23-Ind-A4 Production Management · December 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Technical Examinations — December 2016 — 98-Ind-A4 Production Management. Three-hour, closed-book exam; Casio or Sharp approved calculators only. Format: seven questions, each worth 20 marks (sub-part weights as tabulated on the front page); only the first five questions appearing in the answer book are marked, so candidates effectively choose 5 of 7. All seven are solved below for completeness. The paper asks for point-form answers wherever possible; the solutions below use full working for clarity.
Reference texts: Nahmias & Olsen, Production and Operations Analysis (7th ed., Waveland/McGraw-Hill) — forecasting, inventory (EOQ) and aggregate planning; Sipper & Bulfin, Production: Planning, Control, and Integration — production-management systems; Hillier & Lieberman, Introduction to Operations Research (11th ed.) — LP formulation and project scheduling (CPM/PERT); Pinedo, Scheduling: Theory, Algorithms, and Systems (5th ed.) — parallel-machine scheduling, makespan and tardiness; Hopp & Spearman, Factory Physics (3rd ed.) — variability and production-system inefficiency; Niebel & Freivalds, Methods, Standards, and Work Design — division of labour and work-design history; Liker, The Toyota Way, and the Toyota Production System literature — 5S, Five Whys, and lean root-cause analysis.
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.
Little's law states that, for any production system operating in steady state, the average amount of work-in-process $L$ equals the average throughput rate $\lambda$ (units completed per unit time) multiplied by the average flow time $W$ (the total time a single unit spends in the system from release to completion): $L=\lambda W$. The relationship is therefore direct and proportional: for a fixed throughput $\lambda$ (set by market demand or line rate), total production time $W$ for any one unit is directly proportional to how much work-in-process $L$ is sitting in the system at once — doubling the WIP on the line, with throughput unchanged, doubles the average time any given unit takes to get through it. To calculate WIP on a real line, an engineer measures any two of the three quantities directly on the shop floor — throughput $\lambda$ is read off shipping/completion records over a period, and flow time $W$ is measured by time-stamping a sample of units at release and at completion — and solves for the third.
Controlling WIP therefore matters because $L$, $\lambda$, and $W$ are locked together: the only way to shorten total production time $W$ — and hence lead time, a major driver of responsiveness and customer satisfaction — without adding capacity is to reduce the amount of work-in-process $L$ sitting in the system. Excess WIP ties up capital and floor space, hides quality problems inside large queues (a defect introduced early is not discovered until it reaches the end of a long queue, by which time many more units have been built on top of the same error), and lengthens the time a demand change takes to reach the shop floor. Too little WIP has the opposite failure mode: a station starves whenever its input buffer empties, wasting available capacity and reducing achievable throughput below what the line could otherwise sustain. This is the theoretical basis for WIP-capping systems such as kanban and CONWIP: by directly limiting $L$ to a deliberately chosen level, a plant forces $W$ down to the corresponding minimum without touching capacity, instead of letting WIP grow unmanaged and drag production time out with it.
5S (Sort – Seiri, Set in order – Seiton, Shine – Seiso, Standardize – Seiketsu, Sustain – Shitsuke) is a structured workplace-organization method, originating in the Toyota Production System, that removes clutter, assigns every tool and part a labelled, visually obvious home, and maintains that standard through periodic audit and habit-building rather than a one-time clean-up.
It improves production because a disorganized workstation hides problems — a missing tool, a leaking machine, an out-of-spec part — inside visual noise, and searching for a misplaced item is pure non-value-added time that adds to every job's flow time without adding to $\lambda$. By making abnormalities visually obvious (a shadow board with an empty tool outline, a marked floor zone that is not empty), 5S is usually the first step of any lean or TPM rollout: it builds workforce discipline and creates the visual baseline that later tools (kanban boards, andon signals, standardized work) depend on. Plants that genuinely sustain 5S typically see fewer minor stoppages and safety incidents, simply because hazards and defects that used to hide in clutter become visible immediately, and operators spend measurably less of their shift searching rather than producing.
The technique referred to is the Five Whys, developed within the Toyota Production System under Taiichi Ohno as TPS matured through the 1950s and into the early 1960s. It is a root-cause-analysis method: when a problem or defect occurs, the investigator asks "why did this happen?", and then asks "why?" again of the answer just given, repeating the question (traditionally five times, though the number is a guideline, not a rule) until the causal chain reaches a true, actionable, process-level root cause rather than stopping at the first, most visible, or most convenient explanation. A representative chain for a stopped machine might run: the machine stopped → why? a fuse blew from an overload → why? the bearing was insufficiently lubricated → why? the lubrication pump was not circulating enough oil → why? the pump's intake was worn → why? there was no strainer fitted to keep metal shavings out of the pump — a root cause (a missing strainer) entirely different from, and far more useful than, the symptom first reported ("the machine stopped").
The concept works because most problem investigations naturally stop at the first plausible cause, which is usually only a proximate symptom of a deeper systemic issue; fixing that symptom (replacing the blown fuse, in the example) restores production immediately but leaves the true cause untouched, so the same failure recurs. Each successive "why" forces the investigation one causal layer deeper, moving from an equipment symptom toward a process, design, or maintenance-system deficiency that, once corrected, prevents not just this failure but the whole family of failures the same root cause would otherwise keep producing. The technique is deliberately cheap and simple — no statistical tooling or specialist training is required — which is precisely why it works as a shop-floor discipline: it can be applied by any operator or engineer, immediately, at the point where the problem actually occurred, which pairs naturally with jidoka (stopping the line the instant an abnormality appears) so the causal evidence is still fresh and directly observable rather than reconstructed later from memory or paperwork.
