AD-R124 518 HEDGSIM ROUTINES FOR LEADTIME VARIABILITY INVENTORY i/IPOLICY RESERRCH(U) DECISION SYSTEMS BEAYERCREEK OHN S DENNY SEP Si idP-8i-02 F33600-88-C-0530

UNCLSSIFIED F/0 9/2 N

IF END

'IIVA

LL8.,

1.25 11.

fl~ui~hiU%

.IuIR.C. REOUINTS HREATOt, WOFSADRS16-

VOW0

kg4j+tA. VPi~

L

DISCLAIMER NOTICE

THIS DOCUMENT IS BEST QUALITYPRACTICABLE. THE COPY FURNISHEDTO DTIC CONTAINED A SIGNIFICANTNUMBER OF PAGES WHICH DO NOTREPRODUCE LEGIBLY.

U

6%

r.....................* U * * ' * ..

* -2- . OF. .- . .-.. . -

1. TITLE AND ACRONYM , Rcea-a,-, s /' . L.4 r",a QAt bZL.T jL -

4. STATUS 5. STARTINO DATE S. COMPLETION DATE 7. ORGANIZATION REPORT NO,

S. DLIE SEARCH NO. S. CONTRACT NO. 10 TYPE STUDY 11. TIME FRAME 12. COST

I&. SECURITY CLASS 14L DWTIUEUTION LIMITATION 1 MAUR swaiT

"eAs s.S9 Mt'. -z-7-ff R '116 STUDY SPONIOR 1". PERFORMING OMGANigAT

= , e X~ PE. S-.72e oE ri.

RESPONSIBLE INDIVIDUAL RSPONSIBLE INDIVIDUAL A. S r-7',. v4p"

AUTOVON AUTOVON

COMMERCIAL NO. COMMERCIAL NO. /-S- ","? , - tE.5

13. ABSTRACT IUNCLASSIFIED)

$'.,ge,4 r.r', _ , ,4 4-4. WA w ra 4c;D4 V-VC 8 r4.o

I& CONCLUSIONS 1UNCLASSIFIEDI

• "FES I t

2& RECOMMENDATIONS IUNCLAESIFIED)

\ dto

XNqC Fr m 331 A,,rmy. . .9 1 'I1 i. I . l

HEDGSIM ROUTINES

for

Leadtime Variability

Inventory Policy Research

0

by

W. Steven Demmy

September 1981

WP-81-02Decision Systems

2125 Crystal Marie DriveBeavercreek, Ohiot 45431

(513) 426-8515

_77777 7'. .......... . . ..

SECURITY CL ASSIFICATION OF THIS PAGE (When Datl Kntered)

REPORT DOCUMENTATION PAGE OE ,OsPLuTI FORM

I- REPORT NUMBER -- 2. ACCFSSION NO. 3 RECIPIFN T"S CATALOG NUMBER

4. TITLE (and Subtitle) S TYPE OF REPORT & PERIOD COVERED

HEDGSIM Routines for Leadtime Variability INTERIM',.,Inventory Policy Research

I t PR a6 PERFORMING O4G. REPORT NUMBER

_ _ __-_ _WP-81-027. AUTHOR(a) 8 CONTRACT OR GRANT NUMBER(s)

F33600-80-C-0530W. Steven Demmy

S. PERFORMING ORGANIZATION NAME AND ADDRESS 10 PROGRAM ELEMENT, PROJECT, T ASKAREA & WORK UNIT NUMBERS

Decision Systems2125 Crystal Marie DriveBeavercreek, Ohio 45431

It. CONTROLLING OFFICE NAME AND ADDRESS I. REPORT DATE

Directorate of Management Science September 1981Hg. AFLC/XRS 13 NUM,.ER OF PAGES

Wiqht-Patterson.Air Force Base, Ohion14. IT MTING AGENCY NAME & ADORESS(iI dlferenl from Controlilng Office) 1S SECURITY CLASS. (of this report)

ISa DECLASSIFICATION DOWNGRADING -

SCHEDULE

16. DISTRIBUTION STATEMENT (of thle Report)

17. DISTRIBUTION STATEMENT (of the .betact entered In Block 20. If fiflermet from Report)

IS. SUPPLEMENTARY NOTES

I. KEY WORDS (Continue on revere Olde II neceEsary end Identfy by block number)

AGo bybok"ohr

:2|0, ABS CT (Continue on reverse side It necessary and Identity t

y block nwu,,her)

This paper documents Fortran Source Code for simulating GarmnaLeadtimes and Negative Binomial requisition sizes in the HEDGSIMLong Supply Simulation Model.

DO , ON. ,, 1473 EDITION OF I NOV s IS OBSOLETE

SECURITY CLASSIFICAION OF TNI' PAnt t , 'i, ..

Rp p..- 7 --.7-7

Table of Contents

I. Introduction

Appendix A. Job Control Language Programs

INV.OC.HIINVR.A

Appendix B. Fortran Source Listings

B.1. Forecasting and Levels Calculation Routines

FORS76LEVELNLPGFORSN BRO P

B.2. Negative Binomial Requisition Size Routines

DEMPARNEGBINNEGBN1RANDEM

B.3 Modified HEDGSIM Routines

INITEMINORDINVRSMENTERB

F I tag.1,, ,,,. "0--

Avallabuity Codes

Dt

Introduction

This paper documents a series of subroutines developed in

support of inventory policy research concerning the impacts of

lead time variability upon D062 Economic Order Quantity Items.

The subroutines are designed to operate within the framework

of the HEDGSIM Long Supply Simulation Model. Appendix A contains.i

, Job Control Language (JCL) statements required to utilize these

new routines with other members of the HEDGSIM simulation program

library. On the other hand, Appendix B presents the Fortran

source program listings of new routines developed for this study.

The new routines documented in this paper may be assigned

to one of three different categories. These are: (a) routines

for proposed forecasting or safety level calculations, (b) routines

for simulating negative binomial requisition sizes, and (c) modified

e- - HEDGSIM routines required to implement the above programs.

Let us now consider each of these categories.

Routines for Proposed Forecasting and Safety Level Calculations

This category includes subroutines FOR576, LEVELN, LPGFOR,

. and SNBROP. Subroutine FOR576 is the same as the original HEDGSIM

routine with the addition of an outliers test when the forecasting

1. -.- ;.. - . . ... *. . .... . . . -- . * . * . * .-

1-2

code ICDFOR - 3. When ICDFOR = 3, the subroutine checks if the

largest observed demand exceeds the average demand plus four

times the mean absolute deviation (computed using the remaining

seven observations). If so, FOR576 assumes the large demand is an

"outlier" that is not expected to occur again in future quarters.

In this case, the forecasting calculations exclude the outlier

data. Subroutines LPGFOR and SNBROP compute optimum reorder

, levels using the Logarithmic-Poisson-Gamma (LPG) and scaled nega-

tive binomial models, respectively. Subroutine LEVELN calls

*. these subroutines and also provides other safety level computation

options within the LEVELN logic. As noted above, listings of

these programs may be found in Appendix B.

Routines for Negative Binomial Requisition Size Simulation

Subroutines in this category include DEMPAR, NEGBIN, NEGBN1,

and RANDEM. These routines implement the generation of negative

binomial requisition sizes using techniques described in Reference 2.

Subroutine NEGBIN utilizes the twelve most recent observations

of actual D062 demand histories to estimate the parameters of

a negative binomal distribution of requisition size. It also

constructs the cumulative distribution function (CDF) of this

distribution. In turn, subroutine NEGBN1 utilizes this CDF to

determine the specific requisition size associated with a randomly

chosen percentile of the requisition size distribution. Subroutine

RANDEM provides a uniform (0,1) ramdom number stream which is

: ~..................... -•........ ... ,....... ..... ...... -...?..---,.--.-, - -, - -----

1-3

*.... used exclusively in the demand generation process. This guarantees

that exactly the same sequence of requisitions is generated for

a given random number seed regardless of the management policy

being evaluated. Finally, subroutine DEMPAR calls subroutines

NEGBM1 and RANDEM as needed to generate the specific requisition

streams associated with a given demand history. Subroutine NEGBIN

is called to initialize the negative binomal requisition size

distribution by subroutine INITEM, while the ramdom number generator

RANDEM is initialized by the MAIN program at the beginning of

a simulation run. Subroutine DEMPAR also includes new logic

to insure that very high activity items do not cause the future

events list to overflow. With the new logic, after 450 requisi-

tions have been generated, all remaining units of demand associated

with a given quarter are placed on one (last) requisition. Only

extremely high activity items are impacted by this change.

Modified HEDGSIM Routines

Subroutines included in this category are INITEM, INORD,

INVRSM, and ENTERB. As noted above, these routines contain very

slight modifications to the original HEDGSIM programs. Subroutine

INITEM now contains a call to subroutine NEGBIN to initialize

the negative binomal requisition size simulation procedure.

Subroutine INORD has been modified to generate GAMMA distributed

lead times with a coefficient variation equal to .353. Data

4

___ __, L

i- . . .

1-4

collected by Hayya (1980) indicates that such a distribution

describes a number of D062 items (See Tables 1-1 and 1-2). The

program INVRSM is essentially identical to the HEDGSIM MAIN program,

excepted it now contains a call to initialize subroutine RANDEM.

When simulating high activity items with average requisition

sizes that are close to one, very large numbers of requisitions

*: may be generated within the simulation model. If policies are

being simulated which offer very low levels of support, this

can result in very large numbers of back orders. In turn this

*may cause the HEDGSIM backorder file to overflow. Subroutine

ENTERB prevents this from happening by cancelling all new back-

orders once the backorder file is filled. With the present coding,

once five hundred requisitions have been backordered, all subse-

quent requisitions are cancelled.

'I •,.

1-5

Table I-i

Coefficients of Variation of Lead Times

Observed by Hayya (1980)

for 62 High Activity Items

Coefficient of Number of

Variation Items

.1 8

.2 13

.3 15

.4 11

.5 6

.6 2

.7 2

.8 1

.9 3

1.0 1

N 62

Median .36

'

N! ~~~...... . ,-.-.-..',•. ....... .-................

r-6

Table 1-2

Gamma Probabilities forMean = 1 and Coefficient of Variation = .353

x P(x) P(XAx)

.100 .000 .000

.200 .001 .001

.300 .007 .007

.400 .022 .030

.500 .048 .077

.700 .101 .255

.900 .119 .490, .602

1.100 .098 .700-- -1'f' -.T1.300 .054 .844

N -8 .8921.500 .035 .927

1.700 .017 .969

1.900 .007 .987

2.000 .005 .9922.100 .003 .9952.200 .002 .9972.300 .001 .9982.400 .001 .9992.500 .000 .9992.600 .000 1.0002.700 .000 1.000

Note: Underlined values have been incorporated into SubroutineINORD.

.4

. . . .. . . . . . . . . . . . . . . . . . . . . .

References

1. Demmy, W. Steven, HEDGSIM: The Long Supply Simulation Model:Volume II Program Listing and Narratives,Working Paper 80-10, Decision Systems, Z15 Crystal Marie Drive,Beavercreek, Oh 45431, Dec 1980, 97 pp.

2. Demmy, W. Steven, Modeling the Probability Distribution forDepot-Level Requisition Sizes, Working Paper 80-07, DecisionSystems, 2125 Crystal Marie Drive, Beavercreek, Oh 45431, Oct1980, 160 pp.

3. Hayya, Jack C., Lead Time Variability in Inventory RequirementsProjections Air Force Contract 33615-79-C-5143, Item 0004, Phase3, Technical Report and Summary, 1962 Norwood Lane, State College,

• Pa, 16801, June 30, 1980, 71 pp.

-"

APPENDIX A

'1 JOB CONTROL LANGUAGE PROGRAMS

INV.OC.H

INVR.A

-p

-.

-' - C ~ ~ - - - . - . - *

20 5 IDENT UPI640,KRS-EK 109.0c."

30 5 III70,,,lf#(40 0 NOTE *e*s4a.**.s*[NSA.JCL DATA FILE FOLLOVS THIS LI1NE50 1 OPTION FORTRAN,NONAP60 s SELECT INVA/03J/IHYRSH.O65 $ SELECT INVR/OSJ/SMBROP.070 $ SELECT HEBO/O#J/911*ULA.Os0 s SELECT HED6O9JJAE9.D90 5 SELECT H4EDG/O#J/CUN.O100 5 SELECT IfEDG/OIJ/CUflB.O110 s SELECT MEIO/ODJ/DENPR3.O120 S SELECT NEWGOBJ/ENTR13.O130 s SELECT HE06/OBJ/FILLDO.O140 $ SELECT NEIG/OWJF0R373.0150 $ SELECT HEDSOIJ/INITAL.0160 S SELECT HEO/DDJ/INITNt3.O170 $ SELECT NEDW/IJ/II4RD3.O180 s SELECT HEDB/OIJ/LEVLN3.0Ito s SELECT HEDO/IJ/LONGSP.O200 s SELECT HEDO/OD.I/ORDER.O210 $ SELECT HEDGIOBJ/OUTREP.O220 $ SELECT NED6/ODJ/PFAC.O230 s SELECT NEDB/ODJ/PLOTR.D240 $ SELECT REDO/ODJIRECEIV.O230 $ SELECT HIDS/ODJ/RE7.O260 $ SELECT HEDO6/OIJ/IATN2.O270 $ SELECT HEDSDJ/SSTAT2.O260 $ SELECT HEDO/ODJ/ZERO2.O290 $ NOTE R..s.ss.*,eE OUT INES FOLLOW -----300 4 *OTE .e*i**ss *sREUS ROUTINES FOLLOW THIS LINE310 s SELECT REOQS/STATUS.O320 S SELECT REGS/FORUPD.O330 6 SELECT REQS/LEVEL.O340 6 SELECT REOS/EI4TER.0350 4 SELECT REGS/REMOVE.0360 6 SELECT REQSIURIFEL.S370 $ SELECT RIQSINFEL.O360 $ SELECT REOS/RANlU.0390 s SELECT REOS/6P.O400 $ EXECUTE410 0 LINITS 7094Ks,i#K420 6 PRMFL O?/XlSRSINVR/1062OC.H430 $ FILE 08,126440 6 FILE 69oA38

*450 s NOTE ..e..SELEC1A NEDO/PFAC.1 FOR PROGRAM FACTOR$460 6 DATA 04470 6 SELECTA NEIO/PFAC.1

It4V.OC.1I

490 s DATA 05490 8060500 1 1 0

310 0 0 0 0 0 0 0520 0 0 0 0 0 00000 00.0 0 00000

- 530 7 2 38540 2 1 2 ? 1 2 1550 6 36 0 99560 .20 300. 500 19500 .5 1 C7570 1 30 1 500 8 0 SINULATE 500 ITEMS FOR 30 UTRS580 2000590 NOTE **************************RINE/6O/PUNCH.E*600 $ CONVER NSPIN610 s INPUT HNEDIA620 $ OUTPUT HODICI630 s FILE INA3S640 $ PUNCH OT650 1 ENDJOB

S

C....

-.:

°'

-.'

:" INV.C. H

.~

-%S

20 WDENT 1AP1596,XRS-DERWV INVR.A30 S LIMITS 1599,14K40 s NOTE ********i*INSN.JCL DATA FILE FOLLOWS THIS LINE50 s OPTION FORTRANtNONAP

*60 6 SELECT INVR/ODJ/INVRSI.O65 6 SELECT INVR/OBJ/SNBROP.O70 s SELECT HEDG/OJJ/SIIIULA.Oso s SELECT NED6/ODJ/REQ.O

*90 $ SELECT HEDG/O3J/CUK.O100 $ SELECT MEDG/ODJ/CUMB.O110 $ SELECT NEDG/OBJ/OENPR3.O120 S SELECT NEDG/OIJ/ENTR13.0130 s SELECT HEDG/OBJ/FILLDI.0140 s SELECT HEDG/OlJ/F0R573.O150 $ SELECT HEBB/OBJ/INITAL.0160 $ SELECT HEDO/ODJ/111TH3.0170 $ SELECT HED6/OBJ/INORD3.O150 s SELECT HED6/ODJ/LEVLN3.0190 6 SELECT HEDG/OlJ/LOHBSP.O200 $ SELECT HED6/OBJ/ORDER.0210 s SELECT HEVO/OlJ/OIJTREP.0220 $ SELECT NEBO/OVJ/PFAC.0230 $ SELECT HEDG/ODJ/PLOTR.G240 $ SELECT HEDB/03J/RECEIV.0

*250 5 SELECT NED6/O3J/RET.O260 $ SELECT IED6/GBJ/STATN2.0270 $ SELECT NEDG/ODJ/SSTAT2.0280 $ SELECT HElO/DIJ/ZERO2.O290 $ NOTE *******.4****',.6****PRED ROUTINES FOLIOS ----------300 s NOTE ss**********REGS ROUTINES FOLLOU THIS LINE310 $ SELECT REIS/STATUS.O

*320 $ SELECT REOS/FORUPD.O-330 6 SELECT REGS/LEVEL.O

340 6 SELECT REQS/ENTER.O350 s SELECT REGS/REMOYE.O360 5 SELECT REQI/VRIFEL.O370 6 SELECT REGS/INFEL.O360 6 SELECT REGS/fANDOO390 6 SELECT REIS/GP.O440 s EXECUTE410 6 LIMITS 15,4#Ktt1I(420 f PRNVL 07/XlS,RvSrINVR/l062Sff.N430 $ FILE 499X29440 $ FILE 09,638450 $ NOTE *****SELECTA NEIG/PFAC.D FOR PROORAN FACTORS460 9 DTA 04470 S ISLECTA NIGIPFAC.31

INVR.A

480 S DATA 05490 9030

*500 0 10 0510 0 01 0 1 0 0520 00 0 00 0 00 01 0 0 000 00 0 00

e.530 7 238540 21 2 91 2 1550 6 36 -99 99

*560 .20 300; 500 19,500 .5 1 C2'570 1 2 1 30 9 0 RUN 2 1RSp 30 17EMS560 25

a.650 $ ENDJOB

a.R

-i

484 AIA 0

-q

'., **v

FORECASTING AND LEVELS CALCULATIONS ROUTINES

FOR576

LEVELN

LPGFOR

SNBROP

* I-

CAIALVG(/F I[[F Of1 ~Cl R -' P.I(J: "F M/ ~&*b?4~III3f&J[)' 1i 4 !1( kI), OW) i.

? o*-F ' 1"9 1.

70 COX9 Isj;/ztp;

90 c()mmirm /1i ~/ ~ .;I (Y) (:(m-u /i wnTI/IrOi?110 CC)OMMON^ 'AM AC/N 01: AA C( I

A)2 COMM ill Al rVAC/tJ Wi- f AC ( 1)1 3) COMMOiW/!41 .0AC/N 1?1P)AC( 1)140 COMMON/1N'0 VF ND/tJi'FMI40V ( IqN rCoO')I li0 COPvMON /JU'SI Z/p Fos I Z ( I1 60 COMMON/N Ii1RU /F kI ~ N Yo)I1lo COMAO.,J/Nt W0/N'fI0( I ,N00Q)

I d'() COMdMON/A)WA I PP( I190 CCMMON/!Sf T/I GLT I)200 COkMMO(N /tN9F'1T/Nlt[NT( I)

210 COMMON/1-iA WMLTA[ M( I)220 COMM)N/Ll1 P?()OA.T-]PPl)(( I)2 30 Co.A3/C3/C)f240) COMMON / I i~ j(j/1 K)IJUG2'it) COMMON / I C')H)O/ I CIIF ot2 2CC CCmm0t/ ICO;1I(/ICi)S IG270 LI=(2 to) II)UMZo290 IFUM=O300 IRUM~o310 KK=NI)ENf(N)320 1IF (KK .Gr. 8)KK f330 KL=KK-1340 Do I I=I.KL350 IDUM=IflUM, + NI)FMNr)cN,I)360 IFUM=[FUM + NPFO(N,I)310 1 IP(JM=IQUM + NRFTUP(N,I)

390 IT-MOI)(ITIME, IT('1?)40)0 I?=FLOAT(IT) /FLOAT(IIUTN)?

410 P)M1.-' *FOA (NLFMAC (N ) )+FLOAT( I DOIM +, ?M *FLOAT C NIWMrND( N, KK))

430 FUJQIR*FLOA1 (N RIFACM )+FLOAT( IF UM) + M*F LAT(N P!-.Q(N, KK))440 PUM=R*FL)AT(NRFTAC(N))FLoAT(I RUM)+fM*F)AT(tlr?-.TUP(N. KK))

470 *480*SICOMPUTE LQEVFLI; kJASFI) ON N~t- D)EMAND)S, WHFRF NET 1S GROSS490*11 DF'AAND MINUS SFRVICEABLF RFTUFNS FOP TrHF PAST 24&r s 1I MONTHS,5. 1I*I8flETOrNtS ARE AD)DITIONS To ON-HAND ASSFTS.

F0R573 .SF0R576

p74I.

II F I~ I 'Na. W 4

'0 ' p ,OM I I [ I M ;I 'I -9 ~ ~

'p.C, A- l

C' I' F iiLJ(

I AtA X=-Q9 J )9Ifl 20 1 =I . KKI9~ '.A =N A IiA, p( I.,

'to r~ II~i? k ;!-. .4 if Ait- i~l~:fJe N *I)

130) IF(DFAi..I+.) 1AX) ;o To lo~

1'I5o IMAX=)-

100) 1 CONTI 11)JF

I I(': A0=' (10 A'~ A F V-FCi

IJF( I I 314 t.. 1;! - . 3)l *F'A=.Jt: A .rNI'PTJR N, I

~i CiA,)= (CoJ*IA .# +C11 A 1) 1( -LO AT ( K K + 14)tO I i-C( (AAI.1). F*. ').( 0 1 QMAAO=0.0 1

:It) [I- )FC-I , ,I CO)l ) 3. 11 AkCI flU F THE LA PFbGTsH8oc ~?Ai H FXCFR)f 4 A'

i C ~C II-Ce( I f- I- I I.TR I S TO 11F U SFD)

V 40 1I.-(KZi!0. I; . 3 )(;) '10g 40)9'CIF J(OMA . LI'. I . )rI) TO( 49

9 Ci)Ctoe~ I 0iIMAX,>Thll * *MAI)..' ~%)C I liIfj 'lACK IiT H I G' F IWMANDI

1010 'IT 0!1-( J. *1:) PC> I'-IMAX )W I.

F0R573.SF0R576

I ~ ~ C ),,A: W'j~jt /-P' r 'A:)

I ('40

1010 Il-CI. -0.1 )MAX ) GO F~O -39* I080 1fIF' zNI) Mt.':) ,

3090 1 G , i:.I. )1:, IX:M-.IJ(, N)I 1Y) lL'AI)=rTAL) + A,.';( 1)1:.A -T,* 0'.')

1 120) I'MAi)=IMI I 39C

1 150C IS 9 .iAX AN ()(J1 LI I-')I Ioo)cII 170 IF (AA X. UL. (TI'F' 1+4 .*MAl~) GO( To 40I I8)C

1d. 19 lACKV1 h-()l* V AI- 1J1K* ~~I 2I0 .F(PsrTH'

1 220 AI)R(N ) =4. *ulkST1230 A 04):=* MA 1)12?40 IF ( IFHU(,.6%l. I MRV 11 ':( 6, 33 )I)AX

* 1250 33 FORMA rC****Fo:,?5I6--3ACK OUT OUrLI F OF 'F8. I, UN ITSl)12 oOC127:) 40 couri tulI230C

1290CR.COMP-UTF. STAII)A?) I'FVIATJON OF LFAL)TJMF DR'4ANI)I 300C131.1 JRLT=F L)A r (L rA PM (N )+Lrp POI)(N)1 320 PSIGjLT('~ )=0.'-9415* MAI*0.823/i,0.4?)62i*1LT)1330 IF (PSI .T(N). I.T. 0.0 1) RSIGLTI( N)= 0. 01134 DCI 35()C I lCOMPIJTI AVFIIAW' IFOU ISIT ION SI ZEI 360C1.370 IFcFMiu.r. i)FM=l138,) lR=0)L4/kJ41390J IFC(P.LT. I .)R--I .

* 1400 R~ijSI?(N )=Pa,1410) GO r( 20'Y)')

1420C

FORS73.SFORS76

I Ac

1 ),1~ e-)i): I L( F I F ~ )NP UAC G. 1. (' 1I 0 PI: )' ON

'~1 dI r'-C L.~) V1 N,> IN 1 I XN ( N)I PF RI I I) S 11), 1 ' MNTPA) ii)II.U

1 ~~~i1114 00 (H..4f i 00 11 4X* 4**FP' IN .3- , I=LT ICP'P ,C)S 0

I ' L rAIfl1 , LTP!'?00) )I oOO 200 FONMAT( I i ,4 X. 1,)1 12 1 fI ol 0 -3 0x0 Fo-?',AAT( Ii, * ' LWNAID, 1?FTURNS, A ND FP[ff0,

63 ) 400 HYN~.A f IU H F)Res T ADR AVF -0 UCOSTP.

1056~0 O00 l0P'4A R I1i ,6F 10. 41 009 P FTII161/0 !-ND

'457 .

FO57

CA 1ALo'(3/f- Ft C R I fI ( rJ~ iI HI G/i j3

30~ .F L .sui o r N A V : - (J

50C 1T111S RO(UT IN F COMPtJTF.S oBII:K~ O<fIJFCTI VE ,1FT1NTI OIJoCx: TFrM IN AT I ON, ANJ)O ,~'I? LF:VULS.

d 0 P ALA M ET Fd N~ Q 0=3

I (Y) C110O C 0 OM ON /I i I iJ G/I H b UG112o Commol4/ I CI)F; IPICI)H)IN1 30 Co M PAON /Co . i R r/c o;)fi ir1 40 CO MM N/Cn.) h 1.)/(,0'St11,1)

I0 CO cMMN /C) !P K /CbTIV KI 70 Co MMON/IGR1 1:/G LJLEI kdO COMMON/GSLI:/(;I61F

100 COIMMON/GTLF/(,TLF210) cokomr)/ir INV/IT'INV220 commori I rLEVL/1r1*[-VL230 COMMON/I I1-VL/I D)LFVL240 CO M 4 N/IN I TT-M /N IT FM

250) CO MMON/N AI IS/NDI S260) COMMON /POL ITCYICI)FOQ. I CDiL. EoYA AX, FOOM I N. SLMAX ,SLM IN. ,PLF.TLF. S m2 1) COMMW'I/I CO)S IL/ I Cr):3 Lt.280 COMAON/AIDuVA1)R( 1 )290 COMMON /LTAI)A/LTADM ( I300 COMMoN/LTPIIOIYLTPROD( I)310 COMMON/I I40TY1I ITYCI32(1 COMMON/ IRL/ IRL ( I)330 COMMON/ I WL/ IIOL(I340 COMMON /I SLI/ISU(I350O COMMON/SFVL/ISLFVL(I)360 COMMON/ifuTI/T I )310 COMMON/SGLT/PSfGLr(1380 COMMON/IWQSI1Z/RFG6SIZ(I390 C.OMMON/JCOsTr/IcoST( I )400 COMMCN/,WF/jF(NO(O), PFA( NOQO,30) ,ACODF( 30) ,NCOI)E,AIPC?F410 COMMONI ISMCC / I I5MGC,420 D)ATA Z1I.01430 DATA ITLMI'J, J-hMINl/()999))99,99Q9999/440C~450C CO'APUTFP LANNING FACTORS

410 AMJ)AmCOSHRr

LEVLN3 .SLEVELN

SI 0TW I I Ii j Vf

:~r?1 0

60 5.i

600jO 20 J'l-( I l N ti I F

110 Q1.,C AT= AFOV ** I IM I

10O

/Q .0 CNT(,()T~t1

120

160C SFT Cot F:()I.AI- *0 WAM-1. lWJCJAS!H ORDER C )ST-C, C,'1/0 ('0 I?=CO'io'V'I) I

7O0C BRUANCH: if?' FY) FoWULA COI.

810 GO rO ( 110.,120, 1 30, 140. 1 Ci, 160. 1 10, 1 t0, 190) IC Jr-OO8 202

*83')" 2 Ft:i ~ /0 Gui [)l:L1 NE i-,rh Poi-icy840C850 1 11) IF ( AiDO)P.(, ?. 1)) 0) To 62

60T, 20(1880) 62 IICIl)?o.00.)( To 64890 0=6.*RMI

910 64 0--3. *RM R920 GO) To 200

940C AFL( 'if1o Po! ICY- -I)FC 1910950C9 di 120 ()St)?r C ). *(P*AI/ (Co!'hLl)*(uC9 10 A('OSTW)*l)C

IF CACC)ST...CifI;PK) (30 To ?00990 CO PCOSoI(?2100 os O i)? r( 2. *C m*A D/ ( C SHl_ * UC)1011) (GO TO) 20X)

LEVLN3.S

* LEVELN

S. .. 2~ * ~ -

:" ,)2 , Q, C O N lI H OFJ|10 it) 140 C(),4 . F N l-

I )4;) 1 &30 CO N I' I NUI -

101) 140 CON 1f" IN UFII 0u4) 1 10 C ON I'l N U 1-i (hi I 60o CO 1*11I 030 190 CON rt N U

() &') 90 C()N rI 1NU

"I. (win WQl fl"( 6,8 1 Qt)ICI)F()O, 10) -1.I 10 0 8 195 FOP?4AT( ' ****I.FV T.N- tIllI)F-I -( I , )IM(JIA CO(DF. . ".II l0& ' IClOQ)=' , 13, ICI .=", I i1 120 SrOP

*7 IJY)C

I 140C CHECK OIWl)DF SI/F LITAl;1 150 200 CONrIINUF1 160 F M X=E()OMA X *M Q

17) IF(0.GT.,AX) O=EMXI 13 8) FMX =IEOQM I N* IMI?1 190 IF(O0. LT.F.tX) #)=FMX1200 IFP0.LT. I. )0= 1.1 21 "C1 220C BRANCH !iY ';AFFTY I.EV-I. FFVMJLA C(IW ICDSI.

* I1230C1240 GO To (31:), 320, 330, 340. 350, 360, 37r), 380. 390) , I CD.L. 250C1260C JSF 12 MONTH SUPPLY1270C128) 310 co;r I NUt. -

1290 0= 12. k PM PI300C

1310 Go 1o 50')1320C1330C 23 AUG 08 ,UIDFLINF LTP POLICYI 340C1350 320 SL=0. 25*PLTI360 GO) TO 500I 370C1380C AFLCM 57-6 POLICY1 390C1400 330 L=SQR'r(RFrSl(N))1410 GO TO 31 .i1 420C1430C PT-F')PMIILA To MINIMIZE UNITS IACKORDERFD1440C1450 340 Z=I.1 460 6O frO 35d14-70

LEVLN3.SLEVELN

4,14 PT-F04U mhl.A TO IM I OA1/F Pt 0I11) 1-- UlP, IJAC oI+t- 1:)

I I 49',

1 '-130 3-D CON rI NI P-1 11 1 (SIG . LF.)S )~1V.001

' I C.')0 'I=- I . 41 1 ()/j 1 G~PNUM=AxtI)A* IG.

1 PP N01'A=AM)A*;i1(3*( 1 .. ISAtP( U;~15'9 ) LVI()v=2 . *CT ; IILJ )*(jC* /* 1 4 14 *0I C0) P'K=0. 10/ , A-oG( PNJ'A/1)t6J ()A)

I 62') (:0 ) 5001 o3oc'I 649)C

* I 6'3)OC MAO1IFTF I i-) ST.I)V. F* ACtI AL rAMMA LPAU TI AF VVA IILI TY

* I 6/0C AbSUJMF CI)FF OF VA,?'fl LI( =.3",3. All) I PF RIOD =PXPECTI) LEA.1 68()C1 WO( 3W0 CONfI 4LIF:1 11 PMFA4L=I .

-: 1itOSI(L=.3'i)3*PMEAtIIL1 .12 0 V A RL= 6 1 (A 21 it30 VA PD=SI(;**2

' 141) 5 1G0LD=53IK;* I /53')C

1 ic/)c flEVISiE SP; FOR LT VAU1AIILITY

I/80 -iG~JT .EANJL *V A RD)+( PIA **2 V* A RI)1/190 1IF (I IU(.'r. OaVTP( 6 36 U91IGOLDr).Sfo. S F' /, OLD1 800C181~I0 3 63 FORAAT (T20), 119 (G)L, 0=11, F I (). 1 910S ; LTrO=11F 10 * I, " PATIO=11,F inI 82f)C

- 1 831C NOW LJSF D1062 SORT( /)FoRMIJLA- 1840C

1 891 Go( TO 33o

- I89)c SCAL1Th NEGATIVFE IN"OMIAL -AOOFI.I gorC191) 370 CONTINUFI1920C

LEVLN3 .S* LEVELN

91 i)c CO;4PJ:J U- IICAl ',IrflCK Si'00' OUT P[?O)IAIAHLTfY* I 9"N)C

Ii V 0 PLIT=( 111)~I 1) 1 C) /( AMI #A 4A)

()I Oc Fi 'P Ck'[ i * vI CA l. Fl i.1. P f?ViiA~ii I L.ITY

2 2040 ( FC:?I T. ". C 1- T0)1 3 1

2 080 A VI 1 1+1') 1( Z 4

2 110(W2 12:) F R~~A I?2 1 3(X:

2I0C2100( ELT-*FLUI 0AT(I.TA)M (N + LTPl?0D)(N)2 1 PiC2 2180C2Abl COI:F. O'F VAR. OF LT=.3532 IYI~C2 20r0 CVLT=. 353221 ry,2 2 2 0,1 FNO SCAt U!) NFlG. B IN.* RE-oI?IFR P() IJT

2 240 CALL SNitOr ( AVF PFU.OED),r:LT,CVLT, FCRIT.I PO)P)

2 26 -C 3ACK IMP)o THE SAFETY LEVEL2210C22260 371 CO)N r 114 0

*2290) SL=IiW)-;LF2 30()C2 3100C2 320C SKIP SL LIMAIfS233C (0T O2 344) GoT -0

* 235r)*FILF FXPFITr.62360C---------------------------------------------2 3/()C PXPONFIAL A PPR)X IMATI ON MOI)FL2380OC2390 30C~I~I2 400) I-(A).LF.). ) GO TO 3812410 II-(AIl).LE.o.) Go TO 38724202

* LEVLN3.S

LEVELN

2 l VC Wi )1 .. cr r (W f I M A L- F0 0 1 r P Q()JA I -I

2 -1 30C. - - - .t ... . .

-4 )P( iJ1 = (,)*C ()H JI.I)*U(')/'( A !b *A|[)~2 11 o)c:,24?.'/(). II.1 r ,if' II Mtx I I h i1? [sAK lI. IT.Y

;)4k") I IL . -P(,i

i 241F( l F I Il.L. I.'- ,. F'l 1'f 32,20 IF(P- I I.L. "1'. ). 0) i . ( ()9

2'w 30C?-)4-)C LJAl: I'. <= 3i) = F ) = I*-.I *IXi'( 13*ZT) FOR /T

'-' ~ ~~ 2560 "=')

ii-(':ILI . 1. ).C,), / " - AL ;( I .- i' -II1.)/. 331 /(-.463)2 S J )(."

25 ,." t.,,r' IrC- MAA I.- A NI) ',A i[ l'F' 1.:VF I. FIS(), MAt)2 oO'"261 )C ,IN,: I-IT .40* 1 A,*(.H2 3S +').42625*91.TM), W li AVE2 (JOC2o ) OMAI) = :3 P; /(+ 0 4)20*(2 Ht2/+O.4o l. I'M)2 640C[:. 2&)0C N(.i 4 '(4P) F "'AFt rI i i VFL.2 ooOC26/0 SL = /f * .i3A) * . I[ ('.l.',)

* 2 09oC210C OGKll THe I.IMI I2ALCULATIr)N2 110C

"2I2,) (3() To) 60o'

2 /30C2 14OC DCf~ f";1. l') Zl?)2 I5OC2 160 3i81 CONTINU2 1/0 SL = 0.2 18) GO TO o002 i90C

2810) 390 CONI' NUE* 2820C

2 830C U.SF -,PI.1I-FXPO)NFNrIAL-(;AiiMA MOI)FL2f14 OC--------------------------------- -------

21350 IJF( AJ. 1.F0 .) C) TO 39/28uO If. (AXI)A. -I.o. ) (O l' ') /

2880C COMPUT OIPTI'AAL ;,roVKOiUl P POBALI LI TY2890C2900 POUT = ((Q*2(o)LiIi)*UC)/( A,41)A*AI')2910C

LEVLN3. SLEVELN

. ..

~~~~~~. . . . . . . . . .. . . . -. , - - ... .' .-' ,. . . ,. ... .... . .. *".*._• .._-- - - - - - - - - - ----. . . . ., . . - - -. . ,. .. :,, • , .-.. "

., , , cj - ..-;i ,. .- ,. -

(Y, ;" ,111. PAU.. F L - -

p-- f"IA.PlAr-IIT

PF)4. I . I. 0.999'Ot1 1-. 92 ?)o )?9oe) II-(PFI L..I.O C. ) .;() 1() ,391/

2"I} 1r(P'l-ll.. ;l. ().99v) ilI _. = 0'. 99,9

* ~ 2)'- )C:3 )lIF-MAII hA o MAI, A, I.ND) L I IAl"

'i 301 1)c.,

3020C qlJi,'4, 9;l;lT = .d94)3-AW)*(.j2.3 +}.4262'*DLM), WF HAVF30 3C

*~i 3040 O,PAD = SIt;/(.*')4'*(.,i:3/b ().42(25*L-,.3ob0 ' :-- A .)/4

" .'30(1Q] { i 'L. " '4,. i'ki/.i•

301()C3080) NO I COMP',IIF FD(JI)PFl. LFV-l309)C

3 I') CALL I-P..; Q CA[ , (YAA), OrILT,PI- I LL, [ PiP31 I (C3129 J[(IP()-.Lf.•() I P =()3 130 SL= I P!O-;"I. r

U 3 14"CS 31'30C

3 1 6OC SKIP "II F LIMIT CALCULATION* 3110

3180 GO" r() 6003190C3200C .iFr ?oP T{o ZEr-O3210C3220 397 C'01NFI NUF3230 1IPOP=O3240 S1.= RO- :?L f3250 C.( To 0003260C32 1O*******************************,I***** *******************************,

32d0*****3290 500 Cotl F I N Ul1

3300C3310C BIA ,"H 13Y SAF-TY LFVEL LIMIT COI)F, ICPSLL3320C3330 Go To (',IO,52)),ICDSLL3340C3350C X)Oo2 LIMITS, AS (F JUNE /I336U0C3310 910 CONFINUF3380C

: "::' LEVLN3 .SLEVELN

-.9V -" -'' '- ' ' ' ' ,"•" - "- . .-" -" . , " , ."," . ," -- . ,. .

"-........... - i **- " I , . i

77 -J-.-.-. ..- -

S)K L PA I F 'Ai I-TY i-1VJ1i..

1.I'Af I'S 0. TO LF',-) MAN LI-AUF I *W

-i4 )LA d. I34b,( I F (31- 1t 4-M ) ~',L =',LA

-3410C L.I1A I i. [(0 L.P-'LS I 'TAN 3*'J 13 d4OC3490) L M =.i3500 I C'L G (4 . M )'=L ki.3s 1 0**

35 30C.L tIM! F) 6A:041- (IN MO N]h OF W1I- cLY~3540C

3510 2 Qa[3ISF (S Lu . .LM P -1 M

3 ))c ~ JPPI:jZ L.1,M!IT3 CAM -SLM =iLM AX* PM P

*~ 30C3640 Go To( 00

- 366)C3010 600 c (mF I,,Iu I-3 080C3690C comPUi-)v LPVFL,)

3110 S-!:VI. ( 'I ) =SL+O .3120 1IROM 'N) =Q+0.53130) 1 POL( ri ) =1;L+ RLT+0. 53140 IF(IROL(N).LrT.O) IR)L(NM 03750 ITL(N) =SL'IMAX*?Mp+T?LT+frL-F*PMP.0.b3100 IF(IL(N).T.0) irL(N)=o3170 IPL(N)=FL-OAT(1TfL(N.))+GRLF*PMR+o.53780 IF(ITLCN).!.F.ITLMIN) ITIAN)-ITLMIN3/90 IF(IILN).LF.[RLMIN)IFRL(N)wIfLMAIN3tJ00 ISUL( 1 )=6;SULF*RAMR+O.,3810 3000 CONTI NUE3b2U I)L =F LOAT (1 I Rol- N)3831) IF(IHBUG.LTr.6 PFTUPN3840 RK(=O.

3850) IF(SIG.GT.).) R K =SL/t.il(;3860 wpirF(6,.,9o3)NIRQITY(N),IPwL(N),TTL(N),TpL(N),ISUL(NRK,3870& SLI'F'JOWiAL),PFI.LJ880 83903 F~imMAT(4X,-,****LcqVFLN--N--i-,1),I I W)TY =- . 5. IROL=',.1'i,3890A ITL='1 Pi I PL=',15. IS(ILU.'.IP3. ?K =,,F9 &4,390()& /9T50,0 51-=,,F9.I1 PFNO1=,',F6. 3. AD-' 1:9. 13910& A PFILL =11F6.3392C3930 IPFTURN3940 FND

LEVLN3.S* LEVELN

tie.-, su1iJ ri i FXP[ I) M * ?, 0I AD,oT~i.'f ,CUMPX4 /oA%.

C()WA(Vi /I N'/I AT( 0l)

4 /V )I- SFT /'IIT F! AGS.

4 e29 f PNTSZ IWT ( I I4 o, C UMPThO.4 b40 ClJfMPX=.

*4 USOC*S4 3861C INIIIALIZF PD1F IAPA~iM;EFZ3, 4870C

4.983 AI= 9. 3 314 89 0 BI4 900C

*4920 B32= /.9/9

4930C4940C ';A.VA CONSTAIJI* FOR MEAJJl AND .V=. 31754950 CI= 1.0OI1izi/34 960C

* 4970C

* 499(X;5 QOOC

*501 oC INITIALIZFE FOR T I NTEGRAI* ION502 OC5030 DT I15040 T=IDT5050) CUMPT=0.5060 CUMPX=O.5070C50130C dFEGIN "T" INTEGRATION L()P5090OC5100 Do) 100 1=1,100

* si10C5 120C COMPJTI: :TANJIARDIMF ERROR 7.T

I.; 5130C5140 TC.TR= T*jr*?LT15150) tT (x - P*TOTP)/ (OMAI)*S0RT(TOTR)51160C

LEVLN3.SEXPLTD

3 -.7

4~~- A. I .P I

2

5211 XT =0/*.;

& ~JPi)A Yt C:IMIl~AfIF li PIMJAB3IL yrIFS

53') CLJMP 1* CI.1AP + (;r",J31) cumIx =c&jmpx + Pxf13 34 Y:

53c') I-((IPNr',.01i.o) .A'JI), (Mo)(1, IPNTSZ) .1-0. 0)). 1;) RN r=I

If~iiNT';F.) PIfF(6,63) x ,,GOF,rFc'JMPt)-~,CU.'APX, F Z

5 4 3 9,7IIJC:PFMrNT Tt) 44 OC

15 i ) ,1 r+D)T*~ 5400IC

5 54 1 (C 6T0.' IF- CUMPT 999

5 49 0 IF (C(JAPT.;T. o.1),9) (3 To 120

~I ()c--------------- IDJ OF "T" L%~----5520 100 Cof~U

17)541) 120 CONTJNUF

5561) FtiO

* LEVLtI3.SEXPLTD

i SUi3POU 1* I V4- - XP. 'AM ( ll?Af F. AD fl I .1I~ ~ L... I r?([-

v) Ux". COMi''J f' A RF -() 4 ) FP P0 M~ IIII [N0k) T: I V F~~~ ~A FILL.I kAIr- OF j~ I

40 10(.I4 -02 ')C 6Hli LOWV i)(0INI* FOR~ P.1). k

4050 Xl = OJA ff*foTR - 5.* QMAIL'f406') XLoA = I-I 4( XI.00V + 0.5i)40) IF(XLO0! .T~.0. XLOW o4 (',) CJALL FXPLI> ) CXl-c)W, OPATEC(MAI), T(IrP.CUIMPX)

4 10() TF(PFI LL-. U.CL~iAPX) GO T 1() 0(X4 1 I 904 1 2((, V'F PY LOA1 bU PPO~f NFOIWI).4 1t3)C SiET E(I1~POINT TO( XLOM

* 4 14C4 V).() I P'OP =XLO

-. 4100 RiFTu ?N4s 1 /;)(4 180C iFl LON POIIN[ FOP SEARCH4 19C

*4200 ~5(-0 cotjTrINUF421() PLOW1= CUMPX4,..2')C4230C COMP.JTF 1)1fl.TA-X424C4250 DX = (NADLT4260 IF- (LX. LT. I . ) i)K = I.4270 1 F (lDX. GT. I .) D)X = IFI X( DX + 0.~,

-~ 428C4290C INi[LTZE HIGH VAIJWS Fol? SFAPCH4 30C4 310 X- XLOW + DX4 432')C4 433CC FIIV) P(Di)L <= X)4 34C4 35( 10 CONrI N IPE

-C LEVLN3 .SEXPGAM

4 30 CA LL F X P . ) X X. )P AlT'- 'AMkt .T Or I UMilX

P43 .00 ',;) 3F('!RM.T( P-- X P,; A M. X ='" i*F i. I , of CM11X F-

.41( )C

44,,")C iiAir- ilf: HioUIJI)lF) 1111'~ ~ i~.r F1 - R AFE4 43 ')C IF- '-M(, '.;) To 09 ANI) lNl*FPLAl'F FORI P~OP.4 44 f),,4 4') (P IL.A CIuMiX ) (;0 TO 600)

4410C iF ckJ'Aix > .*)g, -),rr)i Arl IAAYV.-4 4 8,1C

44-),I) l(CJMPX .u;*. 0.99)) t(A) To 58dQ

4t, I O No, IF, HAVF '-o KI-Fil f'?Y I!40; IlF';Ff FORn SEARCH

*453) XL()w = X4540) PLOW = C1J,,X4 % 0CV 4561 X = X + DJX4t10' G;O TO ' V

459V)C SET TROV THIS X

4610 5d() CONTINIUE4620) HOP = x+0.4030) Rf"-TUIN464()C4 C60C THP RP P; I1o(JNDIE1. NOW INTFPPOLATF.

* 4600C46/0 600 CoNrINUE4 6k3C462 X = XI.okl + (PFIIA. - PL-OW)* (X -XLOW)/ (CIJMPX - PLo.W)

* 4710 IPOJP = IFI)C( X + 0.5)4120C4/130 w- TU 141

* 41/40 ENDI

LEVLN3 .SEXPGAM

CA rALo' ;/F-ILF rCI 11 I JV/.P P

ow

/C Fi-O'TNAl NJvrFuI O() Of. PGFO I?.LIOC

c

25, CIARACFIqP Ai))LP*l

* 4,CDoc T(K+1 ) = T(X,K) FOP? [HF CUrmENT Xcc T2(K+ I = (x-i , K) FROtM PI?FVIOUS X CALCULATION'

* bc80C1Oc 1?1WAI)U75, 13) P AlAM FTF RS91C

* 92 90) CONTINJFV? PRI NT , k 1Y, Tfk393 PFAD(3',13) 108, 1019 4C95, 13 FORMAT (V)100 CALL L&VGO1 b 00 LPG RECURSI ON

* ~ 120 CALL LPGREC1 30C D)O SCALED NEC BINOMIAL CALCULATIONS140 CALL LPG3142C143C CALL NAHMIAS EXACT LP(; ROUTINE1 144C145 CALL LPGI146C15 iW ~ RITE(6,13) 'CONTINUE (Y OR N)1@j'55 RFAD(5,13) AIlX)L RI 60 I F( AI)OLR. E). "Y" )Go To 901/IC STOP.1 71 END

I1/3C174 SIUiPrn)TINP LP'01 /5 COPMMON/LP(;PPM/T I *L . A Al .131,11)7, 11)817 1.3 FoRMAr(v)I J8C1/19 I)IMENA3ON r(200),T2(200)

I:. 181 VRITE(6,13)182 WRITF(613)I9 W) ITF(OI13) "LP(O.S--FXACT LPG iPOB CALCULATIONS USING RECURSION"191 WRITEC6,13)192 WRITE(6,13)

LPGFOR.S

?)fl id8('~,f -PII 4i ,2 30 RJITF I , F)

250c b0LV/F F0'4 IH TI

2Q0_- FSTIMbATP PAAiIW I16 FOP1.)GJ0Oc S = * .f) I4E' V 13 VAR. Tr( I.1FAN !?ATIO

S 310 S~f

330 Ui= II*jF1340CJ5() B 1= 1/13

~ 3/o) Rl=-Ti/C (i-ri )*At-()(,( i-ri)3 W) RLI = t.Ji/EI*P1)390C400 4RITF(6,13) IIAVF. WF0 'iIZF "R410 WPITE(6,H)0

* 420 WRITE~o, 13) *'TIIFrA =",,T ,'llAibIA =11,Pl-430 W1R1TEH.1:3) --ALPIIA=81, Al l'iJFTA =1,14 40C4 450C

4/0 WRI1TE(0913)4803 WPI TE (6, 13) IIIAiFAN =",PMi490 "P1TF(6.13)5 00c ESTIMATF THE FIRSr FOUR MOMFNTS PMIqRM2,RM3qRM4 OF THELPO DISTRII510 DI=J*(-l520 C4 =-fr&l*Ti/(AL0G(l.-Ti))5 530C540C550 RMI - A I*C4/)15d0C

* 510 RM2 = AI*C4*(BI+C4)/[Di**2580eC590 PM3 =A1*C4*((131**2)*(1,T1) +2*C4**2)/1J1**3

* 600C610 RM4 =131 **3*(144*TI.T1**2) + 1J**2*C4*C3.*AI 1 .)620 R94 =RM4 + 6*BI*C4*C4*A1 *C4**3*(3*A 1.6.)630 RM4 =AI*C4*RM4/l**461 (40C650 WRITF(6. 13) -"MOMENTS"660 WRITE(6,13) "'RM1 R#M2 RM3 RM4"0670 WRJTE(6,13) PM1,RM2,I?ki3.RM46 dO C690C COMPUTE STANJDARD)IZED) MOMENTS

* 700 I'JITE(6.13)'110 S - SIIRT(RM2)720 vIRITE(6I3) "COEF OF VAR -,. S/RMI730 WRITE(6,13) *RM3/S**3- WRM/S**3740 WRITE(6,13) J'RM4/S**4. " RM4/S**4

760C OUrPUT LPG PARAMETERS TO FILE

.770C780 r4RI7F (8,13) RMI,S,'RMI,RM3/S**3,RM4/S**4790 NfRITE (8913) TI,RLI,AI,3.1800 RETURN801 FNI)

LPGFOR. S

40 S 11..?M. . . .i

! .- iOJ' S Iij'dl1.Jf tI J, 1.P' .(:

S L.lt fl:(; 'J l [ , ')J : .\I.'CIJL.A I ON

6~ 31 C,,:.833 (::'.'PM V/LP.;P* ';/ VI, M. 1,A I ,,i 08L,/,1 #

'- ,3.1. 1)I I 1 . "I( 1 ,)) , IIN( I(I"))b 4f)

S 8Y)C " INF : i P )I? )[t AII.I1Y CAL.CIII O'lNS

8(,b W JHTF 0,1 3) *.P :,' rI ,Fi IA , 8 ",1 I, PLI AI Ii /) C= -WI/A.)';( I.-I'lv;tjo C I = k/ LdlI + t31)

9(0 .l mI i 0!J X = 009 IOC

9 20 .l. 2= 29 30%940 02 =091-()c

960C 'iFr CONSFANTS FO1R US.* IN LCURSION,:. 9 iOC

9 80 S 1= I990 HfI=(BI/( ,?LI+;ii ))**AI1 1000 H I =S *HI

01,io SI = SCALE FAC'IORS 1020 i2=(C/(RLli4~ )I 030C1040 414I'TE(6, I 3)"C,C I ,HI ,1I2C,C I,HI ,1121041 13 FORMAT(V)1050C1060C FVALUATE H( X=O)I QIoc

..: 1080 T(I) = ()1090 T2(1) = HI

" 1100 SI = il1110 C2 =C2 + SIISlI 120C1130 ViRITF(6, 13)1131 WRITF(8,13) 0,S1,02

11410 WRIT'( 6.13)1150 WRITt-.(6, 13) "X H(X) FMX)I

1151 WRITH(6, 13)1160 WRITF(o,13) 0,SIC21 170C1180C1 190c EVALUATE H(X) FOR X .GT. 01200 1200 CONTINUE:1201 L2=RL2I20P Do Io05) IX=I,L21203 X=IX

S" 1204 IXPI=IX~l.* 1220 SI =

1230 T(I)-0 LPGFOR.SLPGREC

lii ". -. .-.,..-. .- .-. ,,--. .-...' -..... '"'.... .. .... ::: .': . . .. - ... . : . :- ..

'.. e!4, X125") i'( IX*l i-= F] *i12*( AI X- /I )IX)*f2( I X

121) IF( X .130. 2 )(1)T I 380I 2OC

1 300C310 1X) I W) K=I ,X-IaI

1 32') T(K+I)=(TI/X) * (I*(AI+K-I)*T?( K) +(X-I)*T?(K+I))1 330 51 =SI +1(K+ I1 34') IF( 11 .1 . 0 )';) TO 13N)1 350 WI I _F(6,IJ"X,K,T((,K),SI ",X,KT(K) SI1 361 I J60 CONTINUFI 31)C PICK 14.1 F(X,X) rriM IN SLIM13/5 13dO C ONTI NUH1 380 S I =S I +T( I (+ I-:"-I 3)')C

"I 400C WHIfI "(6,I3) TOTALS FOR H(X)141 OC1420 0 = C2 + 51/5714.30 WITF( 0, 13) IX, S.I C21440 WITF(8, 13) IX,S-,C2I1450CI 460C IH CUM PPfO FXCr-FIYS .99, SToP

1 480 IF( C2 .GT. .,)9 )() To) 1670149,0CI500C VRIT(6,13) T(K) TEMS FOq rflBUGGING

.- ,'.51 0C1520 IF( If)8 I.F. 0 )GO To 1560153) 1.) 1550 KK=IIXPI1535 K=KK- 1

::1540 WRITI..6,13) "X,K,T(X,K) =>"$,X,K,T(KK)

1550 1550 CONrItUt1560 i.,60 CONTINUE15/0C1580C RECORD T(K) VALUES FOR USE IN NEXT PASSI 590C1600 Do 1620 KK=I,IXPI1610 T2(KK)=T(KK)1620 1620 CONTINUEI 630CI 640CENI) OF X .O(OP1650 1650 CONIINUE1660C1 065 1610 CONTINUE1670 PRITF (8,13) -99,-99, '99M END OF LP(O"1680 RETU QN

S 1683 FND1 690C ***************************************END OF LPG RECURSI(IN

LPGFOR. SLPGREC

. * .*, .*-*

[ ( - .- " " . . , . ," . - . . 1- . . . - . . - , -- . - , . . . . . . . . . . . . . . . . . . . .

Ii

A i

..I Q Ir U. A)CiSL .--" .' ')4l) / .. 'l /f l I I/$°)**, I / IOIJ 11:)t

I - ---- - - - -' -) = -. /( (r I-Q AI F ;l ( I -0)I 14 C1 /4")C II -21,. * I-( ') )I IF IIIur1 .1 14 :x

I)c 'II NAP Y ',I-A'; I IA; f I N;l N

I ly )CI d1-.)C jo .V1: Folk 1'1[-. VAL -ill: CII ; I Vl:. ANII .3Il K(" AV'-. ' 1F:,I'-1;[Ifi1()Ib 1/1- t- I()

I1830(" .SI[ OiP IN) I() INIS F-OR )IIAl?(:I1I ,4,)C-8" 0 K= o

;Z- Le,) 'J9=,99 )

, I d ) P9=FNP( )9 )

I 9I0) R(I =F'N( (Q 1)!-!.'.9o00 GOTo ?080.91 )c

"'-I O2 :c CHF.C,, IF( PO .LF. Q

1 ).31)- 1940 CONIINIJES140 IF( P0 . ;I. P )(o) ro 2o1-,95 D)C

I 9&)C PF-'IET TOP OF IJ'TFPVAL1910 R9=II)8.') 09=01990 GOT() 2080I) I C

1 992 2000 CONrINUF-2 000C? M0OC PF-SPT 130TTOM F INTERVAl.2020 R1 =R2039204') (Go 'o 208:)205 OC20oOC HALVE TIHE INTERVAL, AND RE-EVALUATE THE FUNCTION?o/OC

* 20/5 2dO CoNrINUE2080 K=K+I20)0 Q= (0 1 +092 100 oi=FN R(O)2 I2C2130C IF( 1 1,6 WITtIhN .001 OF Q0, )Go To RETURN2140C

2142 23 F(mRAATt" ***IISFCH--K,OfR0,",I5,3F8 3)2150 IF( AfS(R-R,) .LT. .001 W0 TO 21802 10 IF( K rpT. 15 )GO To 21802110 GOT()o 19402175 21 d( CONfINUE2180 RETURN LPGFOR.S2 18 1 END BSRCH

.................... ______t. ta%

2 182? FtJNCHON t-'J1(O)218 Fd FNR=- r;/ I -O0) A L I( I-'2184 PFTU~RJ21835 FNI)

-. LPGFOR.S

BSRCII

2380 SUJI3OUTINF LI-P;l2?40") 1 1 -1.NS I ON Y ( 1O0, 101)2410 CO.IMMN/LIhG' PM/T I R LI ,A 1, 0 1 11 1), 1 IM241 WP ~ITF( 6, i) "T1 I P ROGRAM CO MPI'U F I:XKM f* P u H )i PO I'HF LPG D)I ST"2412 1 3 FO PM A( V )2420 V"?I KF( 6, 3) -rtlFTA =",TI , "LAAtMIA =".11H * 'AI9IIA =", A) *FTA =11.13)

2430 fllIP' (6,1.) 1,2,.3,4-; 2440) WP1 fF-(o0,3) T 1. A13

2450 C = -R /AIW-(I -TI)246r) PM = -TI / ((I - r ) *ALOG( I -Ti I WL. II ~/B 12410 CI =C/(PLI + ill )2430 L2 = IFIX( 10*MI)

2490 C2 =02500 DO 2190 IXP.I=I,'-2+I

* 2504 X=IXPI-I2506 1 K=X

* 2510 Y(IXPI,I)0O2520 FI=I.25? IC2522C COMIJU E (- I)

25? 3C2530 IF( X. LT. 2. WGO To 25 10S2540 DO) 25o0 K=1,IX-I25 50 F) = FI*K2560 2560 CONTINUE2565 2570 CONTINUE

* 2510 Y (IXPIIXPI )=I./FI2580 F1 = I2590 IF( X.GT. 0. )(-,o To P6302609 SI =(131/011_I *+i~))**AI2610 00 TO 27402620C

* 2625 2630 CON1*INUE2630 S I=0.2640 DO) 2/20 KKIIX2641 KPI=KK4I

* 2650 IF( IX qQ0. I )O) fO 26102660 YCIXPI,KPI)=Y(IXPI-IKPJ-H)/UXPI-1) +Y(IXPJ-I,KPI)

* 2665 2670) CONfINIJF2610 FI=1.2 680 1D0 2700 .]J=IKK

* 2665 J=J.J-l2690 FlI - FI*(AJ + J)*CI2700 2100 CONTINUE2710 $1 = 5I + Y(IXPIKPI)*FI2120 2720 CONFINUE2730 51 - SI*(BJ/(PLI + 81))**AI*TI**X/X2735 2/40 CON r[IN UF&

LPGFOR.SLPG1

=' 11 , . .. , , . M,, -. ,, .= ' -€ 4, ,. .. . , . ''t - , - - . . - - - ,, o ..', .

274:) (2 = C2 + 5121W) IF( I)8 .LF.() )0() TO 2:1()2/6) w? 'E( 6.13) X,51 ,.C2110 MI?ITF (8.13) XSIC22111 -1'/80 CONrINUF2780 IF( C2 .rT. .9) )'30 TO 28Y)21'0 2790 CONrINUF2795 2800 CONTINUE2dOl KITE (8.13) -)9,-99,-'-)92810 PE ru th2815 END

I.

d

LPGFOR. SBSRCH

-I

.. : 2 [uLa..

2d830C2840 SUUR)UF Ir'i: LIP ;22vs4 COUMdrN LP ;RMfF' 1.I I. I ,A I, :il [ 11)I, 1 082 t50 h.?I fE( 6,.3) "5";ALF'") PtI-SON,

k 2i5, I 3 FORMA ( V.. 2 80o 1)c = 6, 1 .0 "LAMIA - IL I "ALPIIA =", Al "3ETA =,81

2 2880 C = -RI-/ALo(;( I-I1)2d99 (3= I,1(1.-TI)2, )90 KI = TI*C2910 C4 = (fIl/(KI+31 ))**AI2920 N = KI/(KI+1)29 30C2 02940 D() 3090 MM=I,10012945 M=MM-I2950 PI = I2960 IF( M.NE.0 )(() To 3000

:. 2910 PI = C4

2980 GOTO 30402 990C0 2995 3000 CONrINUE3000 WX) 3,020 11=1,M

* 3005 1=11-I- 3010 PI = PI*((AI+-I-I)/(M-I)*'.)

3020) 3020 CONfLINUE3030 PI = PJ*C43035 3040 CONTINUE3040 C2 = C2 + PI3050 IF( ID&.LE.0 )C) TO 3080

,* 3060 NPITE(6,13) MC3*M,PI,C23070 WRITE (8,13) C3*M,PI.C23015 3080 CONTINUE3080 IF( C2.GT..99 )GO TO 3100

" 3090 3090 CONTINUF3095 3100 CONTINUE

* 3100 RETURN- 3101 END

IN

--- NLPGFOR.S

S"':" LPG2

.o

3 120)c **kk****i**skw* ifx S***Akt A t** a* itAk****

3 139-)23140 SUiRU I"[: LPt;3

-1 .' 31423 144C %4(AfI VF i1IN,0 MI A. AIPIPOXI M(A HA3146C314 1 COL().4 L P, ;W Q M/f I, PL I , A I, d I . 11) I. I !)b

311) V4,RIT (o , 13 ) "III I P (1 j .'1A) C ()M UrFS LP(; ,VI 10 CAI.F-L) 1IN"SI 1-),) 13 F () iM;AT" V )

:!.|!':310 P I .. T!: ,- 13 )

3 1/9 'I,, rF(6, 13) "'IF'IA =", frI ."LA 130)A =", t. I,"ALPHA =" ,AI. 'IBFfA =". HI318) WPIT'i(6, 0 I 3)1 190 ,WIML.6. 13,) IMFG; INot IAL PWI?)341 11-_ITI FS"

3200 WJRI I.( o, 13 ))3210 VMITE(o. 13) " X P F41

3220 WPIT--(6, 1.)323f) C = I/(,.-TI)3240 RKI = -TI*RLI/AL(;(I-TI)3250 C4 = (BI3/(PKI+il))**Al3260 W% = RKI/(UKI+BI )3270 C2 = 03280 DO 3550 MM=I,10013282 M=MA- I3290 P1 = I3300 IF( M.NE.0 )a) TO 33/03310 PI = C43320 A = -I3330 H = IFIX(C/2 +0.5)3340 S? = PI/(C/2+I )3350 GO(O) 34403360C3305 3310 CONfINUFE33/0 DC) 3390 11=1,M3375 1=11-I3380 P1 - P1*((AI+M-I-I)/(M-I)*V)3390 3390 CONTINUE3400 P1 = PI*C43410 IA = IFIX((2*M-I)*C/2+0.5)3411 RA=IA3420 13 = IFIX.((2*M+I)*C/2+().5)

3422 R13J=13430 S2 - Pl/

" 3435 3440 CONTINUE3440 PL3 C23450 DO 3520 !X-IA+I.IB3453 X-IX3460 F3 - C2 + S2*(X-IA)

S 3.470 1-2 - F3 - RL33480 PL3 - F3

, 3490C- 3500 WRITE(6,13) IX.F2,F3. 3510 WRlITE (8,13) IX,F2,F3

3520 3520 CONTINUE3530 C2 - C2 + PI

* ' 3540 IF( C? .pT. .99 )GO TO 35 603550 3550 CONTINUE3555 .3560 CONTINUE LPGFOR.S3560 WVRITF (8,13) -99,-99,-99,"FNI) OF NB" LPG33570 RETURN3ri75 ENf)

le.

, * -- *0* * ,-..- . . . . .-.-.- , . . ... ... . . . .•... . .. •. .. .. . . . . . . .• . .

*.

369O SUblhoUr INE LP(;,I3600C [.%I- :4. S3610C COMPUTE IFOUI',IO()N SIZh: R VS THFTA TAbLF3620C3630 D) 3610 I=1,1003635 TI =I*.OI304') B = -( I-TI )*AL_(3( I-TI )3650 R = 11/13360() WPITF(o, 13) T1.J13665 13 FO(MAf(V)36/0 3610 CONTINUE3 08) RFTU RN3690C **************************** *************************

371 C DI-FINITIONS IN NAIIMIAS" PD)GRAM LPGI.S3120C3730C LAMB ;?L I3-40C A LPH A I3750C BET 81t 30t0C ,EA4 RM I3/10C CNSr C.I3180C LIM RL23790C CUM C23 11o0c FACT F,3810C SUM SI3820C KN RKI3830C P R1) P I3840C CN C33850C CONST C43860C LAST L33870C FX F238800 FFX F33890C SL S23900 FND

LPGFOR.SLPG4

".1. - - - - . . .. . . . . . . , . . . .- , . . .- - - . .. ... .. . . ., . -,: .

* .- - -. '*-" " ". - ' . ', '' . : .' _.r ". '= , " -"*" " - - '- " - .. - .- ' ' , " - . .

.4CAi1 AL( C /F T i j(- it~s'J lI' N !rV/ PH 4hj.:

If .k 0i I = 1 I jN1V Rl/Oj)IJ1/Z: 4fif-1i. !( C 1), N'),2 J~;i~O *s-A~cJLAT- iALjI NU [IV -is NoM AL (cL 1 (;A L j0 Nh

41.) 'Wit !AW I I NI~:~ ) N ROP~ A VF- v i r, , vi rj , v-c RI 1, i ?)

00 rOI IMA 144,/1 1'u R~~~ I

I IocI 20 IF( 14 ro.t i. )) ra t1(o, 1 3) AVFI--,1)t1 *i-iLr,cV LT,FcI? IT

1 40C CIFK FRN :PA IO' No P-FtNALTY FOR S11WTAGE'* CASEI )()c I '~T11i1,Vf L ! J~ORW 1 PONI!T To) Z FI

170 JcD .j.Q o To) 6o)I 1)I F- (FC I IT. 1. . W ;') fo o I

1 90c

I F(P I.) FI.T= I220 1 F( DI.I .r). I )N =0. I230 1IFCCVLT.LF.().OIl )CVLT=0.0I, 40) CALL qSRCH(AVFqFQ,O)

24-) T I= 0uoo S=CVLr*FLT

.> 10 =S*S/FLT280 U 11 I*!LT

2 90C300 81OO/310 A I =131*FLTf320 RI -'fI/(I -T IA LOG( I. -'rI)

*330 RLI -I/(ELT* I).340C

30 IFcIwr6,GT.0) WRITF(6,13)" 81AlA*30? RI ~L1 Ic RK I'310 13 FORMAT(V

* *IOC390C EST144ATE SNIH PARA.%FfF3RS4 O0C410 CaI./(i.-Tl)420 RK I -T I* QL I(ALo(I .-T I)4 30 JF(JWIT6.G.'T.') IRTF(O,ou3)IJi6AlR1 ,RLI,CPKI440) 63 FORMAr(BF9.3)

* 4SOC400C (PC X=u. )-Po

490 WRI(I/RI(I1e.B1

* .. . ~)0ocSNB RaP. S

y.r (It' I I I' I Al I -P WX A 14, IL I Tri P:s

5 40) X=O.

f-XL=O.~CjO PX=P()

A)/) I~fX F i.. (i T,) .fX N=C/2 .

clOC IS C,>(iI6 F~-XIT L )).

* o40 -

Io IF I i r o (j, . u i? I i -o, 1 3) x XA)tFX X L F XL'I

69 W 2?f CONNi IUF700) iF(( 14o;.)AJ)(X.L..0. ) )W ?ITF(0,93)XN,PX,FXtl. XL.f-XL

Yl) 3 FOJMAr( X, F 0. 2 2FIO.S )I I XN.;F.F~rFG,( 10 410

/30) 1 qvN6 . 9) )(() r() 51()

750C COMI'tJ rE N'T tJF-G. ITN PIOLJ.7002-

FKJF 1 \I SNI8 PROMI I IllL X*ITF:?VAL. IS FOUND

89A X =~

dJ(30 )CL=XN840 FXL=FXN81-0) XN=XN+C

* 8W0 PX = PX *C(Ale' X-101 X )*W8/0 IF(PX.1.1 .. ) GO To '101dcio FXN=FXN4IIXd90K GO) To 220900(1%9 t0C INTERPO~LATE Tr) Fl NO4! X*

93) 410 CC)NrNUE940 XCRIT=XL+(FCRI'r-FXL)*(XN-XL)/(FXN -FXL)

* 950C9 CX)CROUNDI To (;ET FINAL VALUE

980 1 RoP'(XCPIT+.Ii990 rFru?NI oooClboloc li1lti PROTECTIO)N LIMIT. SET ROP To UPPER LIMIT OF X.I 02()C1030 1-l0 TROPo(XN+rfl.-))1040 RF TU IN1050C10.: t60C DEMD4A' 01? FCIT IS ZE~RO. SFT RPOP=0

I0$()H 601 CONTINUliSNBROP.S

I Us) ('I3 Ioo I I?01'=C)IIII') RETUPIJ1 120CI I 30C P's =0, So Di)t Fl:FA IlLi CALCUL.ri fl4

p.'1 114 X

I 1'l() 701) UO(NfItlUI--1 160 -RO AVI *P0*O)I*i:LLU*(I .+i.*CVL-T)

I IT) 123 I-ORPAAT( ********5'NJHPrP. IPX~ ;S50 SFT RPo='" I1)I 190c

* 1200 RETIJ1210 RV1 220C1230 SU817OUT1141F BIOCIMM?,0)I 240C125 0 C OMM N / IWT/I WT(2 0)

*I 280iC--------------------------------------- A- RFQ ShYZI FUUAIh)!1.4I 290C------------1PFTCTION FN R() -0/C 1 -0) *AI(Y;1-0)I 300CI 310C V3FF ) i- 9)FOR FNR( 0) DFF IN ITION.1 320C1 33001 34 0C- - - - - - - -- - - - - - - - -I 3F)OC 11INARY SFARCH ROUTINEI 360C

13HOC SOL/': FOR THE VALUEF OF 0 WHICH GIVFS AND)

1 .3900O AVE. R1WOIIISITION SIWE OF ROI 400C1410C 5FT UPt FMP) POINTS FOR SEAI?-H

* 14200*1430 K- 0

1440 09=.9991450 149-FNR(W)1460 01-.001147o) RI=FNP(Q1)1 48) GoT() 20)80

SNBROP.S

113 IF( R G

I t-40C-1 55,V tiv-sfiT rop OF 1 NTFUVAL1560 P9-P

i 151:) 9=01580I -O0 20801590C1000) 2000 CONTINUE1610C1620C hP-SET BOTTOM OF iNFPVAL

1640 Q1g=16& r8) GOo 208)

30/oc HALV'E Tli4 INTERVA.. AND) RE-EVALUATE THE FUNCTION- 1 680C

I6O0 2080 CONTINUE1700 KIK+I1/10 0=(01+09)/21720 R=FNR(O)1730C1140C IF( P IS WITHIN .001 OF RO, )GO TO RETURN

•1 150oc

3160 I F(I I).GT. )))I'?ITE(6,23) K,RO,R,O1770 ?3 FORMAT(" ***BSRCH--K,PR0,Rr l,15,3F8.3)1780 IF( ABS(R-RO) .LT. .001 ) ) To 21801790 IF( K .;F.25 )Go TO 218o1800 GOTO 19401810 21 d0 CONTINUE1820 RETURN1830 END1840 FUNCTION FNR(O)

- 1850 FNR--O/(( I-0)*ALOG( 1-0)1 860 RETURN

S1870 END

SNBROP .S

NEGATIVE BINOMIAL REQUISITION SIZE ROUTINES

DEMPAR

NEGBIN.

NEGBNI

RANDEM

N

*4

-. - . . . . . . -.

.3. %kf *~ ~

-7:7 - 7 77 77 . .. . . .

I0. SU I)f II - M' 1iA ) P-8Q 11 P4 1 P'i)

~~:) ~ PA:4A.4F I'- * * NI . -izA

/o CO~iA10VG.J / P~/Ifp1.IWCt,iMti/ IT rI II I~~ i

k I) CO ,J m 0N /1Ir u) F/I T(21

1 30 CO:A.ONINFN4PY /Nf-N 0? Yl~1 40 CoCMMOJ/%JFU'-iAX/JfF'IMAX

1 00 COM-A* 1.4 /PfRI ;4-/PH I :?F1 /0 C(,AMJ4N1NT1fNI*FNT( I )

* I180 CO&MM')N /1 IN: ANI)/I D)W~I) ( I ,N IX W)1 ,( C04tPJ/Dt IhU i/I Iil-TIJH I *N000)2003 COMM ON / I PG/I Q 0( I .N 00O)?210 I-(1:J.'. 1) GO) 1 0 25i

*220 =fr'AE/IYEAR +12 :) icr~ITIM1/IT0Tq? +1240 ITW=( IfIMF--( IY-I )*I fYFiAR)/IThEEK +I

* 250 WPITs-(0 I,0 i) IY, I OIT, ITW260 10)3 FC)IMA IA" iWMPAI?----',)( ,"YEAR NO.", 1.4,9X,"OQTR NO.'4, I 3,X,2101n ",'F1:K No.' 13)?too T CwNfINUF290C300C 1'JCREME'JT PEiRIOD COUNTERS310C320 1 IPE t.- IDPItoI330 Do 100 N=I ,NJTE-M340 101 Y- 1)FM1) (N, II)PFR)

*350 1 Rf:T=I ETU 90, 1 PE R)300 1 RonI IliCJf(N. IL)PFR)370 IF (I 01sUG. '. I )RITE (6. 0 13N. DE NT(N) IDPE 01.10TY. I FIT. I O380 8013 FoIA(4X,'****D)EPAR--N.,15,'O t&ENT-,I',0 IDPER0,15.

400~ II-(Ne)INTC*J ).*LF. 0) Go To 10o410C420C GE.NcPATf: SER~VICEAB3LE RFTUU#JS* IF ANY4300C440 1F(IQETf.LF.0))0 To 30

470 j) C01,JTINUP480C490C REFLFCT RFOUISTION FOR ITFM N5 00 c501C502C SET RFOUISTION CC)UNTEIR KNTREO TO ZERO503C

DEMPR3 .SDEZ4PAR

h) CI I )i 1:; ,

0 LJs IM I .. ? A IIAi I AL Ij-AAj1

GF1i- 11F 110 r 1.1-ij Rlo A ) I P N N; F A L NT IiI* PF-) I~ f) Tf

() v- Uk l- LoAX- 11 (-- 0 J , a [oi O V )- Iu-('hN t:). W 1~l 3U ) N i'r r (NA IDPF I OTY sh~4 I N [ I~ QUI4f~

j d) 11 R= IO - ih('I2 LE(6 .3)IR[12F-,II, Ju

10(C 10id I-ND AOF 00ROPI1

930 II-=ITTt? .1*1IFK

8k02[)INPITFCAL TF-IM~-PI,, Fo TINA ROUISITIONf49C3&)RORTC4

L9I90NVLTMET OLAE A . EKI o i~) (100 Pli RFOUl) () N[F QUA I .T

DEMPR3.S*4~.:DEMPAR

CA i .I~ N . I y I N ) I~ ~

I0 1(1 N IJ

I 109) CALL. FjNfD' I r. i, I P[Il Jq,)

131): Ao I o ilifWi'

1 14,,)C RA Dt '. P, N F' I JN I ;F:Nfil?ATFl'. Nf-GL[N RFO :U FS.

'4' I I3. S

DEPS

F , .': : -. . - . .... : .. ... - . - . . . . . .... . . . . .. - . .. -.-.. i -

II , .I D'-.i -1 I W -' A" '.,;!'1X- )','11 1 ON"')'I F.

C,61 '..1114,') i t; [0 A :P-) . (if- P.

I J0) j i i 1 'J I 11 ( 4 ,CP, 1I0,63.., IWO 10, ii

i)AL, IA W: A / , , I), 31 , l'V, I 116,1 0(X), f162/*1).) i.AiA 'h ).il0 '( i*1 09

* ? i * ..I,9 .. i) :* I .(0,

* .' ), .b I / .* , . / I . W , .9i . 6. 1 ,

.1 ,.) 1,. 1 . ehI ,.60,. t#,.06,.%), .0,. n0/

1 . )) 0A:A I I ,'(./ I ,3 31)K. I 2, 3. /* 1,

S.132. .A,2,A.4,C. o,?,,, 10,

133!& 1 4, Z,. tf, I, . 1, fP ,2),;f 5, 0,1 J4'14. 1, I' , I 2JO, , 3,40, /0, I10,S1 W, *,1 u,1'), 20, , 30, 8() , ISO, 300,I JO?. ) I, ', 10,1 I' 2(,e'- 3,(),t U,200,600),

~~ii1 I I~ 2( 4£ 30 .,O 80 0(, , 200, 00.,001 32' 1

I: 40X."F I:JA tl I ";4t I)WMAtNf) L A''F CAFO(OPY

; l41,1)C: 1420 1)0) If) I=) ,k4

1" 4230 Do 10 = I H*14Y() 1M1I

- 440 M= ICA( I)S1450 IF(IQ[FY.I.F.M) GO f) 30

1400 I0 CON l ,UF14/OC

* 4H10C Lu}-! IFItI n:F Iii(l Is IT IoN S I ZF

1500 3) CON rI N OF1510 b) 40 1=1,101520 I F (CP OH ( I, I M) (;G-. P.) Wo I0 601530 40 CON I IUF1540 0 CONTINUE1550C1560C SET RHOUISIfION SIZE1510C1580 1F(I.GT. I ) () f() tO1590 1 Fi I1600 RETUR N1610 80 CONTINUE1620 It(I.LT.I0))GO TO 1001030 1 R1 1) ( I (), I M)1640 RETU N1650 10X) CON"INUF1660 DP R04MCPIM) ( I, IM)-CPRcO 1-I, I M)1670 PP1IOH-R-CP Rt( I -I, I M)1680 1)Ie=IRM(I, 1M)- I R( I-I, I M)Icoo IR=|RO(I-IIM) IFIX(RPPRO*I)RC-DPPOa+.5) DEMPR3.S

* -. :0: 1 /0rd 0I GETREQ" 110 END

/I h, C0 MPU I i ;IA14l1 A '-A N X Q

3(1 X 9 =i J C

2 320 -1 Oc I 1,1 01J11.f 0!1$ F RATIWN V)J SUMF P=.()4 39);I 330C

2 oOc UjSI; AV [-'.,.% J: IN VAl ()I:*

2380 1~ W9=. 0439l39) P(,,=( xq- I )/:'V

*'40;) 09=P)+I

* ?4,?OC -fP 0. JS AVF 1UFIM VALLIFS2430C22440 IF(,'.LI.0. )C )4

?490o 30 To I Io246X(24 10C COMJUI: VAI?( X) ESTIMATE2480C240) 59 CONTINE2.)O V=O.

2t)20 V=V+C(I)*(XCI)-X9)**?26)30 00 CONT I NUE# 25401 V=V/(FILOATL(NPT-I )2510 S-SONTV)2560C

X50( IF VA'?IANCF > (X9-1). CONTINUE To 100. opi liRW IS F.25h()C A Nli;AT[*VF B~INOMIAL MODEL DOPSN-PT FIT.

2600 IF(IbvT(3)..-;F.2) WpirE6.73)NPTX9,V.S,S/X9.(XUl).1m,.NPT)2610 13 F0RNAT(T2o, NPr=-,r30,[II/fl: 202~'tT20. 'MIAN-,'C3.F 13.21

0 3.39. T20,,lVAs?-l.-3OFI 3.2/T20,lSTI) IEVul',30),FI3.2/

2 65 rIA T?0.'COFF OF V--*.T30.FJ3.2/2660& T20, X( I ),T 30, 2OF 6. 2

2 615 IF( Ivl(3)J;F. I)? 6H0& WUTE (0. 63) NPT, X9. V,S , SX9, XU)II INPT)2690 03 FC)UMAT(4(0****'),'v4FMiIN. VAPCX c= MFAN.-P,

2 1l0& T-?O.'NP,MFAN,VAR.5lIO DFVC.OF.V w,4F32

2 /3O -I)C )- 0F.2

2140C CHWCK FOP? CON4STANT REQ SIZE. IF NOT , CO To 512150C2'1oJ IF( (V.GT. 0.05) *OR. (NPT.L.T.4) GO0 TO 51217 0C2 MOC iUbF CONSTANT R4EG S IZE

*.2190OC

OEMPR3.SNEGBIN.S

%.11 1 I 34 1~ i Id S

-143 N . f I) o 1(

I44 Al 4''a pl4 Ri .j) =1.+ I

J 4w) 1 tsli C('11N J[N-i

3iHFu1.) 1)0 tJ()N I1 N'U

'51) 1 ) d)O) Co N 1,INU V

3 :1il UI I-A'T Po) I N I' I NTo P P YE'7) (I TA UL I~

3 5 ")C

361 i NOCQj 1.

V3020 210 IF( IbWT1 3 ). 1. . To 25 0

3o4:) 1 1IoMA1!( //T'0., F(tJlSl[1U)J SIZE C.bi.F.'*//

-136cf) [)()- 3() 6,2=1,Rjs I qQ51

'169 ;223 FORMAT( 14, 1CiI 1I1.4)J 100 230 CONFINLIE:713 250 CONTINUE

1 /20IF ( IVT( 3).(;F.2 )WRITF(6. 323)3130 323 -OqMAT(//T2O),'*INITIAL ORQUISIT1ON COUNT5S'//3140& T/. 'orwu',T1 5,NJTS -,T2.I9REQ'//)

3760C USE MONTF CAR~LO To SETr FIRST NI)HIS3110C RF() coutirs corisisrENT WITH THE NEG BIM ESTIMATES

3 79() 0 tit.300IorY=jIIEAJI(I

3810 KNr-o3820) ITOT*()

* 3830 IF(I'TY.LE.O)Go To 310* 3840C

3M50C GNFRATF RPQIISITIONS TELL TOTAL ONITS=-IQTY.

~ -.- h'DEMPR3.S

NEGBIN.S

fill) +.

4) 830 o) P ) 10+ "

2 H70C (()MP~iff lJ(;A I VI IJINOMIAl. Pf'A?AMETFPRS2880C2ti90 I()() 09l=v/( X9-I

2?9.30)C2 94 OC LI:1*2950C I l140S( I)=IrP. ~II l oNlw SuZI:S-) 60C P. IP') ( I) =PPolAB3 IL ITY IPFOI IS I ['ION SI1ZE <=I J?FQS CIh N2970CIW~ OF POINTS IN~ PFOtIISITION SIZE C.L).F. Api

P9,P'9,O)'4N~I3ATIVE 13!NoMIAL PAIPAMFTFRS

301 OC CO.APIJT-: N!:(;AT1VF BJINOMIAL PPOBAILITIFS3020C U6SIN4 P- AND 09103 ()C304 )C INIFIALH/F VARIABLESij09() 1/0 CONTIiJUF3000) IF( IbT( 3.;.2)wRJiTE(bo. 13)P9,P9.09.30/0) 1/3 FORPMAT( //'JId. O~N PARAMrFEi?s'*/

W'3090C3100) Yz~o.3 11Q P= I/( 09 **?9)3120 F=P

3140 P8=P.-)/093150 IPEQ(I )-I3160 PREa5( I1)-F3110 NHEQS-13 1 80C3190C CO~MPUTE NEGamwiV BINOMIAL PROBARILITIFS3200C3210C MAX QPNOISITION SlZF ALLOWED- 1000 UNITS3220 Do 190 1-1.1O03230 1 P RNr= I3240. IF(I.GT.AO)IPRNT=O

*3250 II(M0))(1().E.Q.0)IPR4T-I3260 IFf CIWT(U).GE.3).ANO.(IPPNTbEQ.t))WRITI-(6.183)1.Y,P,AVE32/C) 1133 FOR0MAT(O I,Y,P,F.AVEdP,1I0,FlO.0,3F10.4)3280 Y-1-13290 P(YR)(~ )P~3300 FP3310 AVE-AVFi (I-+)3320OC3330C RECORD APPROXIMATION~ To. F(X) A37 LEAST EVERY .01 INOR'e

DE1MPR3. SI4EGBIN.S

0

i 1"'1/ 0) I.) '="A"l1) -,1 (

'-" P,, 1 ,"A 11. N (;Ilr I (l, I is: r. L) l f) f= IlYO I+l1

KN=N 1+ I-.[;l'I ( I fnr.[. I ()1,)(; i') 0" €)i 23 ,2J:i:

SS~Ii NIIA~li .I ;: ~IZ tI1L iT~IONS IfilAI. 10 KNT.:94! IC

I .) C I + I ) 0KI-T

, IF ( I , 3..E. )E .E(,, I ,II)FMI)( I ,I PO( I400v) I3 0 ?imAf ( J I 10)

" ~ 4 41 lIC

402() .3..4') C0.J INU:4 )3i) I- li f'J I

4 04') ENI)

DEMPR3.SNEGB IN. S.1

4*. 1) :A )A A *X

4 14 ' .'A /

4 1 C:. Mn /N ;611JI)V Np r; Pl 1, PI, T U;( I (Y) P P!v:e, (I )

4 1/ 1'~ Vl h', A If( 0, 1) PA !I100 IQAl M NWtAill-I;,.4 1 -0)c l'I : ? !hI- 1111- CM04e-?SPI'NDI NG ~i I i SI -I4 1 *''.c

42') I-C ( ?.1. 'ThI-~ I ) AM Y*0 4 VC)4 221 42 (:(JF I NA4230) 4-3. CON r IJ0 -4 24 .)C4250C S S:F1 IIUF pfQ1JJ .ji ON IIt?4 260C

*42/0. 1 If- I i~~. GII) 11 40')4.2 J I h=11?1: 4( )42;91') RFTU 141

4310C 4,,')0 (:)I rN JF4 ')0 11- (1.1-IT. N4il*0WiWO D) 4,104 331) 1 i.i=I EOS(14 ?FOS)434.) RFrU '?N

* 4 3Yj,)C4 4360 4-10 CON[1NUIF

4 30' IIMI=IRLU- I

4400 IRDI=UdI-IRIMI*4410) IF( I ;4IF.;I. I )Go To 510

4430 W TU I#J* - 4440C

4450OC I NTFRPOLATF TO DJFTr:?M INF IW)J IS ITION.4 4460C

4410 510 CONr7I NIJ4 M41() DPROB3PRfE)i ( I )-JPRE0S.(I4414490 14' W~d- 11-1RI:)0( I M I )

* 452(X,

DEMPR3.S

NEGEN1

*7 I

4~3'C -!~ANEM-(0.I) RkNrxOM N(JMLER GENERATOR.4b"40C PAM) WM -- U (0. 1 ) ANI)OM NUMBPR~ (W;INFRATOR.4560 FUNC~H)I IMA1l[F;AMX4 51 OC A CALL WITH X < 0. INITIALIZFS THF RANDOM NUMBER STRF.AM.

4590) 20 I# =RIO*RAN )FM4 000 RNIAM0L)(RN, J1)

* 4605 RANf*F~i=[N I III4010 RIFTUQN

*4020 10 kiO/.O**l i4630 BN=IO.O*It)4640 RAtJflEM=-X4650 c) To 204600 END

DEMPR3 .SRANDEM

-~~~ IIA N. LI j.ga I tIf I * MM

I W~ [ II A

(4), Ci,~JJ 0 H'A M( 1I( , Tll IOJ I II' I F-1 I I'

* I :-': (OMMOW I N1.11 1' / J rII R, OM M OIN I* 1: 1 N1 YP

I Ifi CMMoN'/ I NFBJ;2 /1 -04

I 90 COMMONII l 10P/ I-OIt 1 , I I I 11(A H (3I? W ~COMM1N / 114: AN I)/ I I if- M N1)( 1 AN (W)

2 I1 C ( )m m )N I 'I P 0 1 ,.) A pt~ kI-)s( I220 ColMAc)tJ/ I.S Wi'~ i'/1 NVACI (.1)

2 (J COMMON /!J.t~'/JII~U

130 CMM0)4/ 1prCj!,T~ )

210( COMMON/FI )FM'I/) 40(y( * ))2 o C OMM OI.'IN [i!fi? r 0 P TiUiR (I N 0:0 j

X) C OM M (h N R1 ) 14t'J I , *NO(O )300 COMWAN/NPT /IL )FN1 (I310 COMMON/1NVI)J 1NVI)UI1( I )J 20 COMAM 4 IN U1j jI F/ 114; )V( I )330o COMMON/NIS() i /N1UTIM I )340 c Om mON / 4 13011 %JI N r I U ( I)350) COMM(EJ/A~ 110) R/NHOI I W( I).360 COMMON/Ii1)rl/Nikj R11 I )

380 COMMON /141:) 1A[)/? (IMAi)( 1)393'. COMmfEN/LjPR0I)/LT'PW?0U( I

4 00 COM(ON/[.TAI)M/I ADM(I41 COMM'*/JN/COT420 COMMo1 /AD1?/AI)P( I

S 430 CC)MMON/SUL/Ib!iI1_ I)440 COMMON/I REU /1Rf?(XI, N(XY))4 IiO COMMON/11U4/I w'iVi ~-TOu 1, NoQO460 COMMON/II -t1A I )

47() C(,MM,,NIN/1n.I n.( i )480 COMMO'/1 RL/ IROL ( I)490 COMMN/IP0)TY/It~oTY( I) INITM3.S

.500 COMMO0N /1Mr SR? /I?MTHR( I)5 10 COMM)N/RMFEAN/IkMFAN( 1)520 COMM0M/RFR':ND/RTPE'JI)( I

* 530 COIAMON/RMAeI /kMAI)( I )

5 40 C(IM M MN/ V?5IUM / ? hflSJMi (I1

I..,

i ON m -I Di R/i IC)

VCr.MUJR/ I NCI)F )IC

.440

660C IPFA 1)EMIA Il' I A] A FOR oi. ' IM N I-IN'(M LWA~ CAL ON11I L pWOi( LQI =NLU

090) 00( 1-) N=IN[IFM

/00 14) CONrTJ4U F

7 20C PFAU) 11 EM DAl A I Nt-,uT r F IL LQ130 C

7 of) c PFAI) BCD I NPU V

'Igo 1? VA1) (1 R.i, 80f i0, I- Fl 3=20)) A 1-C, IF if'J ,II I WNY:T( N) NA NO N,,.p F~CID, I o Ii, I o j,tioO.,. LFI'PM ( N),LT pUI q0) T PPL I i

820 P IPPP i?=FL0.Af ( IP'P q /l 100.6,30 CICjJ.F) )iv'?I TF( 6,11)I0) [KNT, AI.CF!-N ,IM, UCO5T(N N).NOUN. MGTCI),8 40 ~ 1kt-i, i my.rAflM( ), Ll PROMN I IPITI IPPPR

6 ;C c RA1) A MANDI,Rf:'r1JRN,), AND) 14:0-[ ?POUENCY

890C

9 )o RI)( liej. 8' CIFI 1 O , J..IIbF

930 RFA)(I'C,(Ki)(IF0N,),J RF- .II)PEI),J11P

950 ( o( "04 (i)c9 Mc Rf-AI) IINAHY i"ArA9 ?%JC990) 20 Z )NTI N I

* .*,.INITM3.S

I N I. KN 0-1 0)1 Ai .-- -A . , -I')N I N, -, '- 0(')', 1'( 14 N 1 N- - -f I, I l N , 1 -,

Ify, ).'IAI) (N), 1. tfr, 0) ) I )Ji j 1 , , I 14', k'* . (1 ') 3[( 1 Fi JG.t -) I ) 'I t ( fl, i0I () 1 KNI, Al., ,JIJ,':t).ii(tJ), UM ) JN,

I (III'K ..1; G , i)I , 10 , li A' . I ) ,I.I F ) "I ('I) f M-1., Ql +PPP

." o'{ 1Il' ( j FttJ(;*. ;',. I ) :l l'- ( 0, ?1O2f' ) ( II)1.IN)( ,.J ), 1=1 I i)PF:J )p ,)/Vi U1AM(L ' )Al.(', i :I l

IF( !.:4 I(.I ). I ) -'I'(o,8030()( 110! j1llf,)(qd ), .= I, f)iFU)AM 1. ') A ) .:Fi 'J I , I 14--Q

- II I- 1( 6 6 V - I(; ),. I ),: 4' 1 r;-( 80 , 4G; I QI-,)(N, J ),J= I, I II)F R)

Il )C2 : l TJl ioh'U ')A 'A 1'() iIL" w)141-)C

Vt~) ) 0 J F )INA r ( V)I It,:) 8010 FOIMAI(/I-, IXA2 IXA2 A4,A6 A3,IX A2,FII.2,IXA ,A4,

1' 10 "T5) ] ) A I , A 4 , A; 2X o 2 11 , .31 6, F S. 2)

ItO ('iS FORMA r ( f;)I , 101 1O)I w. ) 2 2 F 0 PMA C 'o I: MNI1) IEMANI)/O'i , (-r2 I , 10 110))

1 110 f3o30 ro()1MA r( /i- ,l f -RF"TU ,/1rl I,(1'21, 10110)121;) 6n)40 FOR A rc " I w I-) REQ 1*'P',L21 ,1)1 0O))

12 it) ')30 CO NTI I M1:F* I 24,)C

)1.')C )ET'F1M 1 PAAMIFTT.RS FOR N PGAT1VP IiINL)MIAL1 26,)C P1FO1JI )I" [ON 51 1F GFN N QAT I ONI1,7OCI 12H0 CALl. N'l; I PJ1 290C

. I O 100 CONTINUEI131) IEYU RN

133!)C INITIALIZE IrEM ARRAYS FOR A NEW sIM. RUN3I1:)C

1350 ENTRY IN rr:42

1370 DO ;)I N1,NITFMI 381OC1390C IN[)ICATF ITEM HAS NDHIS PERIODS OF DEMAND HISTORY

% I 400C N)tfH=JII1410 N DET'( N N Ml I14?OC430C Z.) DEMA'11) HISTORY RFCORI)S1440 NRETAC(N)=:)' 4'0 NI)EMAC (N)=0146(0 NREQAC(N)=)O1410C

INITM3,S' F

. . . .

I IiI WLA.) 111-VANO .11 jil AtV A'.

I *~(N 1-.%' <4- sh I*,,F it 14 KN *)f ~ ~ P I IJ-

1 N~l i!'( V I 's ).N III(r,

J J"l Kt.0r1.< IN 10 /1 (/0 1'N,,e ; A -oi11~u:0

1 (')0 NO('I'( N)

b c 'C IF IN I i' A 1. iA C K (),34k Cl (A iN i' ?i f( WO

I o' N11 I OC 'j)=111/11) NN=Ni? )!w 1') CALL. f ( N S~#J

I 10c

I IioOc1 1110 NN:=( A) N)..P~f? A~( ?1 l~() CNA F( ) /*5 ( MI 140Co(

*I 1i ) ?10 C.0TI JJ

1 130) IViiN =II.Z ULF NII~)AI (-II SAITC

1 610 110 C04TrI NO F

36) DO) 130 NIl,NIIFM181o' 1F(fJI)FNTU4 ) LT.0 ) :;o po i 3o

1189 IF(NVACf(N) i.. GO1 TO 120IWOQ~ I J(*'CHl ) = IHOi-'oIIC I 1I I900( I BoP(Ji1(2 IBOOM~)I2 ) +NV ACT N)

* 1910 1 J3OM113)I1jioiolI( 3) +1F X UJCOST (N) *FLO~r INVACTN)

193?0 GO?' Tirnc " l3n194-1 It8(*Opn( I ) Hi1opIM ( I )+I395.3 1001) 0 R( 2 1 HOP 0P( 2 ) 1NV DU F( N1960 1 d(hP(OP(3) I WPM J()+I FIX(UCOST(N)*FLI)AT (INVDJE(N))

1Q1 140 COfN"UE.1 q 990 WFURI42000 200 INRI T( 6, tQ 0)2010 8200 F0RMATCIIII,////20X,-*ED OF FILE ADN......,.,* '//2020 CALL OUTINT3S2030 CALL (1JTC~l NIMf204f) CALL I'LC)T1

?060) FND

,. RUN=;HEDG/OtdJJINORD3.0([ICDNOGO)"f *INORD3.S

SU8ROUTINE INORD(NIO4,INIORoIBOOIROLoIUTY)

PARAMETER N;JQ=38

C

C THIS SUBROUTINE DETERMINES THE RECEIPT TIME FOR ASSETSC ON-ORDER AT THE BEGINNING OF TilE SIMULATIOr:. IT IS

C CALLED AT THE BEGINNING OF EACH REPLICATION AND ITSL-'C OUTPUT IS ST3RFD 1!J TWO TABtLES (IDUE & I0Ok ) TO HE USED

C FOR EACH SH34TAGE FACTOR WITHIN THE REPLICATION. WHENC THE ON-ORDER QUANTITY IS ONE AND A HALF TIMES THEC EOQ OR LESS,, THE TOTAL ON-ORDER ASSETS ARE ASSUMEDC TO BE THE RESULT OF ONE PROCUREMENT ACTION AND

C ALL DUE IN AT ONE TIME. WHEN ON-ORDER ASSESTC EXCEED ONE A4D A HALF EOQ'Sp THIS SUBROUTINE THEN

e C COMPUTES A DJE-IN DATE FOR EACH REMAINING EOQ SOC LONG AS THE COMPUTED DUE-IN DATE IS GREATER THANC IFIVE (IEP503). WHEN THE DUE-IN DATE IS LESSC THAN IFIVEP THE REMAINING ON ORDER IS SET AS DUE-IN

77 C AT IFIVE.C

COMMON/ I DBUG/I DBUGCOMMON/IEBUG/IEBUG

COMMON/NDHIS/ND HISCOMMON/NDEMND/NDEMND(1.NQQQ)COMMON/NRETUR/NRETUR(1,NQQQ)COMMON/ITDAY/I TDAYCOMMON/ITMNTH/ ITMNTH

COMMON/LTPROO/LTPROD(1)

COMMON/LTADM/LTADM(1)COMMON/ I DUE/IDUE(NQQQ)COMMON/ IORQ/IORQ(NQQQ)COMMON/JCTR/JCTRC T*'. C

C WRITE DEBUG MESSAGEC

I F(IEBUG.EQ.1) WRITE(6901)IOH,INIOR,|BOIROL1 IRQTY

A 901 FORMAT("..INORD.S.. IOH"".I6v" INIOR="P16," I8Ox.,I6," IROL.".

&16," I RQTYz", 16)NIC

C ZERO ON-ORDER ARRAYSC

DO 5 I'INQQ2

IDUE( I) "0IORQ(I)uO

5 CONTINUEC-----------------------------------------------------------------C LOGIC TO TEST LEAD-TIME SENSITIVITY

INORD3.S

- % % 'I % -% ** '2 '2 . . - . -. .... ,.,,,'.-."," •,.. .

* VIF(IOPT.NE.2) 13O TO 7

C SET ALL 3N-ORDER STOCK DUE-IN ONE LEAD-TIME INC THE FUTURE.

C THIS IS A VERY PESSIMISTIC ASSUMPTION.* C

JCTR=OIF (INIOR.LE.O) RETURNJ C T R zlIDUE(1)=(LTADM(N),LTPROD(N))*ITMNTH10 IR ( 1)zI N IORRETURN

7 CONTINUEC------------------------------------------ END OF SENSITIVITY LOGIC

CC L ET

C ISTKOBJzSTOCKING OBJECTIVEC NETASSTSmzIET AVAILABLE STOCKC IFIVE=CLOCK TIME 5 DAYS INTO SIMULATIONC CHECKIORz4AX SIZE FOR ONE REQUISITIONC IHOLDIORzIORKING VAR. FOR REMAINING ON-ORDER STOCKC NREOQSOO=IAX REQUISITION ON-ORDER (INTEGER)

I ORE INI ORI STKOBJzIROL+I RQTYNETASSTS=IOH4I OR-18OI F IVEm5* IT DAYCHECKIORzFLOA(IRQTY)*1.5I HOLDIORzIOR

CC IF NRE02SOO > NDHIS sSET EQUAL TO NOHIS TO AVOID ARRAY OVC

KQTRZ1C C3MrvUTE MAXIM4UM NO OF nIITCTANDING ORDERS

NREOQSOOzIOR/lRQTY +1IF(NREOQSOO.GT. %'DHIS )NREOQSOOz tWrHISNDMDSO0DO 50 Jsl,-NRE;)QS6ODO 10 KxKQTR.,8N DMDS aN DMOS*ND EMND NK) -N RETUR( NK)I AVAILmNETASST S+NDMDSI F( IEBUG.EQ.1) IRITE(6.,903)JPKPNDMDS*IAVAIL

*903 FORMAT(" 3RDER NOz"12#" QTRO"Pi2o, NET DEMANSuk.I6v9 to IAVA ILzl",16)

IF(IAVAIL.GT.ISTKOBJ)GOTO 20

C10 CONTINUE

CALL INTI1ME(NoR LT)XMNTN CRLT-24.)IDUE(J)aXMNTH*FLOAT( ITMNTH)IF(IDUE(J).LT.,IFIVE)IDUE(J)SIFIVE

INORD3.S

GOT0 30)

C COMPUTE RANDOM TIME WITHIN QTR FOR ORDER RECEIPT.C SET IDUE(J)=DUE-IN TIME FOR ORDER tJO.J.C

?0 T=RANDU(.2)* KOTR=K+l

ORDQTR=K

CALL INTIME(NRLT)XMNTH z RLT + 3.*(T-ORDQTR)X IDUE=XMNTH*FLOAT(ITMNTH)

I DUE (J) -IF IX ( I DUE)CC LIMIT DJE-N TIME TO AT LEAST 5 DAYS IN FUTURE.C

I F I(I DUE (J ) .GT. I FIVE )GOTO 25I DUE (J)-IFIVEGOTO 30

%"" C

"C SET IORQ(J)=QUANTITY FOR ORDER J.C

25 IF(IOR.LE.CHECKIOR)GOTO 30IORO (J) = IR(TYGO TO 35

30 CONTINUE

I ORQ (J) = IOR35 CONTINUE

I F(J.EQ. NDHIS )IORQ(J)IHOLDIORIF(IEBUG.EG.I) WRITE(6,904)TXMNTHIDUE(J) IORQ(J),IHOLDIOR

904 FORMAT(" T=',F10.8," XMNTHN",F1O.6," IDUE(J) ".,I7,&" IORQ(J)z",I7," ON-ORDER BEFORE PLACING THIS ORDER ",1?)CC UPDATE COUNTER VARIABLES

"-; C I F(IHOLDIOR-IDRO(J))2OO,1OO,40

- 40 IHOLDIOR-IHOLDIOR-IORQ(J)

I STKOBJ=ISTK03J+IRQTYIORzIHOLDIOR

50 CONTINUE. 100 JCTRzJ

RETURNCC PRINT ERROR MESSAGEC200 CONTINUE

WRITE (6,213)213 FORMAT("*** ** I NORD---ERROR--')

IDBUGxIRETURN

END

INORD3.S

7 .* *.*.-.-..*..... *..-.*-...*

-

*I NT I ME. S

CSU dROUTINE INTI ME(NoRLT)

C THIS ROJT INE COMPUTES THE ACTUAL LEADTIME, RLT,C FOR A GIVEN REPLENISHMENT ORDER FOR ITEM N,CC DEFINITI3NSC CP(I) a PROB( ACT LT TO PRED LT <z RATIO(I))C RATIO(I) = RATIO OF ACTUAL LEADTIME TO PREDIC"ED LEADTIME

C ASSOCIATED WITH CLASS IC

COMMON/I WT/ IWT(20)COMMON/LTPROD/L TPROD (1)COMMON/LTADM /LTADM(1)

COMMON/IRNDLT/I RNDLT

COMMON/IT IME/IT IMEC

DIMENSION CP(13),RATIO(IO)

~*CC THE CP(I) DATA IS FOR A GAMMA PDF WITH MEAN

C . AND COEF. OF VAR. = .353." I/ ALpAC HENCE, ALPHA = 8, BETA = 1/8.C THIS IS THE MEDIAN COEF OF VAR. FOR THE 62 ITEMS

C REPORTED IN APPENDEX D OF HAYYA(1980).

CDATA CP/.0OO..3 77,.255,.490.7OO,

.844v.927o.969, .98?1.001

DATA RATIO/O. 3,.5,.7, .9, 1.10,& 1.3* 1.5, 1.7, 1.9, 2.701

CIDBUGaIWT (1)

CC IF IRNDLT a 1# MONTE CARLO TO DETERMINE LEADTIME.C OTHER,,ISE,, SET LEADTIME a PREDICTED VALUE.C

- IF{IRNDLT.EQ.1) GO TO 17CC SET LEADTIME. TO PREDICTED VALUEC

RLT z LTPROD(N) + LTADM(N)RETURN

CC OBTAIN A U(O.I) RANDOM NUMBER RC

17 CONTINUER*RANDU( .2)

CC FIND PROB. CLASS THAT INCLUDES RC

DO 20 182,10IF(R..LE.CP(I))GO TO 40

S.: 20 CONTINUE

lNORD3,SINTIMF

f fi "+, %: , ' " + _ ' + ''" " "+2 ' ,,"v' ,' "+-'" " -""' ." " "*:" ,,+'- . . .x""' ' ,...... -~ . *dli r_. ,,. .. , * f'' " "'""' "" ' " " "" " *",s.I. .. i...-. ,iI. L" " " "' ' '"" "+'

"""" """"" """""" ' """""

-z-N z -.-.

40 CONTINUEC

C INTERPOLATE FOR EXACT RATIO V

C L-

ROELTaRATIO(I)-RATIO(IL)CP DELTuCP ( I)-CP ( IL)

C

V=RATIOCIL) + (RDELT/CPDELT)*(R-CP(IL))

LEADTM= LTPRODCN) + LTADM(N)RL T=V*LEA DTM

IF(IDBUG.EQ.1)WdRITE(6.113)ITIMENRLEADTMVRLT113 FORMAT( ---- INTIME-ITIME=".18.," N =",p14 , " Rz",F4.2?,

& " PLA4dNED LEADTIMEa",13," Vx'*oF4.2.& " RANDOM LEADTIME (MNTI4S)wllvF5.2)C

IF (RLT.LTo.1) RLT=.1

C RETURN

END

al

) INORD3SINTIME

.,..i -4 u ' . E U lu u / O , dI j / E ', l % 0 ,u,. ( C D o N O G O )

- .NTRLA.S" SUhRcUT INE E'Jf Epu(o, IQTY,I"PRIoJTI ME)

C THIS ROUTIP0F vACirORDERS REIJISITICNS FOR IT[1 N

C I QTY=UUANT ITY PLACED OJ 1ACKORDERIPR]=I H16H-PPIORITY REOUJSITIC-

C PRI=2 3)T HE RW I SE

C JTI4E = CLJCCK TI'ME RFQ WAS RECEIVED

COMMOJ/ IL bU / IDJUGC OMMON/ NFIMAX N t,rM AXC OMM0N/ NL OC I -K/N1. DC dKC OMMON/N8O IU/3' U I U ( 1 )C OUMMON/ NBO It1/4 A 1R (1)C O!1*ON N 1S 0 Tk/ '3 0T R (1)

C OrM O N/AIT3U T/ I 01 )IC OMf 0 NB/N8OP1 J OPT ( 1)COPMm N/ 1ACPT/ IF.,ACPT(I)COMMON/I CAN CL/ I CANCL(1)

L:,C 0O M N ()N / I D F S tj I D D F S N :!4 1 )

-7. COMMON/ ILOCd/ ILOC GK(1)COMMON/ IPRIoR/PI PIOR(1)COMMON/IQTY/ I WTY8(1)COMMON/IT IME/II iCOMMON/ I T MbAC TI TMUAC (1)

C RESERVE A STORAGE LOCATION FOR THIS INFORMATION

I PT-I LOCt8K (N. 3 ChK)

c IF 80 FILE IS FULLo CANCEL THIS REQUISITIONC TH -WISE, GO TO 5 AND RECOR0 THIS d30.

IF(NLOC UK.GE.G ) GO TO 5C THERE'S NO ROOM. CANCEL IT.

IF (IDOUG.GE.1) WRITE(6o7) ITIMEoIQTYIPRI7 F ORI:A T (4 X °** ENTERB--ITIME=' Ib,'

& 'BO FILE IS FULL. CANCEL ,& 1 REQ FOR °1IS, UNITS, PRI z')15

CCALL CUM( ICANCL, IQTYN)RETURN

CS5 CONTINUE

C UPDATE BACKOR DER COUNTERS

CNBOTR(N)=NBOT (N)+1

NBOTU (N) -NUOTJ ( N) + OTYIF(IPRI.NE.1) O TO 10NBOIR(NNOIR (N)+1NSOIU(N)=NbOIJ(N)+IQTY

10 CONTINUEIF(IDBUG.NE.I) GO TO 15

-' WRITE(6,13)N,I QTYIPRI.NIOIU(N),NBOTU(N),N&0IR(N),N3OTR(N),IPT13 FORMAT(4X,'****ENTERB--Nuf@I5,S' IQTY',15,p' IPRI='IS,,

& NBOIUu '15, NBOTUU,15, o NBOIR, 15s, NBOTRO',15,

ENTRB3,S

. 5 5 5;; -. : ; , - . , . - ,- . , - . . . . . - . . . . . . - . . . . .. - . . . - . . - . . • .

& jPr=', 15)O1 'NT IJNUE

"' .'-% C DID THIS REJUISITION CAUSF THE tACKORDFR FILE TO OVERFLOWN LO0C UK= NLU Cu -1IF(NLOC8K.GE.3)GO TO 20

C WRITE ERROR MESSAGEWRITE(6,91)

91 FORMAT(IHC,2)X,"EkROR--f3ACKORDEi FILE OVERFLOwFILE DUMP ON"o,& " NEXT PAGE)

WRIrE(6,82)

8 2 FORMAT(1H1,1llX,,23H**3ACkORDFR FILE DUMP**)DO 83 Kal,,kNL'I X

d3 WRITE(6,84) K, ITMBAC(K),IDFS"JB(K),IPRIOR(K)IOTYt(K),IBACPT(K)84 FORMAT(1H #3X,'711REC NO=.l3,5XTHITMBACpI?,SX,7HIDFSNB=,IIC,5X,7HI •

&PRIOR=, I I.5XP6 HIQTYt3,1 7,5X, 7HIsACPT=, 17)

RETURNC RECORD QUA.NTITY,PRIORITY,FSN ID,AND TIME DATA FOR THIS BO REQ

2C ITMBAC(IPT)=JfIME

I DFSNB( I PT)=NIPRIOR( IPT)-IPRI

I QTYBIPT)=I Q"YC ARE ANY OTHER BACKORDERS OUTSTANDING ON ITEM N

IF(NBOPT(N).GT.0) GO TO 40C RECORD POINTER DATA

NBOPT (N) =IPT

IBACPT(IPT)=9RETURN

C IS THE NEW 30 A PRIORITY 1 REQUISITION40 IF(IPRI.EQ.1) GO TO 60

C NOTE-- NEW LOW PRIORITY BACKORDERS ARE INSERTED LAST ON THEC BACKORDER CHAIN. THE REMAINING STEPS IN THIS PORTIONC OF THE SUBROUTINE ACCOMPLISH THIS OBJECTIVE

C SET JPT EQUAL TO THE FILE LOCATION NO OF THE FIRST BACKORDEREDi C REQUISITION IN THE CHAIN

J PT=NBOPT (N)C IS JPT THE LAST LINK IN THE CHAIN

49 IF(IBACPT(JPT).EQ.0) GO T'O 50KPTuISACPT(JPT )J PTuKPTGO TO 49

C RECORD NEW POINTERS

50 IBACPT(JPT)=IPTIBACPT( IPT)=).. RETURN

C SET JPT EQUAL TO LOCATION NO OF FIRST 80 ON CHAIN

" "60 JPT=NBOPT(N)

C IS BACKORDEq JPT A HIGH PRI 8061 IF(IPRIOR(JPT)oNE.1) GO TO 80

C IS JPT THE LAST BACKORDER ON THE CHAINIF(IBACPT(JPT).EQ.0) GO TO 62K PTJ PTJ PTO ISAC PT (KPI )

ENTRB3 S

.4

..

I -7

C0 TJ 6 1C INSERT NEW 30 AS LAST LINK ON CHAIN

,.,,'2 1 8 A CP T(JP'T) I ;) I

IUACPT( I PT)

RETURNC IS JPT TH( JNLY HU ON CHAIN

8) I F(J PT.NE.NCOPT (N)) GO 0 81

C INSERT NEW 30 AS FIRST LINK ON CHAIN

Nf3OPT (N)-IPT

IdACPT( IPT)-J " TRETURN

C INSERT NEW "0 AS LINK HETWEEN KPT AND JPT81 1BACPT(KFT)13T

IBACPT(IPT)=JPT

RETURNEND

.4 .,

I,

I.

" ENTRB 3 S

-.

! ;Z ' , - '','' -. v .. - ...... .. . ? ''*'1..-.-.- ' ' '"-"- . '." "-" -" ... '' .' ' .-.-.- . ."."-"-"-"-" .

001t 1/.J I,(;, 1 'l I11 I , I[I) I JAFAIli3.a

.

"'" ,,'-. I /* I rL i. IIIJi; i./l,Af:l I , i I I - IA 1)AI I 1 .), I1t! )*I i i n; / J/ )I-. d.!i I -I ;/ I 7I I)A FA' )X " A

*.A ~Ai 1*11 .4 1 1 j I

t1!11 ) .x *ilJ i ~.,i-i |;tl.i IN't %, Qi-C( ): I' W I I lAV$- i NNIIALI1i!.IAN,P' IN lr,,, I-'3 TiA I l: IN TiiF. 1?AN.;1: Lll F-) IQI3L.

,*--. /' (7 ~ r'ijt Ilt11u rAi:!; I A W A- , I iA I-, liV M'IlW CAJ PI.() t IllW

'n .; |ltl ~tl , I , ' t t :,.1,-F I 'JP I )PV ::, A 4'4. IIINA1Y -):MA ASI l t" 1) 1--i'l .) IN IN- , I M 1 ,. I , AI'1 -41) IX A.

I 2CD, ,I .s; iPA i.A:,.Ii71 *'|- t J.) )Q =.1

,1 !io IMFS IN [aJ I.,'( 4 ),N~iti!J( 2 1, 1I(I(JEJIJ , I II1(N COO)I PF( NtOOI)*MGITCD( 4I "0 ,.IACI UF I M,'f;'l tCl)

" (fO CA1L FPA . ( I I I 2),I /o) qurAla105 j) LoU IT LP11N t , 1-';K I P1./. 3 1IP 0tli AT( VI ,o- 'INT, LOT I.="LOT, LP [I(IP =iJ,LSK IP

ii200 Id lAI,(iD, 3 IA it.II P1 Jl

WO PI 11NI, I.Owl::? l11i) =" ,PLt,1" UPI'FIR iOUN) =*, IRUB

2 30 " TfIAlI I.I I? Al N0 M N iJl-M I 1i-)FFI?40C

,2' 0h J?=I?%NIJ(-. I

@ 2 COGC? Ioc IN [IIALI/.1 Cou)Jr'-i2 do c;(Y) KNT T= 0300 I)UM =03 10cj20 ISKI P=-)33D 10 C)NTI ftU-3 340 ISKIP = I.iKIP I350 Ii CON'r I NU F360 KIJT = Kf + I370 IF(M0D(KNT, 1.)) I-E.O) RI[TF(6,3rINPUT ITE, # -11,KNT31 .10 RFAD(H, PNI)=.IOO)AICFSPJTP,U/4,UCWiST,NiUN,MGTCD,IOH, fOR,390& LTAD M, L fP M), I PP, RI PP

.O I F0 IRMAT(A2, A?. A4.A6,A3. I IA2,FV. 2,A6, A4,2AI ,A4,A2,4 41010 211.,312,F4.2 )'.' 420 '3 FirlMAT([/,IX,2A3,A4,iXiA6, A3.lX!I2,A3,FIO. 2.lX.,AA4,IX,

;. 4 511,2AI ,A49 A2,2[/,2X,3I .3,1 5.2 )440 33 FO'MAT(A2, A2. A4,AO,A 3. II,2411)41" 4J F)IMAT(3.(/lOX, 031 / ) ,-r , 1 10,TI201F I 1 .0)

460 53 F()'#A A'f(j(/1IOX,.II),T 105,110).. A 1(0 03-. F-O)tRA r 3( Iox . i I T TI I S . I 10

4j) @ Af:(8 )AlC ,FSN, I R, IDFM490 ?FAI8 )ALIC.I 'i';A. I P, IR FTbR EAI)( d )ALC, FiN I R, IRFQ

DATAB3,S

S., * ..,. *... ... . ,...,. . . .': _ .. . .. ... . . . . . . . .-.

IIF

00 3 )N I" Ii

KI f-t

*/40t K PVF-=0/50) KFCI=0

- I4~~~ t KP~fI =K'F.I;!()

19y KUMFO=K i-:,JI K) .

* :11) I I') G ON 1, 14 0 :

8100 einwr $J i Iis ITFAI

i~rJ'~T T I: TF:M IF TOYAI I)FMANDS OR? RE~TURNS F--XCFI)D900C 20 Tiri TlHE UJIPFR-tJIJ)NI I(XJNi) IATF.

"1 910

930 '?ATF=IJ('.OS'T*F [.OAT ( K)i) *4 ./FLC)AT( N00)QsO40IF(IRATF.GT.MAX) Wo TO 15

950C9 00 '?AT 17-IJCOST *V . 0 AT ( K 11-T) *4 . /F LOAT( NQOO)910) Ir;(A'V.Gi.NMAX) r,()10) 1s9b(W JF(ISK[P.1..lSKIV) GO.To II0990 ISKIP-()I OOOC1101 OC GtrAFRFOIJI 'IJTI ON COUNTS FOR FIRPST Hi QUARTFUS1021C 10 00NlNo103000M =0o104C

* DATAB3 .S

I It I I) FA IAAI Y IN Ift *' .1, )):A11

- / I 'A AZ.

-4..1 14)

I lo) I ..KJi I 1.r +JII ~ ~ ~ ~ ('* I{) ljo . Iii. + *

I .'2( k;() PC) I J)

I 2 3) 0 1 f )( )-o F A *1 2e41) 1 .11 C '14f: 1 -tJ1,A1 I N M IJ S , 'I e,) Tr)Lk0 10: . I*- UA I )'4 )T!(I iP -

I .?rL) IR Y 1-j,[c1C 1 ) 01- A, K OFl F, KPFO T1 XLI 2Y ) / 3 IWIPMA r( PQ) 'f6, F 10(. 0)

*I 303 I F- 101 [ F. G1. IP PNT ) GO(F ')(1 31') 14R TF ( (3, 11) , f), 'A

. 1 1-4 P) VfF (6, /1) I W"--1 .14A1) 1/ Fof1'MAT( IlOX, 1 61I)1 31) )2I io()C1 3/1.'C

dI J-31 200) C ()N *?1 J Ij I1 390C(I 40Yr. OIlJTPO F THIS 1iaT:,4 To) F ILF 9

1420 WlITF(9) AlA',FiYJ, I .114, IJCOr,.NOUN, MG.TCD, I fl , I O)R, LTADM,14 43(. i.TP kol) I PP, If I PP1440 83 F.)R.AAi(I /,IX.A.',A.>A4 A6,A3.1.1 A2#F9.2,A6tA4,2A1,A4,A2,

1460 9)3 - MrfX,)

1 401 wRi ri~( 9 )AL l-:i ,IRF1 49) V4RI 'F( 9) ALC ,I'iN .4,1 PE~ 0

I Y~o IOUT=Ioirr.II --A ') 300 C()N1INLJ F15,20 IF ( JT. F. LOUT) Go3 To) 910153") Gc) To I191540 40(W cO' r I NdJF:1 550 I ?I TF( 0, 90 3 ) KN'4, I ou -1 I560 903 Fo'?MAT( /////T40,RCOR)S INI i', 15/140,'RFCORD5 OUT -0915)

1580 FNI

DATAB3.S

PQ

U.21

.

i APPENDIX B

~FORTRAN SOURCE LISTINGS

*'@

j°

.-,

.4.i

C--3F'U1 J AGR;AN(;IAN LOOP

Do( ?00 MPRUNaNrXJNI I(Nnm PiJ!14,(f)SHRThcsH op7?( M RUN)

C4090 FO)RMAT(//1OC'***').BFGi SIMU.AIoJ ',

c PPiWiti!) ITPM:. INPUT FILE INLJ* P1IFNIN[) INLU

J_

C---'IF;IARANDOM ANOIiF IJ1JI BPSTFF

C

IF(A =0LS TA0IEPI) HIAIF-C I SrFrI*.PI:7.0) WILAST ! UANnIm(-AlS 1) I H

I(IT IItW. 0 P'JLA PAW10( -&13S(r~ 1Tr1rvt coec

CALL. ZI'()

INVRSM. S