Question 1 of 7: Planning strategies, preventive maintenance and forecasting categories

Question 1: Planning strategies, preventive maintenance and forecasting categories (20 marks)

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.

All three parts are descriptive. Each is answered in turn, in the flowing prose the cover page asks for on essay questions.

(a) Pure and mixed strategies in production planning

Aggregate production planning reconciles a demand forecast that varies month by month with a production system whose capacity is expensive to change. The planner has a small number of levers: vary the size of the workforce by hiring and laying off, vary the hours each worker is employed through overtime and undertime, absorb the variation in finished-goods inventory by producing at a constant rate, subcontract the peaks, or accept back orders and let the customer wait. A pure strategy is a plan that uses exactly one of these levers and holds every other at its base level. The two textbook extremes are the chase strategy, which matches output to demand period by period by hiring and releasing labour so that inventory stays near zero, and the level strategy, which holds output and workforce constant and lets seasonal inventory rise and fall. A constant-workforce plan that meets the peaks with overtime, or one that subcontracts everything above a fixed base, is likewise a pure strategy.

A mixed strategy combines two or more of the levers — for example a level base load carried by a permanent workforce, a seasonal band met by overtime, and the last few weeks of the peak subcontracted. The distinction matters because the cost structure of each lever is different in kind. Hiring and layoff costs are step costs incurred when the workforce changes; inventory carrying cost accumulates with the area under the stock curve; overtime is a premium on hours; subcontracting is a margin surrendered on units. A pure strategy pushes one of these costs to its extreme, and because each cost curve is convex the sum is almost always lowered by spreading the load over several levers. That is the practical result: the optimum plan is nearly always mixed, and the pure strategies are useful chiefly as bounding cases that bracket the answer and expose which cost dominates.

Pure strategies also serve as the reference points for evaluation. A planner prices the level plan and the chase plan first, because they are quick to cost and they establish the range within which any sensible mixed plan must fall. Only then is it worth the effort of a transportation-model or linear-programming formulation to search the mixed space. In a make-to-order machine shop the chase plan is often close to optimal because finished-goods inventory cannot be built ahead; in a process plant with high hiring cost and cheap storage the level plan usually wins; in most discrete manufacturing the answer sits between them.

(b) When preventive maintenance is appropriate

Preventive maintenance replaces or overhauls an item on a planned schedule, before it fails, and it is worth doing only when a set of conditions hold together. The first and most important is that the item must have an increasing failure rate — a wear-out characteristic, so that an older unit is more likely to fail in the next interval than a fresh one. If the hazard rate is constant, as it is for a purely exponential life, a new unit is no better than a used one and scheduled replacement buys nothing while consuming a good part; if the hazard rate is decreasing (infant mortality), scheduled replacement actively makes the equipment worse. This single test disqualifies a great deal of electronic and instrument equipment.

The second condition is that the cost of a failure must substantially exceed the cost of the planned intervention. The failure cost is not the repair bill alone: it includes lost production while the line is down, scrap and rework of the work in process caught in the machine, secondary damage to adjacent components, expediting and premium freight, and any safety or environmental consequence. Where a bearing seizure wrecks a spindle, or where a stoppage idles a transfer line, the ratio is large and preventive replacement is easy to justify. Where the item can be changed in minutes with no other consequence, run-to-failure is the rational policy.

Third, the failure must be reasonably predictable — the life distribution must have a small enough coefficient of variation that an interval can be chosen which catches most failures without discarding most of the useful life. A widely scattered life distribution forces either a very short interval, which throws away service life, or a long one, which lets most units fail anyway. Fourth, the intervention must be feasible without excessive disruption: there must be an access window (a shift change, a weekend, a planned shutdown), spares must be available, and the maintenance itself must not introduce defects, since a significant fraction of failures in practice are induced by the maintenance action.

Two further conditions round out the picture. Preventive maintenance is strongly indicated where failure is hidden — protective devices, relief valves, standby pumps, alarm and interlock systems — because a failed protective device announces itself only when it is needed, so a scheduled functional test is the only way the failure can be found. And it is indicated where safety, regulatory or code obligations compel it, as with pressure-relief devices, cranes and hoists, and elevating equipment, regardless of the economics. Where the wear mechanism can be measured while the machine runs — vibration, oil debris, thermography, motor-current signature — condition-based maintenance dominates fixed-interval replacement, because it captures nearly all of the avoided-failure benefit while using very close to the full life of the part.

(c) Categories of forecasting technique

Forecasting techniques divide into four broad categories, and they differ in the kind of information they consume, the horizon over which they are credible, and the cost of preparing them.

Qualitative (judgmental) methods convert informed opinion into a forecast. The family includes executive committee consensus, the Delphi method, sales-force composites, market surveys, historical analogy and life-cycle analogy. They use no historical series — which is precisely why they are the only option for a new product, a new plant or a technology whose past has no bearing on its future — and they are the natural choice for long-range strategic questions. Their weakness is that they carry the biases of the people consulted and cannot be validated statistically before the event.

Time-series analysis treats demand as a signal to be decomposed into level, trend, seasonal, cyclical and random components, and projects those components forward. Simple and weighted moving averages, single and double exponential smoothing, Holt–Winters seasonal smoothing, decomposition and Box–Jenkins models all belong here. The defining assumption is that the past pattern will persist: the method extrapolates history and asks no question about why demand moves. That makes it cheap, easy to automate over thousands of stock-keeping units, and accurate over the short to intermediate horizon — which is exactly the horizon that production and inventory planning needs — but blind to any turning point that has no precedent in the series.

Causal (explanatory) methods model demand as a function of one or more independent variables that are believed to drive it, and are fitted by regression or by econometric systems of simultaneous equations. Leading indicators, input–output models and life-cycle models sit in this group. Because a causal model contains an explanation, it can forecast a turning point that a time-series model must miss, and it answers “what if” questions about price, promotion or economic conditions. The price is data: the driver must itself be known or forecast for the future period, the relationship must be stable, and building and maintaining the model is expensive. Causal methods are therefore reserved for aggregate, high-value forecasts over the intermediate to long horizon.

Simulation methods build a dynamic model of the demand-generating system and run it forward under sampled inputs, producing a distribution of outcomes rather than a point estimate. They are the appropriate tool where the system contains feedback, queues or interacting policies that no closed-form model captures, and where the risk profile matters as much as the expected value.

The categories therefore differ chiefly along three axes: the data they need (opinion, own history, driver variables, a system model), the horizon over which they hold (long, short, intermediate, and any horizon respectively), and the cost per forecast, which rises sharply from a moving average to an econometric or simulation model. Practice mixes them: a causal or judgmental forecast sets the annual aggregate, a time-series model disaggregates it to items and weeks, and the two are reconciled through the sales and operations planning process.