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.
Given. Fourteen jobs, each with a fixed processing time (seconds) shown once regardless of which machine runs it (the three machines have "similar capabilities," so a job's time does not depend on its assigned machine); three identical parallel machines A, B, C; target completion within 4 hours ($14{,}400$ s). No individual job due dates are stated, so "minimize the lateness of the worst job" is read as minimizing the makespan (the completion time of the last-finishing machine).
| Job | Batch size | Time (s) | Initial machine |
|---|---|---|---|
| B2401 | 72 | 3,100 | A |
| B7982 | 126 | 4,400 | A |
| B6183 | 45 | 6,000 | B |
| B1184 | 110 | 3,800 | A |
| B9455 | 240 | 3,800 | C |
| B4056 | 32 | 4,300 | B |
| B1847 | 32 | 4,300 | B |
| B6298 | 32 | 4,300 | B |
| B9989 | 192 | 1,800 | C |
| B1910 | 64 | 1,200 | B |
| B3311 | 64 | 1,200 | B |
| B8212 | 32 | 2,900 | B |
| B4813 | 64 | 1,000 | B |
| B7214 | 64 | 1,000 | B |
| Initial totals | A 11,300 / B 26,200 / C 5,600 | ||
Find. (a) A rebalanced schedule that completes all jobs within the 4-hour (14,400 s) target; (b) a better scheduling approach beyond simple machine rebalancing.
Approach. The initial allocation is badly imbalanced (Machine B alone totals 26,200 s $=7.3$ h, nearly double the deadline, while C sits at only 5,600 s), so the deadline cannot be met without reassigning jobs across machines; find the lower bound on the best possible makespan, then search for a job-to-machine assignment achieving it (or as close as feasible), and check the result against the 4-hour target.
| Machine | Initial load | Rebalanced load |
|---|---|---|
| A | 11,300 s | 14,300 s |
| B | 26,200 s | 14,400 s |
| C | 5,600 s | 14,400 s |
| Makespan $L_{max}$ | 26,200 s (7.3 h, misses target) | 14,400 s (exactly meets 4 h target) |
(b) A better way to schedule the machines. The rebalanced schedule above meets the deadline exactly, but with zero margin — any hiccup (a jammed feeder, a late material delivery, an operator break) on Machine B or C pushes the worst job late, since there is no slack anywhere in the schedule. Four changes would make the operation more robust without requiring the machines to run any faster: (1) Sequence within each machine by shortest-processing-time (SPT) first. $L_{max}$ (the makespan) is unaffected by the order jobs run in on a machine, but SPT-first minimizes the average flow time and average WIP across all 14 jobs — several small jobs finish early instead of waiting behind one long one, which matters if any job has a customer waiting on it individually rather than just the whole batch. (2) Lot-stream the largest batches. B6183 (batch 45, 6,000 s) and B7982 (batch 126, 4,400 s) are the two longest single jobs; splitting a large batch into sub-lots that can start moving to the next process step before the whole batch finishes reduces the effective flow time of downstream operations even though the machine's own total processing time is unchanged. (3) Build in a real time buffer instead of scheduling to the exact deadline. Since the current best schedule (14,400 s) lands precisely on the 4-hour target with no slack, propose either negotiating a small buffer into the deadline or keeping a portion of one machine's capacity in reserve so a single disruption doesn't automatically cause a miss. (4) Address the root imbalance, not just this batch. The initial allocation (A 11,300 / B 26,200 / C 5,600 s) was badly skewed toward Machine B before any rebalancing — if this pattern repeats batch after batch, the real fix is a dynamic, load-aware dispatching rule for future batches, not a one-time manual rebalancing exercise each time a new job list arrives.
