A Comparative Study of Forecasting Techniques for the US Air Force Medical Material Management System

Transcription

1 University of Central Florida Retrospetive Theses and Dissertations Masters Thesis (Open Aess) A Comparative Study of Foreasting Tehniques for the US Air Fore Medial Material Management System 1976 Phillip John Van Ess University of Central Florida Find similar works at: University of Central Florida Libraries Part of the Engineering Commons STARS Citation Van Ess, Phillip John, "A Comparative Study of Foreasting Tehniques for the US Air Fore Medial Material Management System" (1976). Retrospetive Theses and Dissertations This Masters Thesis (Open Aess) is brought to you for free and open aess by STARS. It has been aepted for inlusion in Retrospetive Theses and Dissertations by an authorized administrator of STARS. For more information, please ontat lee.dotson@uf.edu.

2 A COMPARATIVE STUDY OF FORECASTING TECHNIQUES FOR THE US AIR FORCE MEDICAL MATERIEL MANAGEMENT SYSTEM BY PHILIP JOHN VAN ESS B.S.E., Florida Tehnologial University; 1975 RESEARCH REPORT Submitted in partial fulfillment of the requirements for the degree of Master of Siene in Engineering in the Graduate Studies Program of the College of Engineering of Florida Tehnologial University Orlando, Florida 1976, ~

3 iii ACKNOWLEDGMENTS I wish to thank a number of people who helped me omplete this researh report, the first of whom is Benjamin W. Lin, my ounselor. His help in guiding my researh efforts and ritial analysis of my paper helped immensely in assuring a report of high quality. I would also like to express my appreiation to the other members of my ommittee, Dr. Christian s. Bauer and Dr. George F. Shrader. Major Joseph Giovale and Captain Rihard Ferguson are thanked for their help in hanneling my efforts in the investigation of the Medial Materiel Management System. I am indebted to the Patrik Air Fore Base Hospital management personnel, TSgt. Thomas Gilleran and Sgt. Robin Wood, for olleting the raw data used in the omparative analysis of this paper. Their ability to fill in my knowledge gaps about the working systems is greatly appreiated. To my typist-editor, my wife, I express my heartfelt thanks for enduring this trying period.

4 iv ABSTRACT A omputer simulation experiment was onduted to evaluate and ompare five individual foreasting models aross nine different demand patterns. The models were based on the Medial Materiel Management System used by the US Air Fore hospitals. Results indiated the best model varied depending on the demand pattern, the safety stok level, the noise level of the demand pattern, and the measure of foreast error~ Aross all demand patterns, exponential smoothing and 12-month moving average were best for the short term foreast used by the system,, regardless of noise level in the demand patterns. Analysis of model s within a single demand pattern showed, in most ases, several models as ranking equally well. When overall system requirements were onsidered, the exponential smoothing method was by far the best hoie.

5 v TABLE OF CONTENTS ACKNOWLEDGMENTS ABSTRACT LIST OF FIGURES I. INTRODUCTION II. DESCRIPTION OF EXISTING SYSTEM III. REVIEW OF EXISTING FORECASTING TECHNIQUES IV. ANALYSIS AND COMPARISON OF FORECASTING MODELS v. SUMMARY AND RECOMMENDATIONS iii iv vi APPENDIX A - DATA FROM PATRICK AFB APPENDIX B - COMPUTER PROGRAMS LIST OF REFERENCES

6 vi LIST OF FIGURES 1. Basis for determining Eonomi Order Quantities 6 2. Basi Medial Materiel Management System flowhart 8 3. Desription of the items used in the analysis Computer Program Results Foreasted demand of thermometer sensor overs ompared to atual demand Foreasted demand of dextrose ompared to atual d~mand a. Foreasted demand of loribrate ompared to atual demand Aspirin: Stok No Dextrose: Stok No Diazepam: Stok No Hydrohlorath Tablets: Stok No Cloribrate Capsules: Stok No Surgial Sponges: Stok No Thermometer Sensor Covers: Stok No. 6515L X-ray Film RP14: Stok No. 6525C9650AG Surgial Pakage: Stok No

7 vii 17. Simple moving average omputer program Data produed by moving average model Moving average method with trend orretion fator omputer program Data produed by trend orreted moving average model Exponential smoothing omputer program Data produed by exponential smoothing model Double exponential smoothing omputer program Data produed by double exponential smoothing model 61 Regression analysis omputer program 62 Data produed by regression analysis model 63

8 1 I. INTRODUCTION Rising inventory osts in US Air Fore hospitals due to inflation and a larger patient load have reated a monetary squeeze on hospital supply budgets. A solution to this problem may lie in a more effiient foreasting tehnique for the Medial Materiel Management System. The purpose of this paper is to evaluate the foreasting model used by the Medial Materiel Management System (MMMS) for US Air Fore hospitals, with a view to determining a better foreasting model for use. The MMMS is an integrated system of foreasting and inventory ontrol. It was felt that a review of the foreasting proedure was needed sine the present data proessing system used was previously done by hand. The extent of the analysis presented was limited due to many fators. The time onstraints imposed restrited the amount of data used in the analysis. Another limitation was enountered beause only two years of historial data were available. The data, however, was aurate. The data used was restrited to high dollar value items so that

9 2 a substantial number of datum points ould be used in the analysis. This also made the resulting omputer output data more meaningful and useful. 'r The amount of the data also restrited the foreasting tehniques that ould be meaningfully applied in the analysis. The data used in the analysis was highly representative of the medial supplies used in a us Air Fore hospital. Surgial, pharmaeutial, and ward supplies were used. Enough raw input data was also available to give an exellent ontrast between the various foreasting tehniques that were used in the analysis. The study ontained in this paper presents a logial and valuable look at the foreasting tehnique used in the US Air Fore MMMS. Chapter II desribes the present system now in use. It ites the various Air Fore manuals appliable to the system and presents the guidelines outlined in the manuals. An example is presented to aid in understanding the guidelines of the system. Chapter III gives a brief desription of the foreasting tehniques and their variations to be used in the analysis. Eah is presented with the mathematial formula used in the omputer model.

10 Chapter IV analyzes the data produed by the omputer 3 model of the existing system. All of the foreasting tehniques are rated on their ability to give an aurate foreast and still maintain a stable ordering system. Chapter V summarizes the findings of the analysis and then presents reasons for the findings. Reommendations are made for system review and adoption of various MMMS modifiations. Studies have been onduted in the past in other areas to evaluate and ompare several foreasting models using various riteria, but no studies were reported.in the literature reviewed on a system omparable to the US Air Fore's Medial Materiel Management System.

11 4 II. DESCRIPTION OF EXISTING SYSTEM The existing Medial Materiel Management System utilized by the US Air Fore Base Medial Supply Offier {BMSOl is governed by Air Fore Manual (AFMl 61-1, Volume V and AFM These two manuals provide the poliies and general guidelines on the medial materiel reord aount of the operating inventory ontrol. The data proessing system utilized adheres to the speifi proedures outlined in AFM The. MMMS is onerned with the inventory levels of medial materiel whose unit prie is less than $100. A few exeptions suh as x-ray film are also inorporated into the system. The BMSO onsiders all reurring demand items for stokage in the operating inventory. Close oordination between the user and the BMSO is vital to obtain valid and omplete information for stokage deisions and subsequent establishment of stok levels. When stokage is appropriate, either a BMSO determined stok level or an eonomi order quantity (EOQ) stok level will be established.

12 An inventory ontrol system is usually based on one of 5 two different methods. They are the fixed reorder point method and the fixed review time or yli ordering method (Greene, 1974). In the fixed reorder point method the quantity on hand is heked whenever material is removed from the inventory. When it reahes a ertain point, a quantity of a fixed size is ordered. In the fixed review time method, the time remains fixed and the order quantity varies. The inventory items are periodially surveyed. At eah review point an order is plaed whih will bring the inventory up to an established level. The Air Fore's MMMS is neither of these two pure forms. It is an integrated inventory ontrol foreasting system. The system's guidelines used are shown in Fig. 1. The following paragraphs explain the various headings. The EOQ method of requisitioning used provides that those items yielding a low dollar value of annual onsumption are requisitioned less frequently. Use of the EOQ redues the number of requisitions initiated in the ourse of a year. This enables the BMSO to devote his greatest attention to those items whih are responsible for the largest dollar expenditure. The top 25 high dollar value items aount for 25 perent of the BMSO's supply budget

13 If the then the and the EOQ Period at whih time Annual Consumption Safety Level Reorder Point Normally, this suffiient stoks is is is reorder point will be ordered to will reour every bring stok on hand up to the.. Stok Control Level ' whih is Less than $ month of 1 months stok 12 months 13 months of stok stok + pipeline + pipeline $ 8.oo -- $ month of 1 months stok 6 months 7 months of stok stok + pipeline + pipeline $ $ ! month of 1 months stok 3 months 4 months of stok stok + pipeline + pipeline $ $ month of 1 months stok 1 month 2 months of stok stok + pipeline + pipeline over $ month of 1 months stok 15 days 45 days of stok (CONUS and stok + pipeline + pipeline overseas) Soure: AFM 67-1, Vol. V, 2 Ot. 72 Figure 1. Basis for determining Eonomi Order Quantities

14 and less than one perent of the total items in the inventory. The normal t!me between replenishment requisitions (the EOQ period), stok ontrol level, and reorder points is determined on the basis of the dollar value of annual issues (AFM 67-1, Vol. V). The quantity to be requisitioned is that amount needed to bring stok on hand and on order up to the stok ontrol level also shown in Fig. 1. The stok ontrol level is the planned maximum quantity of an item whih may be on hand and on order at any time during the month. The quantity requisitioned is adj~sted automatially by the omputer program to the intermediate pak or shipping ontainer quantity. It should be noted that an issue is a demand and a requisition reeived or reeipt is a supply. These terms will be used interhangeably throughout the paper. The MMMS omputer program whih updates the EOQ one a month uses a 12-month simple moving average to foreast the next reorder point. This means that the reorder point stok level hanges whenever the foreast for the next month hanges. The urrent stok level is reviewed by the. data proessing system one a week. A simplified flow hart of the data proessing system is shown in Fig. 2. A

15 8 BMSO I.'NV'RNTOR'l CONTROL FILE MASTER FILE SYSTEM CONTROL CARDS EXTRACTION REPORT INVENTORY CONTROL INVENTORY ADJUSTMENT CARDS INVENTORY EFFICIENC REPT. BMSO Figure 2. flowhart. Basi Medial Materiel Management System

16 . 9 quantity is requisitioned for an item if the present inventory stok level is less than the monthly foreasted reorder point. The reorder point is some perentage of the stok ontrol level. The perentage used is determined partly by its annual dollar onsumption. The example that follows illustrates how the reorder point for eah item is obtained. Variations in stok ontrol levels and EOQ's may be neessary for ertain items and under ertain onditions. Expiration dated items, programmed population hanges on a base, item popularity, and reurring seasonal demand items all provide variations within the stok ontrol system. To aurately determine the reorder point for any given item, the average pipeline time based on routine requisitions and methods of shipment must be determined. Pipeline time is the number of days between the data a requisition is initiated and the date materiel is reeived. Pipeline time length omputations are based on normal onditions and methods of transportation. omputer assigns a 30 day pipeline time. For a new item the One six pipeline times are aumulated, the moving average of the last six requisition pipeline time lengths is omputed to foreast the next pipeline time used in the omputations.

17 Greene (1974) states that the safety stok quantity is based on the time it takes to obtain materiel in an 10 emergeny. AFM 67-1, Vol. V ditates that the safety stok quantity for any item will be a 30 days' supply of that item. The omputational method used to establish the reorder point outlined in AFM 67-1, Vol. V is as follows: Replenishment issues for given number of days X Safety level Pipeline time. d +. d ~n ays 1n ays Number of days during whih issues were aumulated Reorder Point Another way of stating this formulation is: Daily Foreast X ls"afety level Lin days + Foreasted Pipeline time in days Reorder Point For example the Patrik AFB hospital used 220 ases of 5% dextrose solution in 1000 bottles in the last 12 months. Eah ase ontained six bottles. Thus the reorder point is alulated as follows: 1320 X bott 1 es or 30 ases 365

18 li The stok ontrol level is alulated as follows: Reorder Point Amount normally onsumed during EOQ period Stok Control Level The amount normally onsumed during an EOQ period is the foreasted moving average multiplied by the length of the. EOQ period. Using the dextrose example again, a onsideration of the ost per item is neessary to onform to AFM 67-1, Vol. V. The ost of eah bottle is $4.35. Thus the annual dollar onsumption is greater than $1728. This makes the EOQ period 15 days. Therefore the stok ontrol level is: X b ott 1 es or ases The above desription of the existing system is the basis used for the omparisons performed in Chapter IV. The omputer models used in the analysis adhere to the guidelines of AFM 67-1, Vol. V and use the same methods as just shown to alulate the Deorder point and the stok ontrol level.

19 12 III. REVIEW OF EXISTING FORECASTING TECHNIQUES The problem of routine foreasting an be thought of as one of having a sequene of numbers and trying to predit what the next number will be and trying to predit the following one, profiting by our mistakes. The problem of predition requires a great deal of knowledge about what the numbers represent. Given this, are must be exerised in seleting the foreasting tehnique to be used in a given system~ Sine the Medial Materiel Management System under analysis needs a disrete short term foreasting tehnique, only those tehniques suited for disrete short term foreasting were onsidered for analysis. The limited amount of historial data available also dereased the number of tehniques available for analysis. Three tehniques with their variations were seleted beause they onformed to these guidelines. The te~queg were mavin~ average, exponential smoothing, and regression analysis. There are three foreasting variations based on moving average. The first variation is the simple moving average based on a onstant proess. The seond is the moving

20 13 average with an adjustment for a linear trend proess. The third is a weighted moving average whih never was fully explored beause of the advent of the exponential smoothing tehnique. The moving average foreasting tehnique omes from applying the least-squares riterion to a data reord of a fixed length, where eah of the datum points is weighted equally (Johnson and Montgomery, 1974). The following variations were evaluated on their ability to aurately foreast both onstant and linear trend proesses. The simple moving average is a foreasting estimate based on the average of the N most reent observations (xt). At eah period the oldest observation is disarded and the newest one added to the observations. ~+1 1 T = N t=t~n+l xt = NT This gives: whih is the moving average at timet (MT). The responsiveness of the moving average method to hange is ontrolled by the hoie of the number of observations (N) to be averaged. If N is large, the moving average responds slowly to hanges in xt, and when N is small, it responds more quikly. If the xt's are at a onstant level and suddenly jump to a new onstant level, it

21 14 takes N observations for the moving average to give estimates relevant to the new level. With a slow hanging proess a large value of N would yield good results and for a fast hanging proess a small value of N would yield the best results {Brown, 1963). Sine the simple moving average will lag behind a trend in a demand, the seond variation employing a trend orretion fator is often used. The omputations minimize the sum of the squares of the errors between the atual observed demand and a straight line. The line's slope is a measure of the magnitude of. the trend in the demand (Brown, 1959). The values of the oeffiients a and b are estimated by minimizing the sum of the squares of the errors of the straight line xt = a + bt. The least squares analysis gives T a = N 12 s b N(N2-1) where T is the total demand for the past N periods and S is a total where the demand in eah period is weighted by

22 15 the number of periods from the enter of the averaging interval (Brown, 1959). Assuming a trend is in effet, our foreast for xt one period in advane is where xt-n and {Brown, ~959). The third moving average variation is alled the weighted moving average. Instead of weighting all previous datum points equally, an experimentally determined weight is assigned to all past N periods onsidered in the omputations. Due to the emergene of exponential smoothing and adaptive smoothing tehniques, this method has never been used extensively. It is mentioned here just for ompleteness. Q Exponential Smoothing is the name given by Robert Brown in 1959 to a pratial method of smoothing flutuations in a demand history to get an estimate of future

23 16 demand. Brown formulated this rule: "To get a new estimate of the average demand, add to the previous estimate a fration of the amount by whih demand this month exeeds that estimate." This fration is known as a smoothing onstant and is denoted by a (0 < a < 1). The above basi rule of exponential smoothing is written as follows: New Average a(new demand)+ (1 -a)(old average) or restated where t - the number of time periods after the point in time where the estimation proess began xt - St(x) - the past time period demand the smoothing foreast for the next time period st-l(x)- the past time periods foveast (Radhakrishnan and Sullivan, 1972). Simple Exponential Smoothing is usually applied to a onstant proess system. If a linear trend proess or a

24 l.i onstant proess that ould develop a trend is to be foreasted, Double Exponential Smoothing is used. The equation as stated by Brown (1959) is the following: New Average = a(new demand) + 2(1- a)(average omputed last month) -.( 1 - a) (average omputed previous month) Stated in mathematial terms this gives: where 6 -{ a ) St(x) - st [ 2 ] (x) t a as ( x) + U - a ) s t t-1 [ 2 ] lx) and St(x) is as was previously defined. The notation St [Z](x) means double smoothing, not the square of exponential smoothing (Brown, 1963). Therefore the last two omputed values of the double smoothed average are stored to ompute the new foreast eah month. To evaluate the oeffiients in an appliation of exponential smoothing from one time period to another, it

25 is neessary to selet the value of the smoothing onstant, a The auray of the foreasts depends upon the orret 18 hoie of the smoothing onstant. If the foreasting method is to produe stable estimates and smooth out random flutuations in the data, a small value of the smoothing onstant is required. On the other hand, when a rapid response to a real hange in the demand pattern is desired a larger value of the smoothing onstant is appropriate (Radhakrishnan and Sullivan, 1972). To equate the equivalent N-period moving averge tehnique to the exponential smoothing method, the smoothing onstant is seleted to give basially the same results. With the smoothing onstant a - 2 N + 1 this similarity is ahieved. This annot be 100 perent orret sine exponential smoot~ing applies a varying weight to all the data whereas the moving average only averages the last N values with an equal weight being applied to those N datum values (Bedworth, 1973). If some basis exists for satisfation with a moving average method for some N-periods, this method is used to establish the value for a

26 Usually the smoothing onstant, a, is somewhere between 0.01 and 0.3. A widely used tehnique is to arry out a sequene of trials on a set of historial data using many different values of the smoothing onstant, and selet the value of a that optimizes a measure of effetiveness suh as the minimum of the sum of the squares of the errors. The seletion of the "best 11 smoothing onstant is usually a tradeoff between "effetiveness of smoothing" and "rapid response" (Brown, 1963). It should be noted that the value of the smoothing onstant an be reursively updated from one period to the next. This has been termed 11 adaptive 11 or ttmodified" exponential smoothing. Adaptive ontrol of a was not attempted in this study mainly beause a suffiiently large datum base was not available. However, past analysis has shown that adaptive smoo~hing of a onstant proess gives results omparable to exponential smoothing (Johnson and Montgomery, 1974). If the results of a set of trials indiate that the optimum value of a is greater than 0.3, then the validity of the model should be questioned. If the plotted data reveals trends or yli patterns that will lead to ' q ~ large

27 20. smoothing onstant, a more appropriate model should be hosen to foreast future demands. If it is possible to take derivatives of the fitting parameters of an equation, then it is possible to fit data with that equation using the least-squares proedure of regression analysis. A first-order polynomial regression analysis was used for the data analysis. The first-order polynomial that will be used is - a+ bt where N N a = L xt - b L t t=l t=l b = N N N N L (t. ~)._ I xt I t t=l t=l t=l l N L (t)2 - L t)2 t=l t=l (Bedworth, 1973). As the equations indiate, regression analysis is a ontinually summing proess. This tremendous amount of historial data reates a very onstant foreasting proess.

28 21 IV. ANALYSIS AND COMPARISON OF FORECASTING MODELS The five foreasting methods explained in Chapter III were applied to a omputer model of the Medial Materiel Management System. The five methods were evaluated on their ability to meet four riteria. The riteria were the average of the sum of the squares of the errors, ove~all stok ontrol level, inventory flutuation, and stok reliability. The omputer model used is a somewhat simplified model due to the nature of the data used. The data used was obtained from the Patrik AFB Hospital in Florida. Historial data was only available for the past two years. used in the analysis. Nine medial supply items were These items shown in Fig. 3 are a representative ross setion of the supply inventory. All of the items are high dollar value items whih give them a 15 day EOQ period. The items have been stoked for more than two years. The two years of data for eah item used in this analysis are shown in Appendix A. An average pipeline time of 16 days was used sine this onforms to available data at Patrik AFB.

29 22 ITEMS Stok Number Item Identifiation Where Used Items/Unit. ~ssue A~pirin Tablets Pharmay 1000/Bottle 12 Bottles/Case Dextrose ' Surgial Diazepam Tablets Hydrohlorath Tablets Cloribrate Capsules Surgery/ Wards Pharmay Pharmay Pharmay locdo /Bottle 500/BT 12 Bottles/Case 1000/BT 12 BT/Case 100/BT 12 BT/Case ' \ Surgery 1200/Pkg Sponges 6515L G52.5C9GSOA.G Thermometer Sensor Covers X-ray Film RP 14 Wards X-ray 1000/Pkg 500/Ca.se Surgial Surgery 1/Pkg Pak Figure 3. Desription of the items used in the analysis.

30 The omputer programs that were used are shown in Appendix B. Also shown is one year of the analysis of the data using eah foreasting method. The omputer programs onform to the guidelines in AFM 67-1, Vol. V. The programs alulate a reorder point and a stok ontrol level eah month. These alulations are based on the given safety stok period, the pipeline time, and the foreasted issue. The foreast was given in both a daily and a monthly foreast. A weekly available stok level is also given to more aurately show any stokouts. The sum of the squares of the errors was. also tabulated for eah item for use in the analysis. The simple moving average tehnique and trend adjusted moving average variation were both tested with a period of 6 months and 12 months. The safety stok level was assigned a value of 30 days and also equated to pipeline time to hek the stok availability of eah item. Eight omputer runs were made to produe the eight models used in the analysis. The exponential smoothing tehnique and the double exponential smoothing variation used a 12-month moving average for the initial foreast. The safety stok level was equated to 30 days of stok and to pipeline time. The

31 24 value of a was varied from 0.1 to in inrements of 0.02 for eah item. This was done in an attempt to determine the "best overall" value for a Four omputer runs were needed to generate the models for the analysis. (Eah model had 12 different values for o. ) The regression analysis tehnique used the first 12 months of data to establish the initial foreast. The safety stok level was equated to both one month and to the pipeline time. Two models were generated for analysis by the omputer program. The "best overall" value. of a was determined from the sum of the squares of the errors. The data from both the exponential smoothing and double exponential smoothi ng omputer runs indiated a definite preferene for a = 0.1. This value was found to be a very good value for the onstant demand items. It also produed a stable output for the items that had flutuations in demand. Most of the time, demand follows a very slowly hanging pattern, so that a small smoothing onstant is appropriate in smoothing out the random flutuations to give an aurate estimate of the aver age A omparison of the omputed data was made based on an average of the sum of the squares of the errors, stok

32 25 ontrol level, inventory level flutuation, and stok availability. Fig. 4 shows a table with the experimental results outlined. The sum of the squares of the errors for both exponential smoothing variations is shown for a = 0.1, the 11 best overall 11 value, and for a = The last value most nearly equates the exponential smoothing method to a 12-month moving average, the present system used to foreast demand. Four of the 14 omputer runs produed omparable "best" results. These were the simple 12-month moving average models and the exponential smoothing models. All of the models had a low level of inventory flutuation, a low average sum of the squares of the errors, a low to medium stok ontrol level, and an exellent stok availability reord. Due to the fat that the pipeline time was almost half of the safety stok level, the models with safety stok level equal to pipeline time had a lower stok ontrol level but still maintained an exellent stok availability reord. The worst models were the 6-month moving average with the trend orretion fator. These models had a very high average sum of the squares of the errors, a very poor stok

33 Inventory Level Flutuation Lo\ Lo\ Med Med Med Med High High Lo\ Lo\ Lo\ Lo\ Med Med Med Med Lo\ Lo\ N m COMPUTER RUN RESULTS Method N Safet~ Aver.age Used r (Month) StoK of Level SSE (Day:s > Stok Level Stok Avail. Control 1e Moving Average Moving Average With I 500 Trend I Exponential Smoothing Double Exponential Smoothing Regression Analysis EX Med Ex Low Ex Med ~Ex Low Good Med Good Low Poor Med Poor Low Ex Med Ex Med Ex Low ~ Ex Low Ex Med Ex Med Ex Low Ex Low Ex High Ex Med Figure 4. Computer Program Results

34 21 availability aused by a dangerously low stok ontrol level, and a highly flutuating inventory level. The double exponential smoothing models also had an exessive inventory level flutuation. This was due to their responsiveness to the demand flutuations that looked like a trend. The four 11 best" foreasting models were evaluated on their appliability to the present system. The four foreasting models ontain two different tehniques. The 12- month moving average method is the tehnique presently used by the MMMS. The exponential smoothing method of foreasting is an entirely different tehnique. For this reason these two tehni~es will be ompared and ontrasted in their syste~ appliability. When making a judgment of the relative merits of eah alternative, the following three riteria suggested by Brown (1963), whih are usually important, were used: Auray Simpliity of omputation Flexibility to adjust the rate of response By usi~g smme ~ose riterion, all of these an be optimized (Bedworth, 1973).

35 28 The need for an aurate foreast is of the utmost importane. Both of the seleted tehniques aomplish this with equal ability. It has been noted, however, that if a foreasting system based on exponential smoothing were atively maintained over a period of several years, the auray of its preditions ould be steadily improved (Radhakrishnan and Sullivan, 1972). This better auray ould result in a signifiant monetary redution of inventory. In the inventory ontrol system presented, it is neessary to reompute foreasts for three to six thousand supply items every month. Two-tenths of a seond onsumed unneessarily for eah of these items amounts to approximately one half hour. One half hour of omputer time is expensive. Clearly then, simpliity of omputation is important when a large number of different times series foreasts are routinely omputed. In a omplete reords system like the MMMS, there is one field on the historial data tapes for the issue in eah of the past 12 months for every item. The 6-period moving average used to foreast pipeline time requires another six tape fields per item. For a 5000 item supply inventory reord, this amounts to 90,000 fields. Eah

36 29 month in the ourse of the proessing, the information in eah field in the input reord must be shifted one field. The oldest information is dropped and the issue in the past month entered. Then the 6-period and 12-month moving averages an be omputed. Magneti tape presents no real problem as far as available spae for these datum points is onerned. But the longer the reord, the more time (and hene ost) is required for data proessing. For a small hospital like the one at Patrik AFB (30 beds), all of this historial information is ontained on one magneti tape. But given a large medial enter like Lakland AFB, Texas, four magneti tapes are required to store the historial data. Four tapes mean four tape readers. This is expensive equipment. Exponential smoothing does not require keeping a long historial reord. Only one historial datum point per item is needed to alulate the new foreast. This datum point is the old foreast. Given this historial datum off the magneti tape and the past month's demand loaded into the system from ards, the dis stored omputer program an alulate the new foreast. By applying the exponential smoothing tehnique of foreasting to both the item fore-

37 ast and to the pipeline foreast, the number of magneti tape fields an be redued to one-ninth of its original 30 size. So instead of 90,000 historial datum points the systen now has only 10,000. This uts down on the data proessing time required and also an represent a substant ial savings on omputer peripheral equipment. Cost savings our not only from redution of apital equipment osts but also from savings on maintenane osts. This new foreasting tehnique ould easily be applied to the present system. The first old foreast to be used initially an be the 6-period. or 12-month moving average of the present historial data. Given the preeding information, the first foreast of the system ould be no worse than the 6-period or 12-rnonth moving average method would have given. Coneivably, it ould be better. The third riteria, flexibility to adjust the rate of response, is an inventory system attribute that is seldom onsidered but should be. When the urret issue is different from what was expeted there are two onsiderations. Is the differene a purely random flutuation (noise)? If so, the foreast will smooth out the flutuation. But if this differene signifies a new pattern, then the past data is irrelevant.

38 31 The moving average methods urrently used in the MMMS provide very little flexibility. Flexibility to adjust the rate of response an only our if the value of N is hanged. It is very diffiult in the present system to hange the value of N, the number of periods to be used in the omputations. The exponential smoothing method on the other hand an easily be adapted to new trends. Simply hange the value of the smoothing onstant, a Most of the time demand follows a. very slowly hanging pattern, so that a small smoothing onstant is appropriate in smoothing out the random flutuations to give an aurate estimate of the average. Oasionally, the BMSO may predit a hange due to the introdution of a new produt. When a irumstane suh as this arises, the item and its related items ould have their smoothing onstant values inreased up to a = 0.3, or even to a = 0.5 for a period of three to six months. The higher a value would make these produts very responsive to hanges in demand during this period. Then, when the new demand pattern has been established, the smoothing onstant an be dropped bak to its original value for greater stability and auray.

39 32 It should be noted that the BMSO does not have to predit the magnitude or diretion of the demand hange. The BMSO needs only predit a hange is imminent. The routine alulations of the omputerized system an detet and orret for the atual hange that materializes in the demand for eah item probably muh more aurately than any predition ould. Figures 5, 6, and 7 graphially ompare the atual demand of three medial supply items used in the anal~sis to the foreasts omputed by the 12-month moving average model and the exponential smoothing model with a = Fig. 5 illustrates a low unit ount item. The omparison shows how the exponential smoothing model in Otober and November adjusted to the higher demands better than the moving average method. The item shown in Fig. 6 is a medium unit ount volume item. The omparison illustrates how the exponential smoothing model, one given a two month settling in period, traked the upward trend of this item. The high unit volume item shown in Fig. 7 illustrates how the exponential smoothing model, like the present 12- month moving average model, remains stable even when tremendous monthly flutuations of an item our. This

40 5 ' Figure 5. Foreasted de mand of thermometer sensor overs ompared to J w MOVING AVERAGE EXPONENTIAL SMOOTHING... - J A s 0 N D J F M A M atual demand.

41 Figure 6. Foreasted demand of dextrose ompared to atual demand ~ ,_ _.,., ,... ACTUAL DEMAND MOVING AVERAGE EXPONENTIAL SMOOTHING - J A s 0 N D J F M A M J

42 Figure 7. Foreasted demand of loribrate ompared to atual demand. J w U ::.: ,., J A ACTUAL DEMAND MOVING AVERAGE EXPONENTIAL SMOOTHING 6 s 0 N D J... F M A M

43 36 displays the exponential smoothing model's ability to differentiate between a new trend and noise. The omparison of the exponential smoothing method to the presently used moving average methods has revealed the following: 1. The exponential smoothing method was as aurate as the moving average method at the time of installation and ould be expeted to give a better foreast in the future 2. The exponential smoothing method would require oneninth of the historial data that the present moving average methods employ 3. The exponential smoothing method's flexibility to adjust the rate of response is far superior to the present moving average methods

44 37 V. SUMMARY AND RECOMMENDATIONS This paper has presented the guidelines of the Medial Materiel Management System presently used by the US Air Fore BMSO to ontrol the supply inventory. Various manuals were ited whih ontained the guidelines for different phases of the system. An example was presented illustrating how the reorder point and stok ontrol levels were alulated in the omputerized foreasting and inventory management system. A brief desription was given of the foreasting tehniques with their variations that were studied in this researh report. The formulas shown for the foreasting tehniques were the ones used in the omputer models. The omputer models were then run adhering to the guidelines outlined. The data produed was then analyzed to evaluate the foreasting models used. The foreasting models were rated on their foreasting auray as well as an ability to maintain a stable servieable stok ontrol level.

45 38 Beause of the auray, simpliity of omputation, and flexibility to adjust the rate of response of the exponential smoothing foreasting method, I would reommend it be immediately adopted for use in the Medial Materiel Management System. The initial value of the smoothing onstant for foreasting supply demand should be put at The pipeline time foreasting portion of the program would initially have a = This would equate it to a 6-period moving average. After a settling in proess this value ould be inreased or dereased as was deemed neessary. Another reommendation is to equate the safety stok level in days to pipeline time. The present time of a flat one month's stok is unrealisti. With the exponential smoothing method to foreast pipeline time being highly responsive, any permanent inreases or dereases in pipeline time would be adjusted to quikly. The data produed in the analysis showed that no derease in servieability ourred when the pipeline time of 16 days was also used for the safety stok level. However, the stok ontrol level was lowered from 10 to 30 perent. Captain Rihard Ferguson, USAF, presently assigned to Fort Detrik, Maryland, is presently studying the possibility of equating

46 pipeline time to safety stok level. His analysis at this 39 point onurs with these findings. less money tied up in inventory. This lower level means Lower levels of physial inventory an also be more aurately ounted. A third reommendation is to rid the Medial Materiel Management System of one of its main problems: tampering. The raw data shown in Appendix A also shows how the present real life system is ordering and reeiving stok. Tremendous variations in quantities ordered for these high dollar value items are shown over the ourse of the past two years. In the three examples.shown in Cahpter IV, Figures 5, 6, and 7, the plotted values of the 12-month moving average method show how the untampered system ~ou~d have ordered these supply items. This more smooth ordering method also resulted in a stok ontrol level from 30 to 50 perent less than the present system deems neessary. This is a lassi example of reating exessive inventory levels by tampering with an integrated inventory-foreasting system. By installing the exponential smoothing foreasting method into the MMMS an aurate stok ontrol level would be immediately alulated. If this system is left untampered with and orders are plaed when they are generated

47 40 and for the amount omputed neessary, the system would settle out within a short time and overall physial inventory ost would derease substantially.

48 41 APPENDIX A DATA FROM PATRICK AFB

49 42 NATURE OF THE DATA All of the data shown in graphial form in this Appendix was produed at the Patrik AFB Hospital in Florida. The data shown is for nine medial supply items from July 1974 to July The points on the graphs at eah month represent the total issues and reeipts during. that partiular month. A omplete desription of eah item is shown in Fig. 3.

50 MONTHS OF TilE YEAR Figure 8. Aspirin: Stok No

51 j ~4-6~+H 11. I' l I ! i ~!.- i'.! jij f i J AS 0 N D J FHA H J J AS 0 N D J FHA H J 0 '" HON rus OF THE YEAR Figure 9. Dextrose: Stok No

52 'l. I! t. :-1 I t I L t+++th HIIj v ~ A S 0 N D J F M A M J J A S 0 N D J F M A M J MONTI IS OF THE YEAR Figure 10. Diazepam: Stok No

53 Figure 11. Hydrohlorath Tablets: Stok No l-h-h J-1--i I-++1H+++I HONTUS Of 'l'he YEAR

54 J A S 0 N D J f' H A H J J A S 0 N D J F M A M J 40 MON'tiiS OF 'l'he YEAR Figure 12. Cloribrate Capsules: Stok No

55 J AS 0 N D J FHA M J J AS 0 N D J F M A H J Figure 13. Surgial Sponges : Stok No II 10 MONTHS OF THE YEAR

56 J AS 0 N D J FHA H J J AS 0 N D J FHA M J I ~ ' : ''I - 11 ll I I ' I J I -. - I- I -. - I l. - - :! t 8 0 X HONTIIS OF Til YEAR Figure 14. Thermometer Sensor Covers: Stok No. 6515L030747

57 J AS 0 N D J F M A H J J AS 0 N D J FHA M J Figure 15. X-ray Film RP14: Stok No. 6525C9650AG U1 0 1 ~ I T ' - H++I I 10 H I HONTIJS OF TilE YEAR

58 HON'fliS OF TilE YEAR Figure 16. Surgial Pakage: Stok No U1...

59 52 APPENDIX B COMPUTER PROGRAMS

60 53 PROGRAMS USED IN ANALYSIS The following five omputer programs were used in the prodution of the test data needed to evaluate the five foreasting methods. Eah omputer program is followed by a page of the typial output given by eah. The exponential smoothing variations' data page was produed with the smoothing onstant equal to The page of output used the data for the medial supply item dextrose.

61 3.. 5 b 7 s 9 10 l~ 13 l6t ls s:; 5J08 E 10! e C so E>O Figure Simple moving average omputer program.

62 AVAlLt.\BLE DATA F'R0\1 PATRICK AFB FRO~ JULY 74 TO JUNE FORECAST FORE:AST REORDER STOCK weeklrt' SUM OF PER DAY PER ~NTH POINT CO~TR:l~ t STOCr< SQUARES LEVEL LEVELt OF ERROR o.ooo o.b ' so b 36 o.sso 25. ~ o.b Figure 18. Data produed by moving average model. 55

63 56 SJ:>B E E 3 " ~ H ls lb 17 ls u E l 0 ls " ~'t: :n 1\ o 41!S 6.4t 4tS 4tb 47 e C.'j SCI ~~ 53 ~.. =5 E 3C *-tl 50 bo 70 s Figure 19. Moving average method with trend orretion fator omputer program.

64 AVAIL~BLE DATA FRO~ PATRICK AFB FRO~ JULY 74 TO JUNE ~ FORECAST PER DAY o. 9ss FORE:AST PER "1NTH REORDER POINT b STOCK CONTRO~I LEVELt weeklfy STOCK LEVELl so ES SUM OF SQUARES OF ERROR o.ooo Figure 20. Data produed by trend orreted moving av average model.

65 58 l 0 ls 16 e 7 ls 20 so es Figure 21. Exponential smoothing omputer program.

66 AVAIL~BLE DATA FRO~ PATRICK AFB from J~L~ 74 TO JUNE FORECAST FORE:AST REORDER STOCI( weeklrf SUM OF PER DAY PER ~NTH POINT CONTRO-. STOCr< SQUARES LEVEL ~.oevel Of ERROR o.ooo ~ model ~ !t() ~ a.;1o Figure 22. Data produed by exponential smoothing 59

67 60 1.,.. ~J;)2 ~ \. E 10 ls l E ls 3C 35 4(\ so ~ es Figure 23. Double exponential smoothing omputer program.

68 I 61 AVAILABLE DATA FRO~ PATRICK AfB fro~ JULtV 74 TO JUNE FORECAST FOREC~ST REORDER STOCK WEEKLrt SUM Of PER DAY PER ~NTH POINT CONTROL! STOCK SQUARES LEVEL ~ LEVELl OF ERROR BlB o.ooo S.BSS ' so o.sos so ~ oos Figure 24. Data produed by double exponential smoothing model.

69 ~ 7 A q \4 ls lb ~ ~ S ;>q jz 3S 3~ n l ltc i so $JOB 10 l 2 3 I REG~ESSlON ANALYSIS FORCST= MONTHLY FO~ECA~T IN UNIT; PE~ DAY. SL= SAFETY LEVEL IN DAYSCBOTH 30.0AYS ANO PIPELINE were USEO.l PL: PIPELINE TIME IN DAYS. RE0 T: REORDE~ POINT ESTABLISHED EACH ~ONTH. SCL= STOCK CONTROL LEVEL. NE~SL WEE~LY STOCK LEVEL. N= NU~~ER OF MONTHS OF HISTORICAL DATA USED AS FORECAST BASE. ORDER A~OUNT OROE~ED WHEN lnve~tory<reoro ~ POINT ISSUE ~EEKLY ISSUE BASED ON ONE FOURTH OF MONT~LY ISSUE DIMENSION X(5C\) INTEGE~ T,OPtSCL ORDER INITIALIZE NUMERICAL VALUE~ to~.:q ER~OR O. L O SUMXT:O. SU"'-T:O. SlWT X TaO / SU~TSQ O -' PL l6. SL=3o.s FOR~AT(lXeF7.3t2Flu.3t2I7tFll.3> FORt.tAT () 6FS.l l FOR"'1AT(212l FOR~ATC1Xt8CFS.Ot2Xl/lXt8(F5.0 2X)/lX,8CFS.Oe2Xl//l FOR~ATC}X, FORECAST FO~ECAST REORDER STOC~ WEEKLY SU~ OF,/ l,}x, PER DAY PE~ ~NTH POINT CONTROL StOCK SQUARES,/,31Xt 2LEVEL LEVEL OF ERROR,Il FOR~AT(l~l 'AVA1LA6LE DATA FROM PATRICK AF8 FROM JULY 74 TO JUN~ 7 11; 1 t/ ) FORr.tAT(39Xtll3l QEAD ANO w~ite INPUT VALUES QEAO!St3)N,OP QEA0(5 2) (X(T) 'f=l l6) QEA0(5e2l (XCTl T=l7t0Pl wrltecot6l w~lte<6 ~) (X(TltT ltopl ~~~ITE6,5) ~EGlN~ING OF THE COMPUTATIONS l=l 20 t\i:t SUMXT SUMXT X(Tl SUMTSQ:SU~TSO+CT*Tl SU"H=SIJ'-4T T SU~TXT:SUMTXT CT xtt>>!f<t.gt.ll> GO TO 25 T=T l GO TO 2(\ 25 A:CN Su~TXT SUMXT SUMT)/(N SUMTSQ (SU~Tl**2.> A=CSU~XT B SUMT)/~ Fllo1:A R T FOI:?CST=f!'M/3n.S REOPT:FORCST CSL+PLl SCL=~EOPT CFORCST lsel+,5 J~CT.GT.l2lGO TO 30 NEWSt..SCL 3C wrjtet6tl) FORCST.FM.~EOPT,SCLtNEwSLtERROR IrCT.GE.OPl GO TO 90 T T l Ew~O~=ERROR CFM-xT>> (FM XCT>ll J:O 40 ISSuEXCTl/4. NE~S~=NEwSL-lSSUE TO lf(newsl.gt.reopt) GO 70 L L l tr~.ge.2.> GO TO 60 SO OROR:SCL-NEWSL GO TO 70 bo NEWSL=NEwSL OROER L O 70 J J l IFCJ.GE.~.> GO TO 20 w~itec6 7>NEWSL GO TO 4t:l Figure 25. Regression analysis omputer program.

70 63 AVAILABLE DATA FROM PATRICK AFB FROM JULY 74 TO JUNE lb ' ~ ~ FORECAST FORECAST REORDER STOCK WEEKLY SUM OF PER DAY PER MNTH POINT CONTROL STOCK SQUARES LEVEL LEVEL OF ERROR o.ooo ~A 39}, o.8o , , jg , , , , , , , I 39 0, , , , ,322 Fiqure 26. Data produed by regression analysis model.

71 64 LIST OF REFERENCES Bedworth, David D. Industrial Systems-Planning, Analysis, Control. New York: Ronald Press, Brown, Robert G. Statistial Foreasting for Inventory Control. New York: MGraw-Hill, Brown, Robert G. Smoothing, Foreasting and Predition of Disrete Time.Series. Englewood Cliffs, N. J.: Prentie-Hall, Greene, James H. Prodution and Inventory Control Systems and Deisions. Homewood, Ill.: Rihard D. Irwin, Operations Researh in Prodution Plannin2, Sheduling, and Inventory Control. New York: John Wiley and Sons, Johnson, Lynwood A.,.and. Montgomery.,. Douglas.. Radhakrishnan, s. R., and Sullivan,. William. G A. Dynami Method for Foreasting." Journal of Systems Management 23 (July 1972): u.s. Air Fore. u.s. Air.Fore Supply Manual, Air Fore Manual 67-1,,Vol. V, Chapter 8, 2 Ot. 1972, Amendment 4, Setion A- "Requirements." WasJ:lington, D.C.: Government Printing Offie, u.s. Air Fore. Medial Materiel Management System (B3500), Air Fore Manual , Chapter 8, 1 Ot. 1974, 11 Requirements, Requisitions and Due Ins. ' Washington, D.C.: Government Printing Offie, u.s. Air Fore. Medial. Materiel. M.anagemen_t _ System Automati Data Proessing Systems and Proedures/ Il02C/AV, Air Fore Manual , 1 July 1974: Washington, D.C.: Government Printing Offie, 1974.