23-Ind-A3 Facilities Planning · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2015 — 98-Ind-A3 Facilities Design. Three-hour, closed-book exam (Casio or Sharp approved calculator only); any five of the seven questions constitute a complete paper and only the first five answered in the answer book are marked — all seven are solved below for completeness.
Reference texts: Tompkins, White, Bozer & Tanchoco, Facilities Planning (4th ed., Wiley) — the facilities-planning hierarchy, the facilities planning process, facility location and plant-site selection, manufacturing cells, machine space and line-balancing models, computerized layout algorithms (CRAFT/CORELAP), and material handling equipment/systems; Niebel & Freivalds, Methods, Standards, and Work Design (13th ed.) — assembly-line balancing (Ranked Positional Weight technique), balance delay, and production-quantity planning with scrap/rework.
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. Market (final) requirement $=15{,}000$ good components, produced through four sequential operations — turning $\to$ milling $\to$ drilling $\to$ grinding — each with a scrap rate (6%, 5%, 4%, 3%) and a rework rate (4%, 3%, 3%, 1%).
Find. For each operation: the production quantity (pieces) that must be scheduled INTO it, and the expected number of good pieces it produces.
Approach. Work backward from the final 15,000-piece requirement through grinding, drilling, milling and turning in turn: the quantity scheduled into an operation must be large enough that, after that operation's own scrap loss, the surviving good output meets the quantity the NEXT operation (or the final market requirement) needs. Rework pieces are recoverable — they still count as good output after the extra rework labour — so only the scrap rate reduces the piece count from one operation to the next; the rework rate instead splits the "good" total into pieces that were right first time and pieces that needed rework, which is informational, not an additional loss.
| Operation | Production qty scheduled | Expected good pieces |
|---|---|---|
| (a) Turning | 18,040 | 16,958 |
| (b) Milling | 16,957 | 16,109 |
| (c) Drilling | 16,109 | 15,465 |
| (d) Grinding | 15,464 | 15,000 |
For reference, splitting each operation's good output into pieces that passed first time versus pieces recovered through rework (scheduled qty $\times(1-\text{scrap}-\text{rework})$ and scheduled qty $\times\text{rework}$ respectively): turning 16,236 first-pass $+$ 722 reworked; milling 15,600 first-pass $+$ 509 reworked; drilling 14,981 first-pass $+$ 483 reworked; grinding 14,845 first-pass $+$ 155 reworked — each pair reconciling (within rounding) to that operation's total good-piece count above.
To lay out a facility handling multiple products/items, a computerized layout program needs, at minimum: (1) a defined set of departments/activities and their space requirements; (2) a quantitative interaction measure between every pair of departments — either a from–to flow/cost matrix (as CRAFT requires) or a qualitative relationship chart (as CORELAP requires) — that aggregates the flow or closeness need across ALL items/products handled, not just one; (3) a building/site outline or area constraint within which the departments must fit; (4) an objective function (typically minimize total material handling cost, or maximize weighted closeness satisfaction) that the algorithm can evaluate and improve against; (5) a starting layout (for improvement-type algorithms like CRAFT) or a placement rule (for construction-type algorithms like CORELAP); and (6) the ability to respect physical/fixed-location constraints (fixed-position equipment, building columns, docks) that cannot be relocated by the algorithm. Because these programs optimize a single aggregated objective across the full department set, when multiple items/products are handled their individual flow volumes (or relationship needs) must first be combined into ONE composite interaction matrix — this aggregation step, and the choice of relative weighting between products, is itself a modeling decision that materially affects the resulting layout.
Despite the theoretical appeal of algorithms such as CRAFT and CORELAP, several practical problems limit their use in industry: (1) They optimize a single quantitative objective (typically total flow cost or weighted closeness), so qualitative factors that matter in practice — safety separation, aesthetics, employee preference, future flexibility — are not represented unless awkwardly forced into the numeric input, and the "optimal" output can be materially worse than a manually adjusted layout once these factors are weighed in. (2) Improvement-type algorithms (CRAFT) are sensitive to the starting layout and converge to a local, not necessarily global, optimum, so different analysts (or different starting points) can get different "optimal" answers from the same data. (3) The department shapes generated are often irregular, split, or otherwise impractical to build (fingers, non-rectangular splinters), requiring significant manual clean-up before the layout can actually be constructed. (4) The programs require accurate, detailed input data (flow volumes, unit handling costs, space requirements for every department) that is expensive and time-consuming to collect and quickly becomes outdated as product mix and volumes change. (5) Physical/fixed-location constraints (columns, existing fixed equipment, docks) and multi-floor or irregular building envelopes are handled poorly by many algorithms, again forcing manual override. (6) The specialized software and expertise needed to run and correctly interpret the algorithms is a real barrier for smaller organizations, and many practitioners trust an experienced planner's manual judgment over a black-box numeric optimum they cannot fully audit.
