Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Supporting Slides X Systems for Planning & Control in Manufacturing: Systems and Management for Competitive Manufacture Professor David K Harrison Glasgow Caledonian University Dr David J Petty The University of Manchester Institute of Science and Technology ISBN 0 7506 49771 0000 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Overview 10 Qualitative Analysis Quantitative Analysis Management Science Operations Research Analysis is defined as the breaking down of systems into their constituent parts. There are two ways in which this can be accomplished:- Qualitative Analysis. This is characterised by the description of a system in non-numerical terms. A simple case of qualitative analysis would be the description of an individual as tall or short. Qualitative analysis therefore, often involves judgement on the part of the analyst. Quantitative Analysis. This is characterised by describing a system in numerical terms. For example, a person’s height might be measured as 1.80m. Note that this is an objective measurement, rather than a subjective judgement. In some texts, quantitative analysis is referred to as operations research or management science. One of the critical skills required by manufacturing managers is the ability to make decisions. This part of the book will review some of the tools that can be applied to assist in the decision making process. It should be noted, however, that while quantitative analysis techniques can be extremely valuable, the results will always need to be tempered by the experience and judgement of the manager concerned. The quantitative analysis can be represented as shown on the next slide. 1001 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

The Quantitative Analysis Process Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) The Quantitative Analysis Process 10 Define Problem Formulate a Clear and Unambiguous Statement of the Problem Develop Model Models can take several forms Acquire Data Accurate Input Data is Essential Develop Solution Algebraic or Numerical Solution Test Solution Validation See Figure 10.1 in Book (Modified Form). <ANIMATION> Define Problem. By the nature of quantitative analysis, it is essential to formulate a clear and unambiguous statement of the problem <Clk>. Develop Model. Models can take several forms (e.g., physical or schematic models are commonly used in engineering). This section, however, will focus principally on logical or mathematical models <Clk>. Acquire Data. It is crucial that accurate input data is obtained <Clk>. Develop Solution. Once the data has been entered into the model, it is possible to develop an optimal solution. This may be achieved in essentially two ways:- Algebraic Solution. Here, the model consists of one or more equations that are solved to provide an answer. Numerical Solution. In this case, a variety of alternatives are tested until a viable answer is produced. In manufacturing, a common example of this case is discrete event simulation. It is common for computers to be applied in complex cases <Clk>. Test Solution. Before implementing the results of analysis, it is important to verify the validity of the model and input data. It is essential to check that the answers given are consistent with the problem overall <Clk>. Analyse Results. The next stage is to determine the implicationss <Clk>. Implement Results. The final stage is to take the results from the model and implement them within the organisation. Again, this be difficult in practice. Analyse Results Implications Implement Results 1002 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Basic Probability - Definitions Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Basic Probability - Definitions 10 Basic Rules Draw a Card ME CE and Mutually Exclusive Basic Rules. There are two basic rules of probability. Probabilities lie in the range 0 – 1. The sum of all possible outcomes is equal to 1. Note: P(e)i is the probability of an event. Crucial to probability theory are the concepts of trials and events. An example of a trial is drawing a card from a shuffled 52-card deck. There are a number of events that can be tested, however. For example, the probability of drawing a diamond is 1/4 (0.25) and a seven 1/13 (0.077). When considering events, two concepts are important:- Mutually exclusive events. In this case, only one of the events can occur in any trial. For example, drawing a club and diamond is mutually exclusive: a card cannot be both a club and a diamond. On the other hand, drawing a seven and a diamond is not: the card could be the seven of diamonds. Collectively Exhaustive Events. Here, the events represent all of the possible outcomes. For example, drawing a face and a number card is collectively exhaustive: a card must be one of the two alternatives. Drawing a black card and a spade is not collectively exhaustive as in the case of drawing the three of clubs. Face and Number Events King and 7 7 and Collectively Exhaustive and , , Black and 1003 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Basic Probability - Law of Addition - 1 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Basic Probability - Law of Addition - 1 10 Take a Standard 52 Card Deck (No Jokers) Draw a Card and Write Down Result Replace Card Draw a Second Card and Write Down Result What are the Probabilities of Drawing:- a) A Heart or a Diamond? b) A Five or a Diamond? Imagine that you draw a card from a standard deck (no jokers) and write down the result. You then replace the card and shuffle the deck. You then draw another card and again write down the result. Consider the examples below:- a) Adding Mutually Exclusive Events. What are the chances of drawing a diamond or a heart? b) Adding Non Mutually Exclusive Events. What are the chances of drawing a diamond or a heart? The answer is explained on the next slide. ? ? 1004 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Basic Probability - Law of Addition - 2 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Basic Probability - Law of Addition - 2 10 Adding Mutually Exclusive Events A B Adding Non Mutually Exclusive Events In the first case, the events are mutually exclusive (a card cannot be both a diamond and a heart). Therefore the probability of drawing a heart or a diamond is the sum of the two individual probabilities (13/52+13/52). In the second case, however, . At first glance, the probability of the either of these two occurring is 13/52 + 4/52. This fails to take into account the fact that one card is included in both cases (the five of diamonds) and is counted twice. Therefore the correct expression is 13/52+4/52-1/52. A B 1005 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Basic Probability - Independence Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Basic Probability - Independence 10 Marginal or Simple Probability Joint Probability Independent Events a b It can be seen from the previous discussion that the number of possible ways a particular event can occur divided by the total number of possible outcomes gives the probability of any event occurring. Thus if a coin is tossed, there is only one way of getting a head. The total number of possibilities, however, is two (heads or tails). Thus the probability of getting a head is 1/2. This is described as marginal or simple probability. In a series of trials of tossing a coin, the outcomes are independent. That is to say, one throw does not affect any other. This is often misunderstood. The so-called gambler's fallacy is that if a large number of heads occur, then the next throw is more likely to be a tail to "even-out the luck". This is not true: over time, the number of heads and tails will even out, but only because of the increasing number of trials. It is not because of any influence between one event and another. Consider now the joint probability of two independent events a and b as in tossing two coins and getting two heads. By intuition, the probability is 1/2 x 1/2 = 1/4. a Conditional Probability Then b 1006 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Statistically Dependent Events Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Statistically Dependent Events 10 If a red ball is drawn, what is the probability that it will have a spot? 30 Blue 10 Spot 20 Plain 30 Red 6 Spot 24 Plain Bayes Theorem If the two events are not independent, the situation is more complex. Consider the case in the slide. There are a total of 60 balls, 30 blue and 30 red. The 30 blue balls have 10 with a spot and 20 without. The 30 red balls have 6 with a spot and 24 without. The probabilities of individual events are shown at the top of the slot. These can be found easily. The more complex question, however, is as follows:- If a red ball is drawn, what is the probability that it will have a spot? Bayes Theorem can answer this question. This can be expressed mathematically as shown on the slide. NOT Independent 1007 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Probability Trees 10 1 2 3 4 HHH (0.125) H HHHH (0.0625) HH (0.25) H T HHHT (0.0625) H HHT (0.125) H HHTH (0.0625) H (0.5) T T HHTT (0.0625) H HTH (0.125) H HTHH (0.0625) H T HTHT (0.0625) T HTT (0.125) H HTTH (0.0625) HT (0.25) T T HTTT (0.0625) THH (0.125) H THHH (0.0625) TH (0.25) H T THHT (0.0625) H THT (0.125) H THTH (0.0625) 1 2 3 4 T T THTT (0.0625) See Figure 10.2 in Book. This slide introduces the concept of probability distributions. Consider the example of tossing four coins. if a head is worth 1 and a tail 0, then there is only one way to score 4 (HHHH) hence a probability of 1/16. Similarly, there is only one way to score 0 (TTTT). There are six ways, however, to score 2 (HHTT, HTHT, THTH, THHT, HTTH and TTHH) hence a probability of 6/16. If the score is plotted against probability, a probability distribution is produced as shown to the right and also on the next slide. The concept of a probability distribution is extremely valuable. It allows the probability of a particular outcome to be determined without the need to generate the probability tree. T TTH (0.125) H TTHH (0.0625) T (0.5) H T TTHT (0.0625) T TTT (0.125) H TTTH (0.0625) TT (0.25) T T TTTT (0.0625) 1 4 6 4 1 1008 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Probability Distributions Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Probability Distributions 10 Throwing Four Coins Throwing a Die 0.2 0.15 0.3 Probability P(x) 0.1 Probability P(x) 0.2 0.1 0.05 See Figure 10.3 in Book. This slide shows two probability distributions – one for tossing four coins (as shown on the previous slide). This is a binomial distribution. The distribution on the right is a flat distribution. This might be obtained from throwing a die. 1 2 3 4 1 2 3 4 5 6 Score x Score x 1009 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

The Normal Distribution Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) The Normal Distribution 10 M x1 x2 See Figure 10.2 in Book. There are a number of standard probability distributions. The one depicted in this slide is the commonest type of distribution; the Normal or Gaussian distribution. Unlike the binomial distribution, it can be applied to continuous rather than discrete variables. The shape of the curve is given by the formula shown on the slide. The area under the curve gives the probability of a particular outcome lying between two values x1 and x2. 1010 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Statistical Formulae 10 This slide shows some of the key statistical formulae. 1011 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Forecasting - Overview Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Forecasting - Overview 11 To Provide Information To Anticipate Changes Rationale Forecasting is required at a number of levels in manufacturing organisations. Essentially, forecasting has two purposes. First, to provide general information to support decision-making. Second, to anticipate changes so that appropriate action can be taken. Forecasting is required over a range of time-periods. Normally, short term forecasts are detailed. Long term forecasts, however, are typically more general. Short Term. Short-term forecasts are typically highly detailed. For example, a retail organisation will need to forecast sales for each stocked item to facilitate effective replenishment. In many cases, short-term forecasts will be generated automatically (for example, by exponential smoothing). Medium Term. Medium-term forecasts are less detailed. Taking the example of a retailer, it may be necessary to forecast future consumer trends so new items can be introduced. These forecasts are less detailed, but will require greater management attention (for example, to identify new suppliers). Long Term. Long-term forecasts are concerned with important trends in the relatively distant future. For example, a retail organisation will need to forecast consumer behaviour over the long term to plan the building of new stores. Short Medium Long 1101 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Forecasting Approaches Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Forecasting Approaches 11 Forecasting Intuition Extrapolation Prediction There are three basic methods of forecasting; intuition, extrapolation and prediction. The points at the bottom of the slide form the basis of this part of the course. Intuition. Here, a forecast is made subjectively by an individual or a group of individuals. Example: a person might guess what the weather will be like based on no particular, specific evidence. Extrapolation. In this case, the forecast is based purely on past events. Extrapolation assumes that the future can be forecast from the past. Example: we might assume that if it has been raining for the last three days, it will rain tomorrow. Prediction. Finally, prediction uses events in the present to forecast the future. For example, the rate of change of pressure in a barometer gives an indication of future weather patterns. Judgement Conference Survey Delphi Graphical Moving Average Exponential Smoothing Regression Multiple Regression 1102 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Intuitive Forecasting Approaches Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Intuitive Forecasting Approaches 11 Judgment Conference Survey Delphi The Opinion of One Person The Collective Opinion of a group of People Collecting the Independent Opinion of Several People Judgement. Here, the forecast is produced by one person in isolation. This approach has the disadvantage of drawing on the experience of only a single person. Conference. Here, a group of people make a decision collectively. The disadvantage of this approach is that one strong individual may dominate the group and in fact, only a single person has really made the forecast. Survey. Here, a group of people make a forecast independently and then someone reviews their opinions (typically, the forecasts are averaged). The disadvantage with this approach is that there is no opportunity for discussion and sharing of ideas and information. Delphi. The Delphi technique combines the conference and survey approaches. First, people are asked to make their forecasts independently. People write down their forecasts without discussion. The results are then shared within the group and this forms the basis for discussion. Eventually, the forecast is arrived at by consensus. Combining the Conference and Survey Approaches 1103 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Forecasting Exercise (1) Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Forecasting Exercise (1) 11 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2001 105 100 106 105 100 108 107 106 113 109 113 112 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Show this slide to the students. Invite them to forecast the sales for December 2002. Ask them how they came to their conclusion. 2002 114 118 116 115 114 117 116 122 120 122 121 125 1104 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Forecasting Exercise (2) Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Forecasting Exercise (2) 11 December 2002 Sales - 125 <ANIMATION> There is no right or wrong answer to this question. Forecasts are inherently uncertain. It is reasonable, however, to base the forecast on past data. In this case, there is clearly a rising trend and any forecast in the region of 125 is not bad. <Clk> to make the “answer” appear. 1105 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Analytical Extrapolation Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Analytical Extrapolation 11 Moving Average Exponential Smoothing Forecast for next period is the average of previous n data points n = Number of data points k = Number of points used to average xi = Data element F(i+1) = Forecast for next period.  = Smoothing factor Advantage Simple Forecast is a weighted average (most recent is most important) of all data points Advantage Logical Only two data elements needed See Figure 11.1 in Book. Extrapolation is an analytical approach to forecasting. The fundamental premise is that the future can be forecast by an examination of the past. Extrapolation is therefore based on previous events for a single variable. The simplest method is graphical: that is to say past data is plotted on a graph and a forecast generated by inspection. A simple, analytical method is the moving average. For example, a company might average the last ten weeks sales to forecast sales for next week. A more elegant approach is exponential smoothing. This is a weighted moving average where the most recent data elements are judged to be more influential. This is defined mathematically on the slide. If we were forecasting sales, exponential smoothing would work as follows. Imagine we are at the end of June and are forecasting sales for July. We would know the forecast and the actual sales for June. If the forecast for June was pessimistic (as is the case in the diagram), we would increase the next forecast by the amount shown on the slide. While Exponential smoothing is more complex than the moving average method it has two advantages:- Logical. First, it is logical in that it values recent data values more significantly than one from the distant past (a ten week moving average views last weeks data as being equally as important as data from ten weeks ago). Only Two Data Elements Needed. A ten week moving average requires ten data elements to be stored. Exponential smoothing only requires the current forecast and the current value to calculate the new forecast. In the early days of computing, this advantage was very significant, though less so today. Move up by 1106 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Exponential Smoothing - 1 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Exponential Smoothing - 1 11 See Figure 11.2 in Book and Spreadsheet 11-01.XLS. The basic premise of exponential smoothing is that the forecast will move toward the actual data element from the previous forecast value. To provide an element of smoothing, however, this movement is attenuated by the factor alpha. Large values of alpha will cause the forecast to be erratic and impractical to apply. This slide shows how exponential smoothing copes with a demand pattern that is erratic (I.e., subject to random variation). 1107 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Exponential Smoothing - 2 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Exponential Smoothing - 2 11 Trend See Figure 11.3 in Book and Spreadsheet 11-01.XLS. Smoothing factors are normally set in the range 0.1 to 0.3. The greater the smoothing factors, the more erratic the forecast. If alpha is set to unity, the forecast will simply track the demand, lagging by one period. If alpha is set to 0, the forecast will remain at a constant value. The graph in the slide shows how the exponential smoothing technique copes with rising demand. Note that the forecast does not “catch-up” with the rising demand. A later slide will show how this problem can be addressed. 1108 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Exponential Smoothing - 3 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Exponential Smoothing - 3 11 Seasonal See Figure 11.4 in Book. On the previous slide, it was shown that simple smoothing approaches are vulnerable to trend as the forecast lags the demand. Similarly, exponential smoothing approaches are also vulnerable to seasonality for the same reason. 1109 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Exponential Smoothing - 4 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Exponential Smoothing - 4 11 Combined See Spreadsheet 11-01.XLS. This slide shows how exponential smoothing copes with a demand pattern that has random, trend and seasonality effects. 1110 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Trend Correction 11 1st Order Smoothing 2nd Order Smoothing See Figures 11.1 and 11.4 in Book. As stated above, however, simple exponential smoothing is limited when dealing with data with an in-built trend. Second-order exponential smoothing can be applied more effectively in these cases. This approach examines the data for underlying trend and modifies the forecast accordingly. In effect, second order exponential smoothing “anticipates” trend. The principals of second order smoothing are shown on the right of the slide. The following stages need to be followed:- 1. Calculate the forecast for the next period, F(i+1) using the first order exponential smoothing approach (Eq A). 2. Calculate the trend adjustment for the next period, T(i+1), using Eq B. Note that beta is the second order smoothing factor. 3. Add the trend adjustment to the forecast F(i+1) as shown in Eq C. Typically, beta lies between 0.1 and 0.3. Second order smoothing is sometimes called trend correction. Second Order Smoothing Correction “Anticipates” Changes in the Data. Also Called Trend Correction 1111 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Second Order Smoothing - 1 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Second Order Smoothing - 1 11 Random Random See Spreadsheet 11-01.XLS. This slide compares first and second order exponential smoothing for a random demand (no trend or seasonality). Note that there is virtually no difference in the performance of the two methods. 1112 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Second Order Smoothing - 2 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Second Order Smoothing - 2 11 Trend Trend See Figure 11.5 in Book and Spreadsheet 11-01.XLS. Note that in the example, the corrected (second order) forecast does converge with the rising demand. Note that second order smoothing outperforms first order smoothing in this case. 1113 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Second Order Smoothing - 3 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Second Order Smoothing - 3 11 Seasonal See Figure 11.5 in Book and Spreadsheet 11-01.XLS. Second order smoothing is less effective when dealing with seasonal trends (see slide). Techniques are available for seasonal correction, though these are beyond the scope of this book. Note that there is little difference in the performance of the first and second order smoothing in this case. 1114 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Second Order Smoothing - 4 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Second Order Smoothing - 4 11 Combined Combined See Spreadsheet 11-01.XLS. This slide compares first and second order exponential smoothing for a mixed demand pattern comparing random, trend and seasonal effects. Note that second order smoothing does perform better than first order smoothing. 1115 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Regression Analysis - 1 11 Student Attendance vs Student Marks Aftermarket Disc Brake Pads Sales + 5 Yrs vs Car Sales Now ? Is There a Correlation Between Students Marks and Attendance? Is There a Correlation Between Car Sales Now and Demand for DBPs in 5 Years? See Figure 11.6 in Book. Prediction is an assessment of the future based on a number of variables. Unlike extrapolation, prediction examines present conditions to forecast the future. For example, there is a relationship between the average cost of houses in the future and present interest rates. Prediction therefore depends on understanding the relationship between different variables. Consider the graph on the left. This shows the final module marks of a group of students plotted against their attendance at classes. Two obvious questions present themselves. First, is there a correlation between attendance and good performance? Second, if there is a relationship between performance and attendance, how can this be quantified? This problem can be solved by regression analysis. An example of an industrial problem is shown on the right. When cars have reached a certain age (say five years), they start to require spare parts to be fitted. For this reason, a company making Disc Brake Pads (DBPs) as spares might get a better long term (five-year) forecast by looking at the sales of cars five years today, rather than simply considering the past sales of DBPs. There could well be a correlation between car sales now and the demand for DBPs in five years. To take advantage of this forecasting approach, regression analysis would also be required. 1116 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Regression Analysis - 2 11 y What Line Will Minimise Total Distance? (x3, y3) (d4) (d3) (x4, y4) y=a+bx (x1, y1) (d2) (d1) (x2, y2) See Figure 11.7 in Book. The basic theory is illustrated in the graph on the right of the slide. If there is a scatter of points, (xi, yi), the purpose of regression analysis is to find the best line, y = a + bx. The derivation of the basic equations is beyond the scope of this book, however, it can be shown that the gradient of the line, b, that minimises the total distance of the points from the line (in this case d1+d2+d3+d4) is given by Eq A1 (Eq A2 is the same equation but in simpler form). The intercept of the line, a, is given by Eq B. a x 1117 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Regression Analysis – 3 11 See Figure 11.7 and Table 11.1 in Book and Spreadsheet 11-02.XLS. To understand the technique (sometimes also called Least Squares), consider the table on the left of the slide. This shows the base data used to plot the graph at the bottom right of the slide and also the values required to be substituted into Eq A2. Substituting these values, the values of a and b can be calculated. The parameters have been used to plot the line of best fit on the graph. 1118 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Use of Regression Analysis Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Use of Regression Analysis 11 Inside the company Inside the Industry Outside the Industry When considering prediction in manufacturing forecasting, correlation can arise in three ways:- Inside the company. In this case, statistical information from one business area is used in another. The commonest example of this is the forecasting of spares demand. For automotive components, demand for Aftermarket items is related to the number of items sold as Original Equipment in the past. Inside the Industry. Here, statistical information of the general manufacturing sector can be used. For example in the automotive manufacturing components sector, the number of Aftermarket items sold is related to the number of new vehicles sold in the past. Outside the Industry. This normally refers to the influence of general economic conditions to the product demand. For example, large car sales are significantly influenced by oil prices. 1119 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Correlation Coefficients Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Correlation Coefficients 11 Positive Correlation 0 < r < 1 Perfect Positive r =+1 No Correlation See Figure 11.9 in Book. It is possible to measure the degree of fit when a best line has been calculated using the equation on the slide. The calculated value of r has five interpretations:- r =1. Here, the fit is perfect positive. This means as x increases, so does y and that all of the data points fall on a straight line. r =-1. Here, the fit is perfect negative. This means as x increases, y decreases and that all of the data points fall on a straight line. 0 < r <1. In this case, there is a positive correlation, but all of the points do not fall onto a straight line. 0 > r > -1. In this case, there is a negative correlation, but again all of the points do not fall onto a straight line. R = 0. No correlation. These cases can be represented diagrammatically as shown in the slide. Perfect Negative r =-1 Negative Correlation 0 > r > -1 1120 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Multiple Regression Analysis Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Multiple Regression Analysis 11 Multiple Regression y=a+b1x1+b2x2 New Mark Attendance In practice, a forecasted variable may be dependent on two or more variables. For example, house prices in the near future will be influenced by many economic parameters: interest rates, levels of unemployment etc. Similarly, to forecast the mark of a student, it is sensible to consider previous marks as well as attendance as shown in the slide. Note that in this case, the outcome is not the best line through the data, but the best plane. In practice, multiple regression analysis can only be carried out using computers. Details of multiple regression are beyond the scope of this course. There are, however, computer packages (such as the Statistical Package for the Social Sciences or SPSS) that are available for multiple regression analysis. Old Mark 1121 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Improving Forecast Accuracy - 1 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Improving Forecast Accuracy - 1 11 Reduce Lead Time Aggregate Forecast All forecasts have one thing in common: they are subject to uncertainty. In practice, all companies have to acknowledge and plan around this fundamental truth. Details of how safety stocks can be used to compensate for uncertainty in demand in the context of inventory planning is presented in section 16.6 in the book. Accurate forecasts are essential for manufacturing firms. There is a limit to what can be achieved by purely statistical means. There are, however, two strategies that can be employed to improve accuracy. Reduce Lead-Time. If a forecast is made of the distant future, it is inevitable that the forecast will be inaccurate. By reducing lead times and making the organisation more responsive, forecasts only need to be made over shorter periods. Aggregate Forecast. Forecasts at a aggregated level are more accurate than those where the data is considered independently. For example, it is difficult to forecast the height of a person drawn at random from the population. It is much easier to forecast the average height of ten people drawn at random. The reason for this improved accuracy lies in statistical theory. Consider the case of four products being manufactured from a different casting. The demand variation for the four products would be directly transmitted to the demand for the castings. If the design was changed, however, such that the four items were made from a single casting, demand variation would be "damped-out". Eq A, Eq B and Eq C are equations relating to normal distribution. The example is expressed graphically in the next slide. 1122 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Improving Forecast Accuracy - 2 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Improving Forecast Accuracy - 2 11 See Figure 11.10 in Book (Error). The demand for the four individual products is shown in the lower part of the graph. The solid line at the top of the graph shows the aggregate demand. This aggregate demand represents four times the demand of the individual products. The dashed line at the top of the graph shows the normalised demand for the casting (i.e., the variation divided by four). It can be seen that the aggregate demand has less variation than any of the four components. 1123 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Forecasting Summary 11 Essential for all Businesses Three Approaches Uncertainty is Inherent Uncertainty Must be Anticipated Forecast Accuracy can be Improved Essential for all Businesses. Forecasting is important for all manufacturing businesses. Three Approaches. There are three basic methods of forecasting, all with their respective advantages. Uncertainty is Inherent. It must be recognised, however, that forecasting is subject to inherent uncertainty. Uncertainty Must be Anticipated. It is necessary, therefore, to take appropriate steps to compensate for uncertainty. Forecast Accuracy can be Improved. Finally, there are techniques for reducing forecast error by changing the nature of the problem. In business, often too much effort is expended in trying to improve forecast accuracy. There is a practical limit to the accuracy of a forecast. Sales and Marketing Departments are often made accountable for forecasts. It would be far better to focus effort on making manufacturing more responsive so the need for accurate forecasts would be diminished, If We Make this Man Accountable for the Weather, Will it make the Sun Shine? 1124 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Optimisation 12 The most favourable conditions; the best compromise between opposing tendencies; the best or most favourable. Objective Functions Basic Optimisation Linear Programming Sensitivity Analysis One of the commonest problems to be addressed in the general area of Quantitative Decision Analysis (QDA) is optimisation. An optimum is defined as follows:- The most favourable conditions; the best compromise between opposing tendencies; the best or most favourable. This section will review four different optimisation techniques that are applied in manufacturing. 1201 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Objective Functions 12 Different Objectives e.g.: Profit Cashflow Sales Strategic and Judgmental Basis for Optimisation Before discussing optimisation methods, it is necessary to introduce objective functions. This is a precise, quantitative definition of the goal of a problem. Different Objectives. Defining the objective function is the essential first step in undertaking an optimisation exercise. While this seems a simple task, the choice of an objective function is often neither obvious nor easy. In a given problem situation, there might be several legitimate objective functions:- Profit Cashflow Sales All of these are legitimate objectives for a manufacturing organisation. For example, in the long term a company may wish to maximise profits. The commonest reason that businesses fail, however, is not poor profitability, but poor cashflow. Often, companies that are essential sound simply run out of money. For this reason, under adverse trading conditions, it is not unusual for companies to adopt a strategy of maximising cashflow. This can be achieved in several ways; selling off slow moving stocks at a discount for example. This can, however, have adverse effects on profit. Alternatively, if a company is moving into a new market, it may be desirable to seize a substantial market share (i.e., maximise sales). This could be achieved by setting low selling prices. This will of course affect both profit and cashflow. Strategic and Judgmental. Setting an objective function is therefore a strategic issue based on judgement. Basis for Optimisation. Once the objective function has been established, however, the process of optimisation is analytical and quantitative. 1202 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Simple Optimisation (1) Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Simple Optimisation (1) 12 6.38 See Figure 12.1 in Book and Spreadsheet . The simplest optimisation case is that of a function of a single variable. Consider the function f(x) plotted on the slide. By inspection, the optimum lies at around x=6.4. If f(x) is an objective function, finding the optimum value in the range 0<x<10 can be determined by algebraic means. The method is to first differentiate the function to give f’(x). By setting the derivative to zero the point(s) of inflexion in the defined range can be determined by solution of the equation. Using the standard formula for a quadratic equation is shown on the slide as Eq A. By substitution, it can be seen that the optimum value in the nominated range is 6.38. 1203 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Simple Optimisation (2) Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Simple Optimisation (2) 12 Medium Resolution Low Resolution High Resolution See Figures 12.2 and 12.3 in Book. Difficulties arise, however, if the function cannot readily be differentiated. For example, consider the formula on the slide, plotted to three different resolutions. This function cannot be readily differentiated and set to zero (the chain rule needs to be applied). By inspection, however, the optimum occurs when x=5. Problems of this type can be solved numerically. That is to say that all points are evaluated and the largest value selected. By focusing on a smaller and smaller region, improved accuracy in determining the optimum can be achieved. Low Resolution. In the slide, the optimisation exercise starts in the range 0<x<10. Medium Resolution. After ascertaining that rough value, the optimisation exercise can be repeated for the range 4.5<x<5.5. High Resolution. Finally, to obtain a yet more accurate value, the exercise can be repeated for the range 4.95<x<5.05. 1204 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Optimisation - 2 Variables Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Optimisation - 2 Variables 12 (7.1, 6.7) See Figure 12.4 in Book. In principle this numerical approach can be used to solve problems with an indefinite number of variables. Consider the function of the two variables on the slide. The optimum value in the range 0<x<10, 0<y<10 can be established by homing in on the optimum point as in the single variable problem. This is shown on the 3D plot. Clearly, manual calculation is impractical in these cases and a computer must be used. Spreadsheets can be highly effective in this class of problem. 1205 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Linear Programming (1) 12 Linear Objective Function A Set of Linear Constraints Non-Negativity Another common problem is that of optimisation of variables under conditions of constraint. The mathematical space that is free of constraint is called the feasible space or feasible area. A commonly used technique used to tackle problems of this sort is linear programming. All linear programming problems have three characteristics:- Linear Objective Function. That is to say, the objective function can be expressed in simple terms in an expression of the form K=Ax+By. A Set of Linear Constraints. The constraints on the feasible space are also of the form K=Ax+By. Non-Negativity. The problem is solved in a graphical space where x>0 and y>0. Thus optimum answers may only be positive. 1206 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Linear Programming (2) 12 160 1. Power Limitation: 160 = 1.34X + Y Power Optimum Point 150 140 130 120 Machining Capacity 2. Machining Capacity: 150 = X + 1.25Y 110 100 90 80 112 = 1.6X + 1. 4Y Objective Function - Sales 3. Objective Function: Sales = 1.6X + 1.4Y 70 60 50 See Figure 12.5 in Book. <ANIMATION> Linear programming is best understood by considering a simple example. A manufacturer produces two products X and Y. X is made of cast iron and Y of an alloy. The company's objective function is sales revenue and this is defined by the expression Sales = 1.6X + 1.4Y. The implication of this expression is that the selling price of X is £1.60 and Y is £1.40. Ideally, the number of products of X and Y produced would be very large. There are however, constraints. The first is the power available to cast the products. The second is machine capacity. These constraints are given by the following expressions, 160 = 1.34X + Y (Power) and 150 = X + 1.25Y (Machining Capacity). <Clk> to show constraints. The implication of the first expression is as follows; it takes 1.34 times as such power to produce a unit of X compared to a unit of Y. 160 is a measure of the total power being available for casting. Similarly, the implication of the second expression is that it is 1.25 time more time consuming to machine alloy components (Y) than cast iron components (X). 150 is a measure of the total time available for machining. This information can be represented graphically as shown in the slide. Finding the optimum point in this simple case can be achieved by the simultaneous solution of the two constraint expressions as shown on the slide. <Clk> to show derivation. 40 30 20 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 X 1207 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Linear Programming (3) 12 Y 160 150 140 Lab Capacity 3. Labour Capacity: 130 = X + Y Power 130 120 110 1. Power Limitation: 160 = 1.34X + Y 2. Machining Capacity: 150 = X + 1.25Y 100 90 80 70 60 50 See Figure 12.6 in Book. <ANIMATION> The problem becomes far more complex, however, if additional constraints are added. Consider a third constraint of labour capacity given by 130 = X + Y. <Clk> to show constraints. This information is shown on the slide. 40 30 Machining Capacity 20 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 X 1208 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Linear Programming (4) 12 Y 160 150 140 224 = 1.6X + 1. 4Y 196 = 1.6X + 1. 4Y Objective Function: Sales = 1.6X + 1.4Y 130 1. Power Limitation: 160 = 1.34X + Y 2. Machining Capacity: 150 = X + 1.25Y 3. Labour Capacity: 130 = X + Y 120 110 100 90 80 Optimum Point Optimum: X= 50, Y = 80 70 60 50 See Figure 12.7 in Book. <ANIMATION> The three constraints define a feasible region. To find the optimum point graphically, the sales line needs to move down until it touches the feasible region. This is shown on the slide. Reading from the graph, the optimum sales value will be achieved if 50 X and 80 Y are produced. Algorithms exist to generate the optimum values (the most common being the Simplex method). These are, however, beyond the scope of this book. With a larger number of constraints, these algorithms are the only practical way of solving this type of problem. <Clk> to show objective function and optimum point. 40 30 20 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 X 1209 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Multiple Variables 12 Y Material Total Capacity Y Z Objective Function So far, only problems with two variables have been discussed. In practice, an optimisation problem may have an indefinite number of variables. These problems are difficult to visualise and still harder to solve. As before, these problems can only be solved in practice using algorithms (again, the well-known Simplex method) running on powerful computers. This slide shows a problem with three products, not two. Notice that constraints are defined by planes, not lines. Z Material X Material X 1210 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Sensitivity Analysis - 1 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Sensitivity Analysis - 1 12 Problems So Far Assume Perfect Information Sensitivity Analysis Determines Criticality of Base Data 6.38 5.95 f(x) g(x) See Figure 12.8 in Book. Problems So Far Assume Perfect Information. All of the examples used so far have assumed the information used in the analysis is accurate and deterministic. In practice, however, information is imperfect; that is to say inaccurate and stochastic. Sensitivity Analysis Determines Criticality of Base Data. It is often useful, therefore, to conduct sensitivity analysis. Sensitivity analysis involves re-examining a problem to determine what effect a change in the input variables will have on the final answer. Consider the initial function in this section. The graph shows the effect of a small change in the coefficients in the original function:- 1211 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Sensitivity Analysis - 2 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Sensitivity Analysis - 2 12 Profit Different Variables May Have Different Effects Sales Cost Costs = £1000K See Figure 12.9 in Book. There are also cases where small changes in the input parameters have a large effect. A particular case is that of profit and loss models. Profit is the difference between revenue and cost. If costs are fixed, small increases or decreases in sales will have a large effect on profit. The graph shows how Return on Sales (ROS) varies with sales volume (ROS = Profit/Sales, where Profit = sales - costs). In the example, costs are £1000K. 1212 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Sensitivity Analysis – 3 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Sensitivity Analysis – 3 12 See Figure 12.10 in Book. Other models are less critical. For example, optimum lot size models are relatively insensitive. Small changes in lot size have a minimal effect on costs as shown on the graph. By examining the model's tolerance to changes, it is possible to gain an impression of its sensitivity. In many cases, a model can be very sensitive to one parameter, but very insensitive to another. 1213 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Sensitivity Analysis – 4 Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Sensitivity Analysis – 4 12 Test the Sensitivity of the Model Itself Test the Sensitivity of the Model to Input Variables Can be Used for a Variety of Problems When undertaking a sensitivity analysis, one or both the following may be undertaken:- Test the Sensitivity of the Model Itself. Here, the analyst will investigate how sensitive the outcome of a model is with reference to its own structure. Typically, the analyst will undertake tests with a particular model. The analyst will then slightly modify the parameters governing the model and re-run the tests. By comparing the outputs from the two sets of tests (as in the comparison of f(x) and g(x) in the earlier slide), the analyst can form an impression of the sensitivity of the model. Test the Sensitivity of the Model to Input Variables. In this case, the analyst will examine the behaviour of the model over a range of operation. For example, it can be seen from the profit and loss model of the earlier slide that Return on Sales (ROS) is very sensitive to small changes in sales volume. Can be used for a Variety of Problems. Sensitivity analysis is a useful technique for optimisation problems, but it is also applicable to checking the robustness of any model. 1214 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Summary 12 Optimisation Requires an Objective Function Analytical or Numerical Methods Can be Used Sensitivity Analysis Checks the Robustness of any Model Constants Parameters Optimisation Supports, not Replaces Management Optimisation Requires an Objective Function. Optimisation is a valuable technique for the practising manager. It must be recognised, however, that it is dependent on the identification of a single objective function. Analytical or Numerical Methods Can be Used. For most practical problems, a numerical (typically computer based) method is used. Sensitivity Analysis Checks the Robustness of any Model. Sensitivity analysis can be used in two ways:- Constants. To check the sensitivity of the model itself (i.e., the constants defining the model). Parameters. To check the sensitivity of the model to the environment it is intended to model (i.e., the model’s input parameters). Optimisation Supports, not Replaces Management. In practice, a balance must be struck between conflicting and often mutually exclusive objectives. Because of this, optimisation is only a support tool for management. It cannot completely replace human judgement. 1215 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.

Speaker Notes: Systems for Planning and Control in Manufacturing Produced by and Copyright: DK Harrison and DJ Petty (2002) Course Book X Systems for Planning & Control in Manufacturing: Systems and Management for Competitive Manufacture Professor David K Harrison Dr David J Petty ISBN 0 7506 49771 0000 To be used in Conjunction with “Systems for Planning and Control in Manufacturing” by DK Harrison and DJ Petty, published by Butterworth-Heineman, ISBN 0 7506 49771.