Every manufacturer is confronted with the problem

Size: px
Start display at page:

Download "Every manufacturer is confronted with the problem"

Transcription

1 HOW MANY PARTS TO MAKE AT ONCE FORD W. HARRIS Prodction Engineer Reprinted from Factory, The Magazine of Management, Volme 10, Nmber 2, Febrary 1913, pp , 152 Interest on capital tied p in wages, material and overhead sets a maximm limit to the qantity of parts which can be profitably manfactred at one time; "set-p" costs on the job fix the minimm. Experience has shown one manager a way to determine the economical size of lots. Every manfactrer is confronted with the problem of finding the most economical qantity to manfactre in ptting throgh an order. This is a general problem and admits of a general soltion, and, however mch it may be advisable to exercise jdgment in a particlar case, sch exercise of jdgment will be assisted by a knowledge of the general soltion. The writer has seen the practical workings of a firstclass stock system and does not wish to be nderstood as claiming that any mere mathematical formla shold be depended pon entirely for determining the amont of stock that shold be carried or pt throgh on an order. This is a matter that calls, in each case, for a trained jdgment, for which there is no sbstitte. There are many other factors of even more importance than those given in this discssion. Bt in deciding on the best size of order, the man responsible shold consider all the factors that are mentioned. While it is perfectly possible to estimate closely enogh what effect these factors will have, the chances are many mistakes costing money will be made. Hence, sing the formla as a check, is at least warranted. Given the theoretically correct reslt, it is easy to apply sch correction factors as may be deemed necessary. In determining the economical size of lot the following factors are involved: Unit Cost (C). This is the cost in dollars per nit of otpt nder continos prodction, withot considering the set-p or getting-ready expense, or the cost of carrying the stock after it is made. (5"). This involves more than the cost of getting the materials and tools ready to start work on an order. It involves also, the cost of handling the order in the office and throghot the factory. This cost is often neglected in considering the qestion. Operations Research Vol. 38, No. 6, November-December 947 Most managers, indeed, have a rather hazy idea as to jst what this cost amonts to. If sch is the case an investigation will show that the cost of handling, checking, indexing and sperintending an order in the offices and shops is a considerable item and may, in a large factory, exceed one dollar per order. The set-p cost proper is generally nderstood. Indeed, shop foremen in general appreciate only too well what the cost of set-p means on small orders, and so, if left to themselves, will almost invariably pt their work throgh in large qantities to keep down this item. So doing, however, affects nfavorably the next factor. Interest and Depreciation on Stock (/). Large orders in the shop mean large deliveries to the storeroom, and large deliveries mean carrying a large stock. Carrying a large stock means a lot of money tied p and a heavy depreciation. It will here be assmed that a charge of ten per cent on stock is a fair one to cover both interest and depreciation. It is probable that doble this wold be fairer in many instances. Movement (M). It is evident that the greater the movement of the stock the larger can be the qantities manfactred on an order. This, then, is a ital factor. Manfactring Interval (7"). This is the time reqired to make p and deliver to the storeroom an order, and, while it seldom is a vital factor, it is of vale in the discssion. There is another factor, X, the nknown size of order which will be most economical. Ths smmarizing, there are the following factors in the problem: M eqals the nmber of nits sed per month (movement). C eqals the qantity cost of a nit in dollars or the nit cost X/90/ $ Operations Research Society of America

2 948 / HARRIS S eqals the set-p cost of an order in dollars. r eqals he manfactring interval in months. / eqals the nit charge for interest and depreciation on stock. X eqals the nknown size of order, or lot size, which is most economical. The manfactring interval is sefl only in that it enables s to fmd the safe stock minimm, or smallest qantity the storekeeper may allow his stock to fall to before he mst enter an order for more. At first sight this minimm qantity wold seem to inflence the amont of stock and therefore the interest charges. It does nothing of the kind, however, and it will be fond that the stock consists of additions in lots of X and a gradal exhastion of the stock to nothing. The stock minimm simply serves to notify the storekeeper when to enter an order for new stock, so that he will se p his stock clean before deliveries on the new order are made and, at the same time, never be withot stock for any considerable interval. The average stock, if the movement is reglar, it will be evident, is one-half of X. If the movement is irreglar, and it generally is, there is introdced an additional complication. This, however, can generally be neglected or applied as a correction factor to the final reslt. The average stock being X/2, the vale of this stock will evidently be C times this, or CX/2 (vale of average stock on hand). This is the qantity cost only. To it mst be added the set-p cost for the average stock. Since the set-p cost per order is S, and the average stock is half the size of an order, the set-p cost of the average stock will be S/2. The total vale of the average stock will then be V2{CX + S). The annal interest and depreciation cost at ten per cent will be one-tenth this or VioiCX+S). Now since M nits per month are sed, this will be 12M nits per year, and this interest charge mst be divided by the nmber of pieces sed in a year to get the interest charge in dollars per nit, which gives (/240M)(CX + S) eqals /. The total set-p cost for X nits being S dollars, the set-p cost per nit mst be S/X. This now gives, as the whole cost of a nit, the interest charge per piece pls the set-p cost per piece pls the nit cost per piece, or Let this smmation eqal Y. The problem then is the old one of finding the vale for X that will give the minimm vale to Y. As the soltion of this problem involves higher mathematics, sffice it to say that the vale for X that will give the minimm vale to Y, redces to the sqare root of (240MS divided by C). Now 240S/C may be calclated at once and the sqare root taken. Call this reslt K, becase it will be a constant for any case. Then X eqals K times the sqare [root] of M Now let an actal example be taken and see what the reslts will be. Sppose that an article has a movement, M, of 1,000 nits per month with a setp cost of two dollars and a nit cost of ten cents. Applying the formla, it is fond that the theoretical economical size of lot is 2,190 nits. This shows the set-p cost to be abot 0.1 cent and the interest charges abot the same amont. Referring to the Figre I a crve will be seen representing the cost per piece of set-p for varios manfactring qantities and an interest and depreciation charge nder the same conditions. The sm of these two is marked the total cost, althogh it does not inclde the nit cost of ten cents, which is not added becase assmed constant. U 03 J2 0.2 < Q a 0.1 Manfactring 1 V T- EcoDomical Lot Size, Giving Mtnlmm -1-otal Colt?< fotal Cost (Not Incldinc Unit Coil ol Article) Size of Order Crves Interest and Dfprcciailon on Siork Figre I. An increase in the size of the order reslts in an increased interest charge and a decreased set-p cost. The crves show this graphically and indicate a minimm total cost in this case at 2,200 nits. _ y

3 OR Form / 949 It shold be noted that this so-called total cost can vary between wide limits only when the manfactring qantity is selected with very poor jdgment. For example, in the case given, the least total cost possible will be abot cents at 2,190 nits on an order. This qantity can vary from 1,000 to 5,000, and the additional cost will be only abot 0.05 cent. This on an article costing ten cents, is a very small percentage. While this is tre for the vales given it is not niversally tre, and ths it is seen that the general law can be applied with some profit to the specific problems of manfactre. Some actal examples of costs may be illminating. Take, for example, the copper connector shown in Figre II. Here is an article that is being sed at the rate of 1,230 pieces a month, with a nit cost of $ per piece, and a set-p cost of $2.15. This latter cost incldes the clerical work, sperintendence, and so on, as well as the actal cost of getting ready in the shop. It is fond by applying the formla that the correct manfactring qantity is 6,850 pieces. The different vales of the cost are shown in the crves on the Article A Small Connector Material =-Copper.OOiO a ^.0006 Q C.0005 ^0004 U w Monthly Qantity - M Cost per Piece - C i.o135 S = 2.15 Mfg. Qantity =X=6850 Total Cost(Noi Incldins Unit Coil o( Article) '"-., ' Inicrcsl and Depreciation n Sinrk diagram. It will be noted that the loss is mch greater if too small a qantity is pt throgh, than it is for too large a one. For example, if this article were made in 2,200 lots, $0,001 wold have to be added to the original cost of $0.0135, which wold involve a loss of $ On the other hand, if they were pt throgh in lots of 10,000, which is abot as far the other way, there wold be a loss of only abot oneeighth of this amont. Or, in percentages, in the first case there wold be incrred an nnecessary expense of abot two per cent on the original cost, while in the latter case the loss wold have been only abot one qarter of one per cent. It shold be noted that in this case this article wold be pt throgh in lots that wold last for nearly six months. Take, as a frther example, the std shown on Figre III. Here is a piece that is sed in lots of thirty. It is an expensive piece and costs in qantity $5.65. The set-p cost is $1.85. The correct qantity is 48.5 or, say, 49. Here the least overhead for set-p and interest charges wold be $0,076 per piece. Making the article in lots of twenty, there wold be abot the same nnecessary loss as when they were made in lots Article = A Std Material = Copper Qantity per Month '^ M = 30 Cost per Piece. C Dollars, = S = 1.85 Dollars Manfactring Qantity:.X = 48.5 =.10 o Q a O U Total Cost(Not iticld'mi: Unit Cost of Arliclf) ' Interest and Depreciation on Siork V / / ^ o 240 X 30 X U Thosands of Pieces ioo Pieces on Order Figres II and III. In each of these diagrams is shown the effect of the size of the lot on the set-p and interest charges per nit. The set-p cost crves slope downward with increased size of the order while the interest crves slant pward. The sm of the two elements gives total costs the crve of which is the pper one and shows a minimm opposite where the two lower crves cross.

4 950 / HARRIS of 100, or abot three cents each. This is not a large amont, bt at the rate of consmption given, it will involve a loss of $10.80 a year, which is avoidable and, therefore, worth considering. So it is seen, the more valable the article, the more "worth while" it is to apply the formla. There are not many men who nderstand the theory nderlying the economic size of lots, and so a knowledge of it shold be of considerable vale. For example, having once determined that it is wise to pt in orders for lots of one hndred, based on a certain consmption, it is of vale to know that this consmption mst increase for fold to warrant dobling the manfactring qantities. It is frther gratifying to know that the effect on profits from an error is so small as shown by the crves. In conclsion, it may be well to say that the method given is not rigorosly accrate, for many minor factors have prposely been left ot of the consideration. It may be objected that interest and depreciation shold be figred, not only on original cost, bt also on the set-p cost, since that has to be incrred before the parts can be stocked. Sch refinements, however, while interesting, are too fine spn to be practical. The general theory as developed here is reasonably correct and will be fond to give good reslts.

5

Corporate performance: What do investors want to know? Innovate your way to clearer financial reporting

Corporate performance: What do investors want to know? Innovate your way to clearer financial reporting www.pwc.com Corporate performance: What do investors want to know? Innovate yor way to clearer financial reporting October 2014 PwC I Innovate yor way to clearer financial reporting t 1 Contents Introdction

More information

Advanced Fixed Income Callable Bonds Professor Anh Le

Advanced Fixed Income Callable Bonds Professor Anh Le 1 What are callable bonds? When you take out a fixed rate mortgage to buy a house, you usually have the option of pre paying the mortgage. The common term to use is to refinance. And people would refinance

More information

An Introduction to Regression Analysis

An Introduction to Regression Analysis The Inaugural Coase Lecture An Introduction to Regression Analysis Alan O. Sykes * Regression analysis is a statistical tool for the investigation of relationships between variables. Usually, the investigator

More information

Introduction to Linear Regression

Introduction to Linear Regression 14. Regression A. Introduction to Simple Linear Regression B. Partitioning Sums of Squares C. Standard Error of the Estimate D. Inferential Statistics for b and r E. Influential Observations F. Regression

More information

The Scattering of α and β Particles by Matter and the Structure of the Atom

The Scattering of α and β Particles by Matter and the Structure of the Atom E. Rutherford, Philos. Mag, 6, 21 1911 The Scattering of α and β Particles by Matter and the Structure of the Atom E. Rutherford University of Manchester 1 (Received April 1911) 1 It is well known that

More information

The Online Library of Liberty

The Online Library of Liberty The Online Library of Liberty A Project Of Liberty Fund, Inc. Friedrich August von Hayek, The Use of Knowledge in Society [1945] The Online Library Of Liberty Collection This E-Book (PDF format) is published

More information

The time scale of articial intelligence: Reections on social eects

The time scale of articial intelligence: Reections on social eects The time scale of articial intelligence: Reections on social eects Ray J. Solomono Visiting Professor, Computer Learning Research Center Royal Holloway, University of London Mailing Address: P.O.B. 400404,

More information

How to Choose a Leadership Pattern

How to Choose a Leadership Pattern How to Choose a Leadership Pattern by Robert Tannenbaum and Warren H. Schmidt No. 73311 MAY JUNE 1973 How to Choose a Leadership Pattern Robert Tannenbaum and Warren H. Schmidt Since its publication in

More information

Using Credit to Your Advantage.

Using Credit to Your Advantage. Using Credit to Your Advantage. Topic Overview. The Using Credit To Your Advantage topic will provide participants with all the basic information they need to understand credit what it is and how to make

More information

Variable Annuities. Information is an investor s best tool. What You Should Know WHAT YOU SHOULD KNOW 1

Variable Annuities. Information is an investor s best tool. What You Should Know WHAT YOU SHOULD KNOW 1 Variable Annuities What You Should Know Information is an investor s best tool WHAT YOU SHOULD KNOW 1 2 VARIABLE ANNUITIES Variable Annuities Variable annuities have become a part of the retirement and

More information

Why People Don't Develop Effective Corrective Actions

Why People Don't Develop Effective Corrective Actions Why People Don't Develop Effective Corrective Actions Authors Mark Paradies, Partner & President Ed Skompski, Partner System Improvements, Inc www.taproot.com 238 South Peters Road, Suite 301 865-539-2139

More information

About Insurance Europe Insurance Europe is the European insurance and reinsurance federation. Through its 34 member bodies the national insurance

About Insurance Europe Insurance Europe is the European insurance and reinsurance federation. Through its 34 member bodies the national insurance How insurance works About Insurance Europe Insurance Europe is the European insurance and reinsurance federation. Through its 34 member bodies the national insurance associations Insurance Europe represents

More information

BOARD DEVELOPMENT. Financial Responsibilities of Not-for-Profit Boards

BOARD DEVELOPMENT. Financial Responsibilities of Not-for-Profit Boards BOARD DEVELOPMENT Financial Responsibilities of Not-for-Profit Boards Board Development Financial Responsibilities of Not-for-Profit Boards A Self-Guided Workbook The Right to Copy this Workbook Permission

More information

A PROCEDURE TO DEVELOP METRICS FOR CURRENCY AND ITS APPLICATION IN CRM

A PROCEDURE TO DEVELOP METRICS FOR CURRENCY AND ITS APPLICATION IN CRM A PROCEDURE TO DEVELOP METRICS FOR CURRENCY AND ITS APPLICATION IN CRM 1 B. HEINRICH Department of Information Systems, University of Innsbruck, Austria, M. KAISER Department of Information Systems Engineering

More information

MONEY HAS NO PRICE: MARX S THEORY OF MONEY AND THE TRANSFORMATION PROBLEM. by Fred Moseley

MONEY HAS NO PRICE: MARX S THEORY OF MONEY AND THE TRANSFORMATION PROBLEM. by Fred Moseley MONEY HAS NO PRICE: MARX S THEORY OF MONEY AND THE TRANSFORMATION PROBLEM by Fred Moseley 1. Marx s basic theory of money and the transformation problem 1.1 Money has no price 1.2 Circulation of capital

More information

Financial management of not-for-profit organisations

Financial management of not-for-profit organisations Financial management of not-for-profit organisations November 2009 This guide was prepared by Jan Barned, financial management trainer, with the assistance of CPA Australia. CPA Australia wishes to acknowledge

More information

Linking Data across Agencies: States That Are Making It Work

Linking Data across Agencies: States That Are Making It Work Rasterized 300 dpi Linking Data across Agencies: States That Are Making It Work Updated March 2010 By: Rebecca Carson and Elizabeth Laird, Data Qality Campaign; Elizabeth Gaines and Thaddes Ferber, The

More information

Manual on Close-Out Procedures. Third Edition January 1985

Manual on Close-Out Procedures. Third Edition January 1985 Manual on Close-Out Procedures Third Edition January 1985 Manual on Close-Out Procedures Third Edition January 1985 Municipal Securities Rulemaking Board 1900 Duke Street, Suite 600 Alexandria, VA 22314

More information

Getting Ready to Retire: What You Need to Know About Annuities. Table of Contents

Getting Ready to Retire: What You Need to Know About Annuities. Table of Contents Getting Ready to Retire: What You Need to Know About Annuities Table of Contents A. Planning Your Retirement Income ------------------------------------------------------------------------------------------------------

More information

IP ASSETS MANAGEMENT SERIES. Successful Technology Licensing

IP ASSETS MANAGEMENT SERIES. Successful Technology Licensing IP ASSETS MANAGEMENT SERIES 1 Successful Technology Licensing 2 Successful Technology Licensing I. INTRODUCTION II. III. IV. PREPARATION FOR NEGOTIATION KEY TERMS CONDUCTING THE NEGOTIATION V. USING THE

More information

Do-it-Yourself Recovery of Unpaid Wages

Do-it-Yourself Recovery of Unpaid Wages Do-it-Yourself Recovery of Unpaid Wages How to Represent Yourself Before the California Labor Commissioner A Publication of: The Legal Aid Society-Employment Law Center 600 Harrison Street, Suite 120 San

More information

American Retirement Savings Could Be Much Better

American Retirement Savings Could Be Much Better AP Photo/Jae C. Hong American Retirement Savings Could Be Much Better By Rowland Davis and David Madland August 2013 www.americanprogress.org American Retirement Savings Could Be Much Better By Rowland

More information

Excel s Business Tools: What-If Analysis

Excel s Business Tools: What-If Analysis Excel s Business Tools: Introduction is an important aspect of planning and managing any business. Understanding the implications of changes in the factors that influence your business is crucial when

More information

How To Protect and Benefit From Your Ideas

How To Protect and Benefit From Your Ideas How To Protect and Benefit From Your Ideas FOREWORD T his book has been prepared for general use and guidance of inventors. It states the Association s best judgment as to the law of intellectual property

More information

Communication Theory of Secrecy Systems

Communication Theory of Secrecy Systems Communication Theory of Secrecy Systems By C. E. SHANNON 1 INTRODUCTION AND SUMMARY The problems of cryptography and secrecy systems furnish an interesting application of communication theory 1. In this

More information

Employee is also a customer. How to measure employees satisfaction in an enterprise?

Employee is also a customer. How to measure employees satisfaction in an enterprise? Employee is also a customer. How to measure employees satisfaction in an enterprise? Z. Kotulski, Z.Wąsik and B. Dorożko 1. Introduction A working place: factory, company, office, etc., is the place where

More information

Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.

Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing. Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative

More information

Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator

Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator This Guide is designed to offer step-by-step instruction for using your TI-83, TI-83 Plus, or TI-84 Plus graphing calculator

More information

Your pension: it s time to choose

Your pension: it s time to choose Your pension: it s time to choose Thinking about retiring Deciding how to take your retirement income Shopping around for the best income The Money Advice Service is independent and set up by government

More information

Module 8 Surveying and Setting Out

Module 8 Surveying and Setting Out Module 8 Contents: page 8.1 Selecting the Road Alignment 1 8.2 Instruments and Surveying Aids 10 8.3 Setting Out Horizontal Alignment 20 8.4 Setting Out Vertical Alignment 25 8.5 Setting Out Cross Sections

More information