be produced . For safety's sake , Each type per box （ Built in vaccine 100 agent ） The vaccine was tested at each station 50 Secondary simulation production . find , Due to production equipment , Vaccine purification and other reasons , The time required for each station to produce different types of each box of vaccine is not stable , See the attachment for detailed data 1.
Please build a mathematical model , Answer the following questions :
problem 1： Please average the production time of each box of vaccine at all stations , variance , Maximum value , Statistical analysis of probability distribution , In order to facilitate the managers of vaccine production companies to intuitively grasp the ability level of vaccine production in each station , Provide reference for vaccine production .
problem 2： Urgent need of vaccine testing department in a country YM1-YM10 various 100 Doses of vaccine were tested . In a hurry , Vaccine production companies need to plan the production sequence of vaccines , So that it can be delivered in the shortest time , Based on the average time of producing each box of vaccine at each station . Please build a mathematical model , Develop vaccine production sequence , The initial time is 00:00, Calculate total production time , And fill the results in the table 1.
problem 3： In actual production , The time required to produce each vaccine at each station is random . If the company is required, the total delivery time of vaccine is less than the problem 2 Reduced total time 5%, Please build a mathematical model , The goal is to complete the task with the greatest probability , Determine the production sequence , The relationship between the proportion of shortened time and the maximum probability is given .
problem 4： Now the vaccine production company has received 10 Production tasks of different types of vaccines on different scales （ See Annex 2）. Because the production machine needs overhaul and maintenance , The daily production time of each station shall not exceed 16 hour . To avoid incorrect packaging of vaccines , It is required that the production task of each type of vaccine cannot be split , That is, another type of vaccine can be produced only after the production of the same type of vaccine is completed . Please build a mathematical model , When reliability is 90% Arrange production plan under the premise of , At least how many days can you complete the task ?
problem 5： If the vaccine production company plans to 100 Select part of the vaccine for production within days , The daily production time of each station shall not exceed 16 hour , The production task of each type of vaccine can be properly split , That is, each type of vaccine can only be partially completed . Target maximum sales , Please establish a mathematical model and arrange the production plan .
<> Establishment and solution of model ( part )（ See the comment area for all documents and procedures ）
<> Establishment and solution of the first mock exam model ：
<> Problem two modeling and solving ：
<> Problem three modeling and solving ：
According to the first question , Probability distribution of vaccine on each production line , All belong to normal distribution . in other words , In the above formula , We can regard it as the deviation coefficient τ Conform to normal distribution . that , Just use matlab
Generated by random values of normal distribution , The random production time of vaccine can be simulated . In the second question , We use Matlab
All cases are traversed to test the results . In this question , We can use the code of the second question , Add conditions according to the meaning of the question . Repeated calculation α second , Through the method of the second question , Calculate the final time of each time
T, Count the final time in all times T less than 95% Number of minimum times β, Then the approximate probability of the scheme can be obtained P=β/α
<> Establishment and solution of problem 4 and problem 5 models ：
<> The program code is as follows ：
A=[13.284 9.8708 20.0584 7.9886 8.77 19.0741 11.1601 16.0201 15.0146 12.9524
14.9621 19.9075 15.9726 9.9366 13.722 20.0943 16.4961 8.8274 12.0351 7.0109
19.846 17.9281 14.9703 5.9358 13.0052 14.1485 12.0136 18.1143 7.0419 9.0491
20.0129 18.9423 15.1163 18.1283 11.2494 13.8838 19.0876 16.8313 8.9496 16.0524 ]
; Y=[1.593979267 0.793439961 0.809040273 0.999774981 0.613356028 1.315886921
1.032082042 1.229791443 0.991973399 0.20800367 1.051043473 1.121878635
0.648764524 0.988125675 1.15461187 0.876216121 0.901073535 0.226411679
1.220333417 0.294923796 1.222915487 0.899972852 1.082819843 0.039376599
0.866617616 0.914373457 0.694742886 1.134968066 0.130686652 0.196699049
1.849122356 0.898665829 0.858227975 1.138880455 1.279170491 1.227569715
0.685524548 0.97057379 0.181558835 0.260809703]; x=; baogao=0; maxgailv100=;
maxgailv70=;maxgailv65=;maxgailv60=; maxgailv55=;maxgailv50=; T100=
191.7157; T95=191.7157*0.95; T90=191.7157*0.90; T85=191.7157*0.85; T80=191.7157*
0.80; T75=191.7157*0.75; T70=191.7157*0.70; T65=191.7157*0.65; T60=191.7157*0.60
; T55=191.7157*0.55; T50=191.7157*0.50; aa=perms(1:10); b=1814400; for j=1:
1814400 a(j,:)=aa(ZI(1,j),:); end for c=1:b count100=0; count95=0; count90=0;
count85=0; count80=0; count75=0; count70=0; count65=0; count60=0; count55=0;
count50=0; baogao=baogao+1 for i=1:500 q=normrnd(0,1,1,1); x=A+Y*q; x1=a(c,:);
T1=x(1,a(c,1)); T2=x(2,a(c,1))+x(1,a(c,1)); T3=T2+x(3,a(c,1)); T4=T3+x(4,a(c,1))
; for d=2:10 for e=1:4 if e==1 T1=T1+x(1,a(c,d)); end if e==2 T2a=T2+x(2,a(c,d))
; T2b=T1+x(2,a(c,d)); if T2a>=T2b T2=T2a; else T2=T2b; end end if e==3 T3a=T3+x(
3,a(c,d)); T3b=T2+x(3,a(c,d)); if T3a>=T3b T3=T3a; else T3=T3b; end end if e==4
T4a=T4+x(4,a(c,d)); T4b=T3+x(3,a(c,d)); if T4a>=T4b T4=T4a; else T4=T4b; end
end end endif T4<=T100 count100=count100+1; end if T4<=T95 count95=count95+1;
endif T4<=T90 count90=count90+1; end if T4<=T85 count85=count85+1; end if T4<=
T80 count80=count80+1; end if T4<=T75 count75=count75+1; end if T4<=T70 count70=
count70+1; end if T4<=T65 count65=count65+1; end if T4<=T60 count60=count60+1;
endif T4<=T55 count55=count55+1; end if T4<=T50 count50=count50+1; end end h100=
count100/500; maxgailv100(1,c)=h100; h95=count95/500; maxgailv95(1,c)=h95; h90=
count90/500; maxgailv90(1,c)=h90; h85=count85/500; maxgailv85(1,c)=h85; h80=
count80/500; maxgailv80(1,c)=h80; h75=count75/500; maxgailv75(1,c)=h75; h70=
count70/500; maxgailv70(1,c)=h70; h65=count65/500; maxgailv65(1,c)=h65; h60=
count60/500; maxgailv60(1,c)=h60; h55=count55/500; maxgailv55(1,c)=h55; h50=
count50/500; maxgailv50(1,c)=h50; end MAX100=max(maxgailv100) MAX95=max(
maxgailv95) MAX90=max(maxgailv90) MAX85=max(maxgailv85) MAX80=max(maxgailv80)
MAX75=max(maxgailv75) MAX70=max(maxgailv70) MAX65=max(maxgailv65) MAX60=max(
maxgailv60) MAX55=max(maxgailv55) MAX50=max(maxgailv50) Answer documents and procedures for this topic ： print(