Corporate Author: SHIPS PARTS CONTROL CENTER MECHANICSBURG PA

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SHIPS PARTS CONTROL CENTER MECHANICSBURG PA Persnal Authr(s): Encimer, J P Reprt Date: 18Nv1963 Media Cunt: 17 Pages(s) Organizatin Type: N -

1 Alrand Reprt Number: 41 Accessin Number: AD Full Text (pdf) Availability: Size: 0 KB Handle / prxy Url: N Full Text PDF Available Citatin Status: A - Active Title: PRICE INCREASE FACTORS, Fields and Grups : Lgistics, Military Facilities and Supplies Crprate Authr: SHIPS PARTS CONTROL CENTER MECHANICSBURG PA Persnal Authr(s): Encimer, J P Reprt Date: 18Nv1963 Media Cunt: 17 Pages(s) Organizatin Type: N - NAVY AND MARINE CORPS - null Reprt Number(s): ALRAND41 (ALRAND41) ALRAND41 (ALRAND41) Mnitr Acrnym(s): ALRAND (ALRAND) Mnitr Series: 41 (41)

Abstract: Whenever a stck list item has nt been prcured fr several years, it is expected that there will be sme increase in the new unit price ver the ld acquisitin price, particularly because f the

Navy Ships Parts Cntrl Center (SPCC) expect n material that has nt been prcured fr ne year, tw years, r several years.

2 Abstract: Whenever a stck list item has nt been prcured fr several years, it is expected that there will be sme increase in the new unit price ver the ld acquisitin price, particularly because f the increased labr and material csts t the manufacturer. Then the questin arises: What reasnable increase in csts can the U.S. Navy Ships Parts Cntrl Center (SPCC) expect n material that has nt been prcured fr ne year, tw years, r several years. Tw different appraches, ne by histrical data and the ther by the cst index, have yielded apprximately the same average increase: 4.6% vs. 4.9%. It seems reasnable, then, t believe that the real increase is apprximately 5%. (Authr) Distributin Limitatin(s): 01 -APPROVED FOR PUBLIC RELEASE Surce Cde: Dcument Lcatin: 1 - DTIC AND NTIS Geplitical Cde: 4219

Department f the Navy Naval Inventry Cntrl Pint Cde 04 5450 Carlisle Pike P.O.

3 Department f the Navy Naval Inventry Cntrl Pint Cde Carlisle Pike P.O. Bx 2020 Mechanicsburg PA PRICE INCREASE FACTORS 10/18/1963 Special Assistants fr Advanced Lgistic Research and Develpment U.S. Navy Ships Parts Cntrl Center Mechanicsburg, Pa. Submitted By: J.P. Encimer Operatins Research Analyst, Special Assistants fr Advanced Lgistic Research and Develpment DISTRIBUTION STATEMENT A. Apprved fr public release; distributin is unlimited. UNCLASSIFIED

maintaining the data needed, and cmpleting and reviewing the cllectin f infrmatin.

4 REPORT DOCUMENTATION PAGE Frm Apprved OMBN The public reprting burden fr this cllectin f infrmatin is estimated t average 1 hur per respnse, including the time fr reviewing instructins, searching existing data surces gathering and maintaining the data needed, and cmpleting and reviewing the cllectin f infrmatin. Send cmments regarding this burden estimate r any ther aspect f this cllectin f infrmatin, including suggestins fr reducing the burden, t Department f Defense, Washingtn Headquarters Services, Directrate fr Infrmatin Operatins and Reprts ( ), 1215 Jeffersn Davis Highway, Suite 1204, Arlingtn, VA Respndents shuld be aware that ntwithstanding any ther prvisin f law, n persn shall be subject t any penalty fr failing t cmply with a cllectin f infrmatin if it des nt display a currently valid OMB cntrl number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM- YYYY) TITLE AND SUBTITLE Price Increase Factrs 2. REPORT TYPE Study 3. DATES COVERED (Frm - T) xx-xx-1963-xx-xx a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Encimer, J P 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) SHIPS PARTS CONTROL CENTER MECHANICSBURG PA 8. PERFORMING ORGANIZATION REPORT NUMBER ALRAND41 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) Special Assistants fr Advanced Lgistic Research and Develpment 10. SPONSOR/MONITORS ACRONYM(S) 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT APPROVED FOR PUBLIC RELEASE 13. SUPPLEMENTARY NOTES 14. ABSTRACT Whenever a stck list item has nt been prcured fr several years, it is expected that there will be sme increase in the new unit price ver the ld acquisitin price, particularly because f the increased labr and material csts t the manufacturer. Then the questin arises: What reasnable increase in csts can the U.S. Navy Ships Parts Cntrl Center (SPCC) expect n material that has nt been prcured fr ne year, tw years, r several years. Tw different appraches, ne by histrical data and the ther by the cst index, have yielded apprximately the same average increase: 4.6% vs. 4.9%. It seems reasnable, then, t believe that the real increase is apprximately 5%. (Authr) 15. SUBJECT TERMS Lgistics, Military Facilities and Supplies 16. SECURITY CLASSIFICATION OF: a. REPORT U b. ABSTRACT u c. THIS PAGE U 17. LIMITATION OF ABSTRACT uu 18. NUMBER OF PAGES 17 Pages 19a. NAME OF RESPONSIBLE PERSON Jasn Harrisn 19b. TELEPHONE NUMBER (Include area cde! in- c^- zi.??- Standard Frm 298 (Rev. 8/98) Prescribed by ANSI Std

5 ALRAND REPORT 41 PRICE INCREASE FACTORS Special Assistants fr Advanced Lgistic Research and Develpment U. S. Navy Ships Parts Cntrl Center Mechanicsburg, Pa. 18 Nvember 1963

Lgistic Research and Develpment Apprved: Q.L C. W.

6 PRICE INCREASE FACTORS ALRAND Reprt 41 Submitted: <J. P. ENCIMER ENCIME] Operatins Research Analyst, Special Assistants fr Advanced Lgistic Research and Develpment Apprved: Q.L C. W. RIXEY LCDR, SC, USN Directr, Special Assistants fr Advanced Lgistic Research and Develpment H. ELKINS CDR, SC, USN Directr, Purchase Divisin

TABLE OF CONTENTS PAGE I INTRODUCTION 1 H THE STUDY 3 A. Data Used 3 B. Analysis 3 C. Results 4 D. Setting Cnfidence Limits 4 E. Limitatins f the Data 6 HI AN ALTERNATIVE APPROACH 8 A.

7 TABLE OF CONTENTS PAGE I INTRODUCTION 1 H THE STUDY 3 A. Data Used 3 B. Analysis 3 C. Results 4 D. Setting Cnfidence Limits 4 E. Limitatins f the Data 6 HI AN ALTERNATIVE APPROACH 8 A. Factry Magazine Cst Index 8 B. Analysis f the Index 9 C. Results 10 D. Reliability f the Analysis 10 IV CONCLUSION 12 APPENDK A. PURCHASE ORDER FACTORING TABLE 15 APPENDDC B. TABLE OF SUGGESTED PRICES-- 75% CONFIDENCE LEVEL 16 APPENDDC C. COMPARISON OF CURRENT PROCEDURE VS. PROPOSED PROCEDURE ii

8 T crrect this situatin the Purchase Divisin has requested that a study be made t prvide a new factr fr use in determining a reasnable expected increase in csts. T this end the fllwing study is submitted.

In ttal there were apprximately 11, 000 items in the sample.

9 II. THE STUDY A. Data Used The data used in develping a new price factr was btained frm the Cntract Status Histry recrd. A randm 10% sample f this recrd was selected, with the cnditin fr selectin being that an item had t have at least tw cntracts in its histry. In ttal there were apprximately 11, 000 items in the sample. The cntracts used were regular replenishment buys generated by the mathematical decisin rules, and did nt reflect any increases caused by the purchase rder factring table. B. Analysis The cntract histry f items in the sample was examined t find tw successive cntracts that were at least a year apart (using the cntract dcument date). In all, 400 items, cvering all Federal grups, were selected in this fashin. Then the price rati in the unit price f an item was fund by dividing the ld unit price int the unit price f the next sequential purchase. Als, the time between cntracts was cmputed. Example: Cntract Date Unit Price Item A 12/58 $3.52

10 Cntract Date f Next Purchase New Unit Price 8/60 $3.85 Price Rati = $ 3-85 = 1.09 $3.52 Time between cntracts = (8/60) - (12/58) = 20 mnths C. Results A price rati change (increase r decrease) and the time (in mnths) between cntracts was cmputed fr each f the 400 items. Then the average price rati change and mean time between cntracts was cmputed resulting in: Average Price Rati Mean Time mnths This means that the unit price f an item increased, n the average, 8% ver an average time perid f mnths. Trans- lating this int a yearly expected increase by slving (. 08)(1 2)/21 = yearly increase, the expected increase is 4. 6% per year, r an average per annum price rati f D. Setting Cnfidence Limits The 4.6% increase is an average expected increase. But we wuld smetimes expect the increase t be mre than the average. Thus, it is necessary t cmpute a statistic which measures the

variatin frm the average, and this statistic is the standard deviatin. The standard deviatin, symblized by the Greek letter sigma (a), averages the deviatins f all values arund the average r mean.

11 variatin frm the average, and this statistic is the standard deviatin. The standard deviatin, symblized by the Greek letter sigma (a), averages the deviatins f all values arund the average r mean. This value is fund by: 1. Squaring the differences between the value and the average, 2. Taking the mean f these squares, and 3. Extracting the square rt. The frmula fr a (standard deviatin) is: -i^ X) J where: X = the rati change X = the average rati n = 400 (number f values in sample) The value f r fr the sample items is 29%, fr an average time perid f mnths. Cnverting this int a yearly a,. 29/-JJH., we have 21. 9%. Nw, by knwing the average and standard deviatin, we can set cnfidence limits, i. e., we can say that we are X% certain that the real increase in cst will nt be greater than a defined limit. Fr example, we can say that we are 85% cnfident that

the yearly increase in csts fr an item is nt greater than the mean + cr(cr), where the mean is the average rati, v is the standard deviatin, and a is a variable multiplier which changes fr each

27 Then the general frmula fr cmputing the expected cst increase fr any time perid is: Y = T(1.046) + <W~T (.

12 the yearly increase in csts fr an item is nt greater than the mean + cr(cr), where the mean is the average rati, v is the standard deviatin, and a is a variable multiplier which changes fr each cnfidence limit. With a value f fr the 85% cn- fidence limit the average increase is nt greater than (1.04)(. 219) = Then the general frmula fr cmputing the expected cst increase fr any time perid is: Y = T(1.046) + <W~T (. 219) where: Y = ttal expected increase T = time in years since last purchase a = variable multiplier defined by cnfidence limits E. Limitatins f the Data There are tw pssible limitatins in the use f cntract status histry t derive a pricing factr. 1. If the item used in the study is a prvisining item, the unit price n a fllw-n buy after the initial purchase is generally lwer. The manufacturer charges ff his set-up and develpment csts t the initial buy. If a prepnderance f this type f items is used in the analysis, it wuld tend t pull the average increase dwn. Hwever, care was taken t insure that this did nt happen

frequently. Nevertheless, sme f these items are bund t appear in the data. 2. Anther pssible limitatin in the data wuld result frm quantity discunts.

13 frequently. Nevertheless, sme f these items are bund t appear in the data. 2. Anther pssible limitatin in the data wuld result frm quantity discunts. If the purchase quantity n the next cntract in sequence was significantly higher r lwer than the previus quantity, there culd be a difference in the unit prices because f the quantity discunts. Items n which this was apparent were nt included in the sample data.

III. AN ALTERNATIVE APPROACH A. Factry Magazine Cst Index In Sectin II a price factr was develped by examining the relatinship f time between purchases and the price differences.

14 III. AN ALTERNATIVE APPROACH A. Factry Magazine Cst Index In Sectin II a price factr was develped by examining the relatinship f time between purchases and the price differences. Anther apprach t this prblem is t use ecnmic indicatrs which shw that the cst f manufacturing material des increase ver time. If csts d increase ver time, then these csts are ultimately passed n t the cnsumer. ' Factry Magazine, a magazine devted t the prblems f the manufacturer, maintains statistics n all aspects f prductin csts in the frm f a cst index. These indices, maintained mnthly t arrive at an average cst index fr the year, shw the increased csts f buildings and facilities, all raw materials, labr, and equipment frm a base year f Then the aggregate cst index shuld be indicative f the expected increase in csts which the manufacturer will pass n t his custmers. The fllwing figures are the yearly cst index (Base year = 1947). (Factry Magazine, July 1963, page 6.) Year Index 0 (1955) (1956) (1957)

Year Inde: 3 (1958) 169.7 4 (1959) 175.8 5 (I960) 180.1 6 (1961) 183.1 7 (1962) 186.1 B.

Als we want t knw the expected yearly increase in the index.

15 Year Inde: 3 (1958) (1959) (I960) (1961) (1962) B. Analysis f the Index Knwing the year and the index fr each year, we want t find the relatinship between the year and the index; i. e., we want j t find if there is a predictable relatinship between time and the index. Als we want t knw the expected yearly increase in the index. One f the mst widely used techniques t express a relatin- ship between tw variables (time and index) is linear regressin analysis which utilizes an equatin f the frm: y = ax + b In regressin analysis a straight line, in the abve frm, is mathe- matically fitted t data (in ur situatin the cst index and year). Here " a" and " b" are numerical cnstants and nce they are knwn we can calculate a predicted value f y(cst index) fr any given value f x(year). Als, the value f "a" gives the slpe f the line, r the average rise in the index each year.

C. Results The results f the regressin analysis are y = 4. 9x+ 154.2 (Figure I) This means that the average increase in the cst index is apprxi- mately 5% per year (value f " a" = 4. 9%).

16 C. Results The results f the regressin analysis are y = 4. 9x (Figure I) This means that the average increase in the cst index is apprxi- mately 5% per year (value f " a" = 4. 9%). Then the verall average increased csts f the manufacturer, which are passed n thrugh increased prices, is 5% per year. D. Reliability f the Analysis Having develped a linear relatinship in the frm f an equatin it remains t be seen whether r nt it is reasnable t say that there exists sme crrelatin between tw variables, x (time) and y (cst index). The statistic t measure the strength f linear relatin- ship between tw variables is the cefficient f crrelatin (r). If the relatinship is gd, r will be clse t + 1 r - 1. The cefficient f crrelatin, (r), fr the cst index = This value f r, clse t + 1, indicates a high degree f psitive crrelatin. A cmpanin statistic t the cefficient f crrelatin is the cefficient f determinatin (r ). This statistic expresses what percent f the variatin f y 1 s (cst index) may be accunted fr by the relatinship with the variable x(time). In this situatin (r = 96. 5) a large degree f the variatin f the y 1 s is accunted fr (presumed caused) by differences in the variable x. 10

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IV. CONCLUSION Tw different appraches, ne by histrical data and the ther by the cst index, have yielded apprximately the same average increase: 4. 6% vs. 4.9%.

18 IV. CONCLUSION Tw different appraches, ne by histrical data and the ther by the cst index, have yielded apprximately the same average increase: 4. 6% vs. 4.9%. It seems reasnable, then, t believe that the real increase is apprximately 5%. It can be seen n Figure II that the higher the cnfidence level used the larger is the allwable increase in csts. Thus there is a trade-ff between increased csts in the material purchased and the csts incurred in reprcessing the dcument returned by the manufacturer. Fr example, at the 95% cnfidence level we wuld expect that 5% f the time the manufacturer wuld return the dcument. Hwever, we pay fr this by assuming larger increases in unit price. Therefre, we suggest a relatively lw setting at the utset, perhaps at the 75% level, and then t mnitr the results. If the savings in cmmitment mney are significant cmpared t the cst f reprcessing the expected 25% return f dcuments, this wuld be a satisfactry setting. If the facts prve therwise, a new setting and crrespnding increased csts can be easily btained frm Figure II. Perhaps the O & M budget will limit the settings available fr ur purpses. Three examples (Appendix C) illustrate the fact that there will be a reductin in cmmitment dllars which will permit mre accurate utilizatin f budgeted dllars. 12

19 It is intended that the figures presented in this study be applied t " nt-in-stck" items as ppsed t "nt-carried" items. " Nt-carried" items have n previus histry n which t cmpute an expected increase in csts. The technician estimates the current item price based n his experience with similar items 11 nt carried." Therefre it is unnecessary t adjust the estimated cst. 13

20 ^3

APPENDIX A. PURCHASE ORDER FACTORING TABLE Last Knwn Unit Price $ 5.00 D Nt Exceed Unit Price $ 10.00 5.01 10.00 25.00 10.01-20. 00 20. 01-30.00 30.01-40. 00 40.01-50.00 50.01-100.00 100.01-200.

21 APPENDIX A. PURCHASE ORDER FACTORING TABLE Last Knwn Unit Price $ 5.00 D Nt Exceed Unit Price $

APPENDIX B. TABLE OF SUGGESTED PRICES (75% CONFIDENCE LEVEL) Last Price 2 EXAMPLES Years Since Last Buy 1 2 3 4 5 6 7 8 9 10 $1.00 1.19 1.29 1.38 1.47 1.55 1.63 1.73 1.78 1.85 1.92 5.00 5.95 6.45 6.

r five times the increase in the $1.00 unit price item: 5($1. 19) = $5. 95.

22 APPENDIX B. TABLE OF SUGGESTED PRICES (75% CONFIDENCE LEVEL) Last Price 2 EXAMPLES Years Since Last Buy $ Fr year 1 the $5. 00 unit price item increased t $5. 95 r five times the increase in the $1.00 unit price item: 5($1. 19) = $ Then fr each year the expected increase is: Cntract Price = (Buy Quantity)(01d Unit Price)(% Increase) Year 1 Cntract Price = (Buy Quantity) )(Unit Price)(1.19) 2 Cntract Price = (Buy Quantity) )(Unit Price)(l. 29) 3 Cntract Price = (Buy Quantity) )(Unit Price)(l. 38) 4 Cntract Price = (Buy Quantity) )(Unit Price)(1.47) 5 Cntract Price = (Buy Quantity) )(Unit Price)(l. 55) 6 Cntract Price = (Buy Quantity) )(Unit Price)(1.63) 7 Cntract Price = (Buy Quantity) )(Unit Price)(1.73) 8 Cntract Price = (Buy Quantity) )(Unit Price)(1.78) 9 Cntract Price = (Buy Quantity) )(Unit Price)(1.85) 10 Cntract Price = (Buy Quantity) )(Unit Price)(l. 92) 16

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CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the