Project and Production Management

module 8: Production Planning Back to main index exitcontinue Project and Production Management Module 8 Production Planning over the Short Term Horizon Prof Arun Kanda & Prof S.G. Deshmukh, Department of Mechanical Engineering, Indian Institute of Technology, Delhi

module 8: Production Planning MODULE 8: Production Planning over the Short Term Horizon 1. Forecasting 2. The Analysis of Time Series 3. Aggregate Production Planning: Basic Concepts 4. Aggregate Production Planning: Modelling approaches 5. Illustrative Examples 6. Self Evaluation Quiz 7. Problems for Practice 8. Further exploration Back to main index exit

module 8: Production Planning Back to main index exitback to module contents 1.Forecasting

module 8: Production Planning Back to main index exitback to module contents FORECASTING Forecasting is essential for a number of planning decisions LONG TERM DECISIONS • New Product Introduction • Plant Expansion

module 8: Production Planning Back to main index exitback to module contents MEDIUM TERM DECISIONS • Aggregate Production Planning • Manpower Planning • Inventory Policy SHORT TERM DECISIONS • Production planning • Scheduling of job orders

module 8: Production Planning Back to main index exitback to module contents System Objectives PLANNING PROCESS A Forecast of Demand is an essential Input for Planning Plan of Action Demand Forecast System to be Managed • Constraints • - Budget / Space • Resources • - Men • - Equipment

module 8: Production Planning Back to main index exitback to module contents METHODS OF FORECASTING (a) Subjective or intuitive methods • Opinion polls, interviews • DELPHI (b) Methods based on averaging of past data • Moving averages • Exponential Smoothing

module 8: Production Planning Back to main index exitback to module contents (c) Regression models on historical data • Trend extrapolation (d) Causal or econometric models (e) Time - series analysis using stochastic models • Box Jenkins model

module 8: Production Planning Back to main index exitback to module contents module 8: Production Planning Back to main index exitback to module contents FORECASTING • Objective • Scientific • Free from ‘BIAS’ • Reproducible • Error Analysis Possible PREDICTION • Subjective • Intuitive • Individual BIAS • Non - Reproducible • Error Analysis Limited

module 8: Production Planning Back to main index exitback to module contents COMMONLY OBSERVED “NORMAL” DEMAND PATTERNS Constant Linear Trend D D t t

module 8: Production Planning Back to main index exitback to module contents D D Seasonal Pattern with Growth Cyclic t t

Transient Impulse module 8: Production Planning Back to main index exitback to module contents ABNORMAL DEMAND PATTERNS Sudden Fall Sudden Rise

module 8: Production Planning Back to main index exitback to module contents OPINION POLLS • Personal interviews e.g. aggregation of opinion of sales representatives to obtain sales forecast of a region • Knowledge base (experience) • Subjective bias • Questionnaire method • questionnaire design • choice of respondents • obtaining respondents • analysis and presentation of results (forecasting) • Telephonic conversation • Fast • DELPHI

module 8: Production Planning Back to main index exitback to module contents DELPHI A structured method of obtaining responses from experts. • Utilizes the vast knowledge base of experts • Eliminates subjective bias and ‘influencing’ by members through anonymity • Iterative in character with statistical summary at end of each round (Generally 3 rounds) • Consensus (or Divergent Viewpoints) usually emerge at the end of the exercise.

module 8: Production Planning Back to main index exitback to module contents Expert 1 Coordinator Expert 2 Expert n A Statistical summary can be given at end of each round • Mean • Median • Std. deviation 1990 1990 1995 2000 2005 2010 year

module 8: Production Planning Back to main index exitback to module contents DELPHI (Contd.) Round 1 Moving Towards Consensus Round 2 Round 3

module 8: Production Planning Back to main index exitback to module contents Round 1 DELPHI (Contd.) Moving Towards Divergent View Points Round 2 Round 3

module 8: Production Planning Back to main index exitback to module contents MOVING AVERAGES

module 8: Production Planning Back to main index exitback to module contents K PERIOD MA = AVERAGE OF K MOST RECENT OBSERVATIONS For instance : 3 PERIOD MA FOR MAY = Demands of Mar, Apr, May / 3 = (199 + 208 + 121) / 3 = 206.33

module 8: Production Planning Back to main index exitback to module contents CHARACTERISTICS OF MOVING AVERAGES Dt Dt t t (1) MOVING AVERAGES LAG A TREND

module 8: Production Planning Back to main index exitback to module contents Dt t (2) MOVING AVERAGES ARE OUT OF PHASE FOR CYCLIC DEMAND

module 8: Production Planning Back to main index exitback to module contents Dt t (3) MOVING AVERAGES FLATTEN PEAKS

module 8: Production Planning Back to main index exitback to module contents EXPONENTIAL SMOOTHING Ft = one period ahead forecast made at time time t Dt = actual demand for period t  = Smoothing constant (between 0 & 1) (generally chosen values tie between 0.01 and 0.3) Ft = Ft-1 +  (Dt - Ft-1)

module 8: Production Planning Back to main index exitback to module contents Ft =  Dt+(1 - ) Ft-1 =  Dt+(1 - ) [ Dt-1+(1 - )2 Ft-2 ] =…….. =  [Dt+(1 - ) Dt-1+(1 - )2 Dt-2 + ….. + (1 - )t-1 D1 + (1 - )t F0]   (1- )  (1- )2 t-2 t-1 t Weightages given to past data decline exponentially.

module 8: Production Planning Back to main index exitback to module contents MOVING AVERAGES AND EXPONENTIAL SMOOTHING (Equivalence between  & N :)  = 2 / (N+1)

230  = 0.3 220 3 Month MA Demand  = 0.1 210 200 6 Month MA 190 J F M A M J J A S O N D J Month module 8: Production Planning Back to main index exitback to module contents

module 8: Production Planning Back to main index exitback to module contents Linear dt Common Regression Functions t dt’ forecast dt actual demand (for time period t) dt’ = a + bt (parameters a, b)

module 8: Production Planning Back to main index exitback to module contents Cyclic dt t dt’ = a + u Cos (2/n)t + v Sin (2/n)t (parameters a, u, v)

dt t module 8: Production Planning Back to main index exitback to module contents Cyclic with Growth dt’ = a +bt + u Cos (2/n)t + v Sin (2/n)t (parameters a,b,u, v)

module 8: Production Planning Back to main index exitback to module contents Quadratic dt t dt’ = a +bt + ct2 (parameters a,b,c) Parameters Determined by Minimizing the Sum of Squares of errors,

module 8: Production Planning Back to main index exitback to module contents 246 232 Actual Data 230 218 REGRESSION 220 Ft = 193 + 3t (Regression Line) Demand 210 Forecast for next JAN 200 190 Month (t) J F M A M J J A S O N D J 1 2 3 4 5 6 7 8 9 10 11 12 13

module 8: Production Planning Back to main index exitback to module contents n t = 1 Standard error of estimate =  (Dt - Ft)2 Where Dt = actual demand for period t = 7.32 Ft = forecast for period t n = no. of data points f = degrees of freedom lost (2 in this case) 95 % confidence limits for forecast of next JAN ~ 232  14 (* 2 sigma) n - f

module 8: Production Planning Back to main index exitback to module contents CAUSAL MODELS Here demand is related to Causal variables • GNP • Per Capita income • Consumer Price index • ………… Demand for tyres = f (Production of new automobiles, Replacements by existing autos, Govt policy on automobiles, …..)

module 8: Production Planning Back to main index exitback to module contents Dt =  Pt +  Pt-5 +  could be a simplified causal model (Here parameters  ,,,  are estimated by regression from data) For a Causal Model to be Useful The causal variables should be • Leading • Highly correlated with the variable of interest

module 8: Production Planning Back to main index exitback to module contents TIME SERIES ANALYSIS Time series decomposed into • Trend • Seasonality • Cycle • Randomness And Forecast generated from these components

module 8: Production Planning Back to main index exitback to module contents Stochastic modelling ( Box and Jenkins) Various processes eg. • Autoregressive (AR) order p • Moving average (MA) order q • ARMA order (p,q) • ARIMA order (p,d,q) are used to fit the most appropriate model. These models are accurate (for short term demand forecasting) but highly cumbersome to develop.

module 8: Production Planning Back to main index exitback to module contents Current Data Past Data Forecast Control Forecast Generation Managerial Judgement & Experience Modified Forecast Forecasting System

module 8: Production Planning Back to main index exitback to module contents Moving Range Chart to Control Forecasts MR = | (Ft -Dt) - (Ft-1 - Dt-1) | (Moving Range) MR =  MR / (n – 1) ( There are n-1 moving ranges for n period) Upper Control Limit (UCL) = + 2.66 MR Lower Control Limit ( LML) = - 2.66 MR

module 8: Production Planning Back to main index exitback to module contents 30 30 VARIABLE TO BE PLOTTED = (Ft - Dt) 20 20 10 0 -10 -20 -30 Month (Control Chart for Example)

module 8: Production Planning Back to main index exitback to module contents SUMMARY • Importance of forecasting in planning • Various Methods of forecasting • Subjective methods like opinion polls & Delphi • Moving Averages & Exponential Smoothing • Trend extrapolation by regression • Causal models • Time series decomposition • Forecast Control

module 8: Production Planning Back to main index exitback to module contents 2. The Analysis of Time Series

CORRELATION module 8: Production Planning Back to main index exitback to module contents

module 8: Production Planning Back to main index exitback to module contents CORRELATION vs REGRESSION? • Correlation examines if there is an association between two variables, and if so to what extent. • Regression establishes an appropriate relationship between the variables Y X

module 8: Production Planning Back to main index exitback to module contents SCATTER DIAGRAM r > 0 * r < 0 * * * * * * * * * Positive correlation Negative correlation * * * r = 0 * * * * * * * * * * * * * Non-linear association No correlation

module 8: Production Planning Back to main index exitback to module contents THE CORRELATION COEFFICIENT Pearson’s correlation coefficient, r = (1/n) Sum [(X- X) (Y-Y)] sigma X sigma Y (The numerator is the Co-variance between X and Y)

module 8: Production Planning Back to main index exitback to module contents METHODS OF COMPUTATION • Direct computations using the formula • Cumbersome and lengthy computations • Short-cut or the U-V method • Involves any conveniently assumed mean • Suitable scaling of variables

module 8: Production Planning Back to main index exitback to module contents S. No. X Y x= X-X y= Y-Y x2 y2 xy 1 50 700 21 274 441 75,076 5,754 2 50 650 21 274 441 50,176 4,704 3 50 600 21 174 441 30,276 3,654 4 40 500 11 74 121 5,476 814 5 30 450 1 24 1 576 24 6 20 400 -9 -26 81 676 234 7 20 300 -9 -126 81 15,876 1,134 8 15 250 -14 -176 196 30,976 2,464 9 10 210 -19 -216 361 46,656 4,104 10 5 200 -24 -226 576 51,076 5,424 Total 290 4260 0 0 2,740 3,06,840 28,310 Advertisement expenditure (X) vs Sales (Y) figures for 10 years in Lacs of Rupees.

module 8: Production Planning Back to main index exitback to module contents X = 290/10 = 29 : Y = 4260/10 =426 r = Σxy /[ Σx2Σy2]1/2 = 28310/ (2740 * 306840)1/2 = 0.976 Coefficient of Determination = r2 = 0.953

Y = f(X) module 8: Production Planning Back to main index exitback to module contents WHAT IS REGRESSION? • Discovering how a dependent variable (Y) is related to one or more independent variables (X) Y X

Y = f(X) module 8: Production Planning Back to main index exitback to module contents CRITERION FOR BEST FIT? Mean error Minimize ? Mean absolute error Sum of Squares of Errors Positive error Negative error Least Squares Criterion is the generally preferred criterion

Project and Production Management