Mahmut Ali Gökçe 1 Introduction to System Engineering ISE 102 Spring 2007 Notes & Course Materials Asst. Prof. Dr. Mahmut Ali GOKCE ISE Dept. Faculty of Computer Sciences

Mahmut Ali Gökçe This Lecture Review of Week 1 Productivity Modelling Forecasting

Mahmut Ali Gökçe Review: Business Organizations Business organizations are devoted to producing good and/or providing services. Operations, Finance and Marketing are key functions of business organizations. The operation function consist of all activities directly related to producing good and services. Manufacturing and Service systems have many operational decisions in common.  Forecasting  Locations selection  Scheduling  etc. Hence we don’t limit our selves to only manufacturing systems.

Mahmut Ali Gökçe Our Job The design, operation, and improvement of the production systems that create the firm ’ s products or services.

Mahmut Ali Gökçe Recall: Decision Making System Design -Capacity -Location -Arrangement of departments -Product and Service Planning -Acquisition and planning of equipment System Operation -Personnel -Inventory -Scheduling -Project Management -Quality Assurance + System Improvement!

Mahmut Ali Gökçe Review: Value Adding Process Value Adding (Transformation) Process Value Adding (Transformation) Process Product Service Workforce Knowledge Capital Material Inputs Outputs

Mahmut Ali Gökçe Added Value at Operational Level The aim of the business organization should be to add value at each component of the production system. All non-value adding operations need to be carefully screened and eliminated. A non-value adding operation is an operation that does not add value directly transferable to the customer, i.e., if it is eliminated, the benefit accrued by the customer from the product does not diminish. How do we measure the performance of the system?  One of the measures is productivity.

Mahmut Ali Gökçe Some Definitions: Productivity Productivity is a measure of the effective use of resources, defined as the ratio of output to input. Kinds of Productivity:  Factor productivity (output is related to one or more of the resources of production, such as labour, capital, land, raw material, etc.)  Total factor productivity (an overall measure expressing the contribution of the resources of production to the efficiency attained by a firm.)  Both types of productivity can be expressed as physical productivity with output being measured in physical units and as well as value productivity with output being measured in monetary units.

Mahmut Ali Gökçe Productivity Factor productivity  Partial measures output/(single input)  Multi-factor measures output/(multiple inputs) Total factor productivity  Total measure output/(total inputs)

Mahmut Ali Gökçe Measures of Productivity Partial Output Output Output Output measures Labor Machine Capital Energy Multifactor Output Output measures Labor + Machine Labor + Capital + Energy Total Goods or Services Produced measure All inputs used to produce them

Mahmut Ali Gökçe Units of output per kilowatt-hour Dollar value of output per kilowatt-hour Energy Productivity Units of output per dollar input Dollar value of output per dollar input Capital Productivity Units of output per machine hour machine hour Machine Productivity Units of output per labor hour Units of output per shift Value-added per labor hour Labor Productivity Examples of Partial Productivity Measures

Mahmut Ali Gökçe How to use “Productivity”? Productivity measures can be used to track performance over time. This allows managers to judge performance and and to decide where improvements are needed.  If productivity has slipped in a certain area examine the factors and determine the reasons Productivity also can be used to benchmark the companies standing with respect to competitors.  How to position the company with respect to the “best in the classroom”. Determine the areas the company is behind and take actions accordingly.

Mahmut Ali Gökçe Example: Productivity 10,000 Units Produced Sold for $10/unit 500 labor hours Labor rate: $9/hr Cost of raw material: $5,000 Cost of purchased material: $25,000 What is the labor productivity?

Mahmut Ali Gökçe 10,000 units/500hrs = 20 units/hour or we can arrive at a unitless figure (10,000 unit* $10/unit)/(500hrs* $9/hr) = Example: Labor Productivity

Mahmut Ali Gökçe Example: Multifactor Productivity MFP =Output Labor + Materials MFP =(10,000 units)*($10) (500)*($9) + ($5000) + ($25000) MFP =2.90

Mahmut Ali Gökçe From Idea to Product Decision problems  Forecasting  Product and service design  Capacity Planning  Facilities Layout  Location  Transportation/assignment  Inventory  Aggregate Planning  Scheduling  Project Management

Mahmut Ali Gökçe From Idea to Product Methods  L.P. modelling and graphical solution  Special algorithms tailored for certain problems  Simulation  Stochastic processes  IP/NLP  Statistics  DP  …

Mahmut Ali Gökçe Problem Solving Approach of OR Problem Definition Generation of Alternatives Evaluation of Alternatives Selection of an Alternative Implementation of the Alternative

Mahmut Ali Gökçe What Is A Model ? A model is the selected abstract representation of a real situation or behaviour with suitable language or expression. Since a model is an explicit representation of reality, it is generally less complex than reality. The level of abstraction depends on the subject, the purpose, and the environment of modelling. It is important that it is sufficiently complete to approximate those aspects of reality to be investigated.

Mahmut Ali Gökçe Real World - Model World Real World Model f f -1

Mahmut Ali Gökçe Types of Models Physical models (e.g., molecular structures, ship models - scaling and relative positioning are important) Conceptual models (e.g., organizational charts, maps, circuit diagrams, relationship charts - relations among entities are important) Mathematical models (e.g., optimization models, Hooke ’ s law - range of validity is important) Simulation models (computer programs or physical models-simulators to represent reality)

Mahmut Ali Gökçe Purposes of Modelling To understand better the subject of modelling. To describe the subject of modelling. To create a means to exchange views on the subject. To predict and control the behaviour of the subject.

Mahmut Ali Gökçe Advantages of modeling a Business System Definition of business objectives, practices, structure, and constraints Definition and establishment of business parameters and costs Systematic evaluation of alternative system alternatives Quick response through sensitivity analysis

Mahmut Ali Gökçe Tradeoffs in Modeling Realism vs. Solvability Decision Support vs. Decision Making

Mahmut Ali Gökçe Operations Research :Model Types  Descriptive Models (Decision support) Statistics Simulation Queuing …  Prescriptive Models (Decision making) Optimization  Linear Programming  Nonlinear Programming  Network Flows …

Mahmut Ali Gökçe Algorithms to Solve Models An algorithm is a recipe to solve a problem. “A step-by-step problem-solving procedure, especially an established, recursive computational procedure for solving a problem in a finite number of steps.” ( )  Efficient vs. Effective  Optimal vs. Heuristic  Primal vs. Dual  Construction vs. Improvement  Alternative Generating vs. Alternative Selecting

Mahmut Ali Gökçe 27 FORECASTING

Mahmut Ali Gökçe Introduction Forecasting is to predict the future by analysis of relevant data. Forecasts are the basis (input) for a wide range of decisions in operations management and control. Forecasts are typically developed by the ‘Marketing’ function, but ‘Operations’ function is usually called on to assist in its development. Furthermore, ‘Operations’ is the major user of forecasts. One can forecast anything. We will focus on demand forecast. But techniques are there!

Mahmut Ali Gökçe Why Do We Forecast? AccountingCost/profit estimates for new products FinanceTiming and amount of cash flow and funding Human ResourcesHiring/recruiting/training activities MarketingPricing, promotion, strategy MISIT/IS systems, services OperationsSchedules, MRP,inventory planning, make-or-buy decisions Product/service designDesign of new products and services

Mahmut Ali Gökçe Assumes causal system past ==> future Forecasts are always wrong! Forecasts more accurate for groups vs. individuals – canceling effect Forecast accuracy decreases as time horizon increases I see that you will get an A this semester. Keep in Mind… ‘He who lives by the crystal ball ends up eating glass.’ An old Klingon proverb

Mahmut Ali Gökçe Types of Forecasts Judgmental - uses subjective input such as market surveys, expert opinion, etc. Time series - uses historical data assuming the future will be like the past Associative models (casual models) - uses explanatory variables to predict the future, demand for paint might be related to variables such as price, quality, etc.

Mahmut Ali Gökçe Judgmental Forecasts There may not be enough time to gather data and analyze quantitative data or no data at all. Expert Judgment – managers(marketing,operations,finance,etc.)  Be careful about who you call an “expert” Sales force composite  Recent experience may influence their perceptions Consumer surveys  Requires considerable amount of knowledge and skill Opinions of managers and staff  Delphi method: a series of questionnaire, responses are kept anonymous, new questionnaires are developed based on earlier results – Rand corporation (1948)

Mahmut Ali Gökçe Time Series Model Building A time-series is a time ordered sequence of observations taken at regular intervals over a period of time. The data may be demand, earnings, profit, accidents, consumer price index,etc. The assumption is future values of the series can be estimated from past values One need to identify the underlying behavior of the series - pattern of the data

Mahmut Ali Gökçe Some Behaviors Typically Observed Trend  E.g., population shifts, change in income. Usually a long-term movement in data Seasonality  Fairly regular variations, e.g., Friday nights in restaurants, new year in shopping malls, rush hour traffic., etc. Cycles  Wavelike variations lasting more than a year, e.g. economic recessions, etc. Irregular variations  Caused by unusual circumstances, e.g., strikes, weather conditions, etc. Random variations  Residual variations after all other behaviors are accounted for. Caused by chance

Mahmut Ali Gökçe Forecast Variations Trend Irregular variation Seasonal variations Cycles Trend with seasonal pattern

Mahmut Ali Gökçe Types of Time Series Models We will cover the following techniques in this section; Naïve Techniques for averaging  Moving average  Weighted moving average  Exponential smoothing Techniques for trend  Linear equations  Trend adjusted exponential smoothing Techniques for seasonality Techniques for Cycles

Mahmut Ali Gökçe Naive Forecasts Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell....

Mahmut Ali Gökçe Simple and widely used technique. A single previous value of a time series as the basis for forecast. Virtually no cost. Data analysis is nonexistent, easily understandable Cannot provide high accuracy, may be used as a standard for accuracy. Can be used in case of,  Stable series  Series with seasonality  Series with trend Naïve Forecasts

Mahmut Ali Gökçe A i : Actual value in period i F t : Forecast for time period t Stable time series data; last data becomes the forecast for the next period  F t = A (t-1) Seasonal variations; forecast for this season will be the value of last season.  F t = A (t-1) Data with trends: forecast is last value plus or minus the difference between the last two values of the series.  F t = A (t-1) + (A (t-1) – A (t-2) ) Uses for Naïve Forecasts

Mahmut Ali Gökçe Random Variations Demand t Actual Naïve Forecast t Average Smoothing may reduce the errors!

Mahmut Ali Gökçe Techniques for Averaging Inherent in the data taken over time is some form of random variation. There exist methods for reducing of cancelling the effect due to random variation. An often-used technique in industry is "smoothing". This technique, when properly applied, reveals more clearly the underlying trend, seasonal and cyclic components.  Moving average  Weighted moving average  Exponential smoothing

Mahmut Ali Gökçe Simple Moving Average A moving average forecast uses number of the most recent actual data values in generating a forecast. F t = average(A t-n, A t-n+1, …, A t-1 ) where n is the window size (number of data points used in the moving average. Example: Suppose monthly sales data for the past 5 months was 42 – 40 – 43 – 40 – 41. What would be your forecast for the 6th month sales by using MA with n=3 ? F 6 = average(A 6-3,A 6-3+1, A 6-1 )=average(A 3,A 4,A 5 ) = ( )/3 = What would your estimate be if you used naïve approach?

Mahmut Ali Gökçe Simple Moving Average - Example PeriodActualMA3MA Consider the following data, Starting from 4 th period one can start forecasting by using MA3. Same is true for MA5 after the 6 th period. Actual versus predicted(forecasted) graphs are as follows;

Mahmut Ali Gökçe Simple Moving Average - Example Actual MA3 MA5

Mahmut Ali Gökçe Weighted Moving Average A weighted moving average forecast is a weighted average of a number of the most recent actual data values. F t = w 1 *A t-n + w 2 * A t-n+1 + … w n * A t-1,where n is the window size and w 1 + w 2 + … + w n =1 Good thing is you can give more importance to more recent data. Problem is identifying the weights, which is usually achieved by trial and error. Suppose monthly sales data for the past 5 months was 42 – 40 – 43 – 40 – 41. What would be your forecast for the 6th month sales by using WMA with n=3 and w 1 =0.2, w 2 =0.3, w 3 =0.5 F 6 =0.2*43+0.3*40+0.5*41= 41.1

Mahmut Ali Gökçe Exponential Smoothing Exponential smoothing is a sophisticated weighted average. Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast and the actual value of the series at that point. It is similar to a feedback controller. Next forecast = Previous forecast +  (Actual -Previous forecast ) F t = F t-1 +  (A t-1 - F t-1 ) where  is the smoothing constant. Suppose monthly sales data for the past 5 months was 42 – 40 – 43 – 40 – 41. What would be your forecast for the 2nd month sales by using ES with  =0.1 ? What about 3th month? F 2 =42 no data available. Check the actual. It’s 40. Difference is -2. F 3 = F * -2 = 41.8.

Mahmut Ali Gökçe Example of Exponential Smoothing

Mahmut Ali Gökçe Picking a Smoothing Constant .1 .4 Actual Lower values of  are preferred when the underlying trend is stable and higher values of  are preferred when it is susceptible to change. Note that if  is low your next forecast highly depends on your previous ones and feedback is less effective.

Mahmut Ali Gökçe Techniques For Trends Develop an equation that will suitably describe the trend. Trend may be linear or it may not. We will focus on linear trends. Some common nonlinear trends. Parabolic Exponential Growth

Mahmut Ali Gökçe Linear Trend Equation - Notation b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope. A linear trend equation has the form; Y t = a + bt t Y y t =Forecast for period t, a= value of y t at t=0 and b is the slope of the line.

Mahmut Ali Gökçe Insights For Calculating a and b b = n(ty) - ty nt 2 - ( t) 2 a = y - bt n    For further information refer to or any statistics book! Suppose that you think that there is a linear relation between the height (ft.) and weight (pounds) of humans. You collected data and want to fit a linear line to this data. Weight= a + b Height How do you estimate a and b?

Mahmut Ali Gökçe More Insights For Calculating a and b Demand observed for the past 11 weeks are given. We want to fit a linear line (D=a+bT) and determine a and b that minimizes the sum of the squared deviations. (Why squared?) A little bit calculus, take the partial derivatives and set it equal to 0 and solve for a and b!

Mahmut Ali Gökçe Linear Trend Equation Example

Mahmut Ali Gökçe Linear Trend Calculation Question is forecasting the sales for the 6 th period. What do you think it will be? If we fit a line to the observed sales of the last five months,

Mahmut Ali Gökçe Linear Trend Calculation y = t a= (15) 5 = b= 5 (2499)- 15(812) 5(55)- 225 = = y = *6= 181.5

Mahmut Ali Gökçe Trends Adjusted Exponential Smoothing A variation of simple Exponential Smoothing can be used when trend is observed in historical data. It is also referred as double smoothing. Note that if a series has a trend and simple smoothing is used the forecasts will all lag the trend. If data are increasing each forecast will be low! When trend exists we may improve the model by adjusting for this trend. (C.C. Holt) Trend Adjusted Forecasts (TAF) is composed of two elements: a smoothed error and a trend factor; TAF t+1 = S t + T t where S t = smoothed forecast = TAF t +  (A t – TAF t ) T t = current trend estimate= T t-1 +  (TAF t – TAF t-1 – T t-1 )

Mahmut Ali Gökçe Insights: TAES TAF t+1 = S t + T t where S t = smoothed forecast = TAF t +  (A t – TAF t ) T t = current trend estimate= T t-1 +  (TAF t – TAF t-1 – T t-1 )= (1-  T t-1 +  (TAF t – TAF t-1 ) Weighted average of last trend and last forecast error.  and  are smoothing constants to be selected by the modeler. S t is same with original ES – feedback for the forecast error is added to previous forecast with a percentage of  If there is trend ES will have a lag. We must also include this lag to our model. Hence T t is added where  T t is the trend and updated each period.

Mahmut Ali Gökçe Associative Forecasting Time is not the only factor for future demand! We have to identify the related variables that can be used to predict values of the variable of interest.  Sales of beef may be related to price and the prices of substitutes such as fish, chicken and lamb. Predictor variables - used to predict values of variable interest Simple Linear Regression - technique for fitting a line to a set of points. Simplest and widely used form of regression. Least squares line - minimizes sum of squared deviations around the line

Mahmut Ali Gökçe Time Series vs. Associative(Causal) Models Time Series Models: Causal Model Year 2004 Sales Price Population Advertising …… Casual Models: Time Series Model Year 2004 Sales Sales 2003 Sales 2002 Sales 2001 ……

Mahmut Ali Gökçe Linear Model Seems Reasonable XY Y  22 since X=10 10 ?

Mahmut Ali Gökçe Comments on Linear Regression Assumptions:  Variations around the line are random; no trend or seasonality or cycles.  Deviations around the line is normally distributed.  Predictions are being made only within the range of observations. To obtain the best results;  Always plot the data; verify that linear relationship is appropriate.  If data is time-dependent prefer time series analysis.  Identify the all necessary predictors; might use correlation as an indicator of relations.

Mahmut Ali Gökçe Measures of Forecast Accuracy Error - difference between actual value and predicted value Mean absolute deviation (MAD)  Average absolute error Mean squared error (MSE)  Average of squared error Tracking signal  Ratio of cumulative error and MAD

Mahmut Ali Gökçe MAD & MSE MAD = Actualforecast   n MSE = Actualforecast )   n (

Mahmut Ali Gökçe Tracking Signal Tracking signal = ( Actual - forecast ) MAD  Tracking signal = ( Actual - forecast) Actual - forecast   n

Mahmut Ali Gökçe Example: Improving the Accuracy Mont hs Week 1 Week 2 Week 3 Week 4 Avera ge

Mahmut Ali Gökçe Example: Improving the Accuracy Time versus sales plot of 32 weeks for the cars sold. Suppose we were at week 28 and would like to forecast the sales for 29 – 30 – 31 and 32. Let’s use ES with  =0.1 {Recall F t = F t-1 +  (A t-1 - F t-1 ) }

Mahmut Ali Gökçe Example: Improving the Accuracy We applied the formulas and predicted for weeks 29 – 30 – 31 and 32. The accuracy of the forecast in terms of MAD = 0.93 and MSE=1.23

Mahmut Ali Gökçe Example: Improving the Accuracy MonthsAverage Aggregated Sales:

Mahmut Ali Gökçe Example: Improving the Accuracy Aggregated Sales: We can now predict the 8 th month demand given the previous 7 months and weekly forecasts may be monthly averages!

Mahmut Ali Gökçe Example: Improving the Accuracy ES forecasts 6.58 average sales for the 8 th month. In this case error in terms of MAD and MSE would be as follows

Mahmut Ali Gökçe Example: Improving the Accuracy MAD = 0.75 and MSE=1.06 Note that it was MAD = 0.93 and MSE=1.23 without aggregation.

Mahmut Ali Gökçe Exponential Smoothing T3-2

Mahmut Ali Gökçe Linear Trend Equation T3-3

Mahmut Ali Gökçe Trend Adjusted Exponential Smoothing T3-4

Mahmut Ali Gökçe Simple Linear Regression T3-5

Mahmut Ali Gökçe Which Forecasting Approach to Take?

Mahmut Ali Gökçe Resources Textbooks! (MGTSC 352)