22-Mec-B4 Integrated Manufacturing Systems · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2015 — 07-Mec-B4 Integrated Manufacturing Systems. Three hours, open book, any non-communicating calculator permitted. Seven 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 seven are solved here, because the complete set is the study resource. Questions 5, 6 and 7 are explicitly essay questions, in which the examiners award marks for clarity and organisation as well as content.
Reference texts. E. S. Buffa and R. K. Sarin, Modern Production / Operations Management, 8th ed. (requirements schedules, economic lot size, economic order interval, part-period balancing, production planning); R. B. Chase and F. R. Jacobs, Operations and Supply Chain Management, 16th ed. (demand components, adaptive forecasting, aggregate planning, statistical quality control); B. W. Niebel and A. Freivalds, Methods, Standards, and Work Design, 13th ed. (time study, performance rating, allowances, wage incentive plans); D. C. Montgomery, Introduction to Statistical Quality Control, 8th ed. (Shewhart charts, process capability); M. P. Groover, Automation, Production Systems, and Computer-Integrated Manufacturing, 5th ed. (process planning, CAPP, machinability data systems, maintenance); S. Nahmias and T. L. Olsen, Production and Operations Analysis, 7th ed. (forecasting, aggregate planning).
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.
An operations forecasting system does not try to explain demand; it tries to decompose the observed series into parts that behave differently over time, because each part is projected forward by a different mechanism and each carries a different planning consequence. Six components are conventionally recognised, and a well-built system makes a deliberate decision about every one of them.
The average, or base level, is the constant about which the series fluctuates. It is what a simple moving average or a single-parameter exponential smoothing model estimates, and for a mature product it may be the only component that matters. Trend is a systematic drift in that base, upward or downward, caused by market growth, product maturity or price movement; ignoring it makes a smoothing model lag behind the series permanently, which is why a trend-corrected model is used whenever the drift is real. Seasonal influence is a repeating pattern tied to the calendar — a week, a month, a quarter, a year — and it is handled multiplicatively through seasonal indices, so that the underlying level can be estimated from deseasonalised data and the seasonality reapplied at the end. Cyclical elements are the longer swings associated with the business cycle, several years in period and neither regular in length nor reliably datable; they are the hardest component to forecast and are usually handled through leading economic indicators rather than from the demand history itself. Autocorrelation is the persistence of the series: this period’s value carries information about the next, which is precisely why smoothing works at all and why an order-backlog series is easier to forecast than an independent one. Finally, random variation is what remains after the other five have been extracted; it cannot be forecast, only measured, and it is the residual that sizes safety stock and sets the width of the planning buffers.
The practical value of the decomposition is that it tells the planner which part of a forecast error to act on. An error that traces to random variation calls for more buffer, not a better model; an error that traces to an unmodelled trend or a shifted seasonal index calls for the model to be corrected, and acting on it as though it were noise inflates inventory without improving service.
An adaptive forecasting system is an ordinary smoothing model wrapped in a feedback loop that adjusts the model’s own constants from the errors it is making. The motivation is that the smoothing constant $\alpha$ embodies a compromise: a large value tracks change quickly but transmits noise, a small value is stable but lags. No single value is right for a series whose behaviour changes, and in a system carrying thousands of items no analyst can retune them by hand.
The forward path has four elements. Demand history enters a forecasting model — most often exponential smoothing, with trend and seasonal corrections where the decomposition of part (a) says they are needed. The model issues a forecast for the next period. When the period closes, actual demand is compared with that forecast to yield a forecast error, $e_{t}=A_{t}-F_{t}$. The errors are then accumulated into two summary statistics: the running sum of errors, which detects bias, and the mean absolute deviation, which measures dispersion.
The return path is what distinguishes the adaptive system. The two statistics are combined into a tracking signal, $TS=RSFE/MAD$, whose expected value is zero for an unbiased model. A tracking signal that drifts outside a control band — commonly $\pm4$ MAD — says that the errors are no longer random, which means the model no longer matches the series. The system responds automatically: in a focused adaptive scheme, $\alpha$ is raised while the tracking signal is large so the model catches up to the change, and lowered again once the errors return to randomness; in Trigg and Leach’s formulation $\alpha$ is simply set equal to the absolute value of a smoothed tracking signal each period, so responsiveness is continuously proportional to the evidence of a shift. A different but equally adaptive structure, focus forecasting, holds a library of simple rules, simulates all of them against recent history each period, and uses the rule that would have performed best.
The engineering benefit is self-maintenance. The system responds quickly to a genuine step change in demand, yet reverts to a stable, low-$\alpha$ setting when the series settles, and it does so item by item across a large catalogue without analyst intervention. The cost is the risk of chasing noise if the control band is set too tightly, which is why the band, not $\alpha$, becomes the parameter the analyst actually manages.
The two are not competing techniques at the same level; regression is a statistical tool, and econometric forecasting is a modelling philosophy that uses that tool inside an explicit theory of how the economy works. Four differences follow from that.
Structure. A regression analysis fits one equation in which a dependent variable is explained by a set of independent variables chosen largely for their statistical association with it. An econometric forecast is built from a system of simultaneous equations, each expressing a behavioural or accounting relationship — a consumption function, an investment function, a capacity identity — solved together so that the variables determine one another. Direction of causality. Regression is agnostic about cause: it measures association and will cheerfully fit a relationship that runs backwards. An econometric model asserts causality in advance, from economic theory, and the equations are specified to express it; variables that are explained inside the model (endogenous) are kept distinct from those supplied to it (exogenous). Feedback. Because the equations are simultaneous, an econometric model captures feedback — higher output raises income, which raises demand, which raises output — that a single regression equation cannot represent. Use. A regression is used chiefly to project, and it is valid only within the range of the data it was fitted to. An econometric model is used to project and to answer conditional questions: what happens to demand for our product if the policy interest rate rises 200 basis points, or if housing starts fall 15 per cent. That policy-simulation capability is the reason firms pay for econometric services at all.
For an operations manager the practical distinction is one of horizon and role. Regression on one or two causal variables — permits issued, installed base, contracted volume — is a perfectly good medium-term forecasting tool and is cheap to maintain in-house. Econometric forecasts are bought, not built, and they are used to set the long-range planning environment inside which the operations forecast sits: capacity decisions, facility timing and long-term supply agreements. A firm that confuses the two — using a national econometric projection to schedule next week’s assembly line, or a two-variable regression to justify a plant — misapplies both.
