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23-Ind-A4 Production Management · May 2014

Question 5 of 7: Variability as a Cause of Production Inefficiency

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Technical Examinations — May 2014 — 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; Montgomery, Introduction to Statistical Quality Control (8th ed.) — Six Sigma and process capability; ISO 9001:2015 and the Toyota Production System literature — quality management and 5S/lean.

Question 5: Variability as a Cause of Production Inefficiency (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.

(a) Example and a Way to Reduce It

Consider a single machine feeding a downstream assembly station, where the machine's processing time is not constant but varies randomly around its average (e.g., due to tool wear, operator technique, or intermittent minor jams). Queueing theory shows that as this processing-time variability increases — holding average utilization fixed — the average queue of parts waiting in front of the downstream station, and hence the average cycle time, increases sharply and nonlinearly (the Kingman/VUT relation: waiting time scales with a variability term times a utilization term that explodes as utilization approaches 100%). The direct cost impact is threefold: (1) more work-in-process inventory must be carried to buffer the variability, tying up capital and floor space; (2) the downstream station experiences unplanned idle time whenever the buffer empties, which either wastes labour/machine capacity or forces overtime to catch up; and (3) to protect delivery promises against the resulting unpredictable lead time, the plant typically carries extra finished-goods safety stock or quotes longer, padded lead times to customers, both of which are pure costs with no value added. A concrete way to reduce this variability is to implement statistical process control (SPC) on the upstream machine's cycle time and standardize its operating procedure (tooling, changeover method, preventive-maintenance schedule) — converting an erratic, operator-dependent process into one with a tight, predictable distribution of processing times, which directly shrinks the buffer/safety-stock needed downstream without adding capacity.

(b) Principles for Reducing Variability

A useful, general set of principles (synthesizing the standard "factory physics" and lean perspectives) is:

  1. Standardize the work. Document and enforce a single best method for each task (standardized work instructions, jigs/fixtures, SOPs) so that operator-to-operator and cycle-to-cycle differences shrink; this attacks the largest and most controllable source of variability in most manual or semi-manual operations.
  2. Maintain equipment proactively. Total productive maintenance (TPM) and condition-based maintenance prevent the gradual drift and sudden breakdowns that inject variability into machine cycle times and availability, rather than reacting to failures after they occur.
  3. Control and monitor with data. Use SPC (control charts) to distinguish common-cause variability (inherent to the process, requiring a process change to fix) from special-cause variability (an assignable, fixable event), and act on out-of-control signals immediately before they propagate downstream.
  4. Reduce setup/changeover variability. Apply SMED (single-minute exchange of die) principles so changeovers are fast and consistent in duration, since an unpredictable changeover time is often a bigger driver of downstream variability than the changeover's average length.
  5. Improve supplier and input consistency. Work upstream with suppliers on incoming-material quality and delivery reliability, since variable input quality (dimensions, defect rate) forces variability into every downstream process that consumes it.
  6. Buffer deliberately where variability cannot be eliminated. Where a source of variability is irreducible (e.g., genuine demand randomness), use capacity, inventory, or time buffers consciously and size them analytically (e.g., via queueing/Little's-law relationships) rather than by ad hoc padding, so the buffer is neither starving the line nor tying up excess capital.