22-Mec-B4 Integrated Manufacturing Systems · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2016 — 07-Mec-B4 Integrated Manufacturing Systems. Three hours, open book, any non-communicating calculator permitted. Six questions are printed; any five constitute a complete paper and only the first five appearing in the answer book are marked, each of equal value (20 marks). All six are solved here, because the complete set is the study resource. Questions 1(b)–(d) and the whole of Question 4 are essay questions, in which the examiners award marks for clarity and organisation as well as for content.
Reference texts. E. S. Buffa and R. K. Sarin, Modern Production / Operations Management, 8th ed. (inventory systems, economic order quantity, information feedback, break-even and investment analysis); A. J. Duncan, Quality Control and Industrial Statistics, 5th ed. (error of measurement, gage and inspector variability, precision and accuracy); D. C. Montgomery, Introduction to Statistical Quality Control, 8th ed. (measurement systems analysis, process capability); C. E. Ebeling, An Introduction to Reliability and Maintainability Engineering, 3rd ed. (exponential and normal life models, maintainability); R. B. Chase and F. R. Jacobs, Operations and Supply Chain Management, 16th ed. (components of demand, adaptive forecasting); S. Nahmias and T. L. Olsen, Production and Operations Analysis, 7th ed. (forecasting methods, inventory control under uncertainty); M. P. Groover, Automation, Production Systems, and Computer-Integrated Manufacturing, 5th ed. (integrated manufacturing systems, production planning).
Note on this sitting. Question 4 is reissued word for word from the May 2013 paper (its Question 1), and Question 6 is reissued word for word from the May 2014 paper (its Question 3). The full working is transcribed in place below rather than cross-referenced, so this file stands alone.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Part (a) — the common components of demand. An operations forecasting system does not try to explain a demand series in full; it decomposes the series into a small number of components, each of which behaves differently and each of which the operating system must answer in a different way. The first is the average or constant level, the underlying rate about which everything else moves; it is what sets the base capacity and the base work force. The second is trend, a persistent upward or downward drift; because it accumulates, a forecast that ignores it lags the series by an amount that grows with the horizon, so trend drives the capacity and facility decisions taken years ahead. The third is the seasonal component, a pattern that repeats over a fixed calendar period — annual for heating equipment, weekly for restaurants, daily for a call centre — and it is the component that aggregate planning exists to absorb, through inventory, overtime, hiring and subcontracting. The fourth is the cyclical component, the longer swing tied to the business cycle, whose period is not fixed and which therefore cannot be extracted by a seasonal index; it is normally handled by an external economic indicator rather than by the demand history itself. The fifth is autocorrelation, the persistence of a series in its own recent values, which is why a high week tends to be followed by a high week and why smoothing works at all. What remains is random variation, which is by definition unforecastable; the correct response to it is not a better model but a buffer — safety stock, safety lead time or reserve capacity — sized from the measured forecast error. Separating these components is what allows a single demand history to serve three planning horizons at once: the average and the trend for long-range capacity, the seasonal for the aggregate plan, and the random component for the short-term buffers.
Part (b) — the general structure of adaptive forecasting systems. An adaptive forecasting system is an ordinary forecasting model wrapped in a closed feedback loop, and the loop is what distinguishes it. The forward path is conventional: demand history feeds a model — in practice an exponentially smoothed one, since the smoothing constant gives the loop something to act on — and the model issues a forecast for the coming period. The return path is the adaptive part. When actual demand for that period arrives it is differenced against the forecast to give the error; the errors are then accumulated in two statistics, the running sum of the errors (which detects bias, because random errors cancel and systematic ones do not) and the mean absolute deviation (which measures the ordinary scatter). Their ratio is the tracking signal, and it is compared with control limits exactly as a quality characteristic is compared with control limits on a chart. While the signal stays inside its limits the model is judged to be tracking the series and nothing is changed; when it goes outside, the system concludes that the process has shifted and responds by raising the smoothing constant, so that the model discounts old data faster and catches up with the new level, then relaxes the constant again once the signal returns inside the limits. The result is a system that is sluggish and stable in quiet periods and quick and responsive after a step change — the two properties a fixed smoothing constant is forced to trade against each other. Its practical value in an operations setting is that it scales: a planner cannot personally supervise the models for fifty thousand stock keeping units, but a tracking signal can, and it refers to human attention only the items whose behaviour has actually changed.
Part (c) — economic forecasting compared with regression analysis. The two are often confused because economic forecasting usually uses regression, but they answer different questions. Regression analysis is a statistical technique: it fits a relation between a dependent variable and one or more independent variables, and its output is a set of coefficients with standard errors, a measure of fit and a statement about the strength of an association within the range of the data observed. It is silent about causation, it presumes the independent variables are known, and it is a single equation. Economic (econometric) forecasting is a modelling activity that begins from economic theory: the analyst specifies which variables ought to drive the quantity of interest and how they are connected, estimates the resulting system — usually, though not necessarily, by regression — and then uses it to project the future. Three differences follow. First, an econometric model is normally a system of simultaneous equations in which variables are jointly determined, whereas a regression is one equation with a one-way dependence. Second, forecasting requires the future values of the explanatory variables, which are themselves unknown, so an econometric forecast is conditional on a scenario or on leading indicators and its error compounds the equation error with the error in those projections; a regression fit carries no such burden. Third, the two are judged by different criteria: a regression is judged by fit and by the significance of its coefficients, while an economic forecast is judged by out-of-sample accuracy and by whether its signs and magnitudes are economically sensible, and a model can be excellent on the first criterion and useless on the second. For an operations planner the practical consequence is that econometric forecasts are worth their cost mainly at the long horizon, where capacity and facility decisions turn on the business cycle, while the short-horizon inventory and scheduling decisions are better served by the far cheaper time-series methods of part (b).
