Question 3 of 7: Machine Space Requirements, and Assembly Line Balancing by the Ranked Positional Weight (RPW) Technique

Question 3: Machine Space Requirements, and Assembly Line Balancing by the Ranked Positional Weight (RPW) Technique (20 marks: i–5, ii–5, iii–10)

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.

(i) Steps to Determine Total Machine Space Requirements

Total machine space requirement is built bottom-up, from each individual machine's own space need to the full facility total:

1. Compile the equipment list. Obtain, from process/route sheets and capacity planning, every machine type required and the required quantity of each (from throughput/capacity calculations, e.g. the number of stations derived in part (iii)).

2. Determine each machine's static (footprint) space. From manufacturer specification sheets or layout templates, obtain the machine's own physical length and width (and height, where vertical clearance matters).

3. Determine each machine's operating (gangway) space. The additional envelope needed for the machine to function: swing of moving parts, door/panel travel, the operator's working position, and material entering/leaving the machine during the cycle.

4. Determine maintenance and service space. Clearance required for routine maintenance access, lubrication points, and any panels or components that must be opened or removed for service.

5. Determine material storage space at the machine. Incoming (raw/WIP) and outgoing (finished-from-this-station) staging space, sized against the station's buffer policy (Question 5(i)/(ii)).

6. Total the individual machine space, then multiply by quantity. Sum footprint + operating + maintenance + storage space for one machine of each type, then multiply by the number of that machine type required.

7. Sum across all machine types. Add the totals for every machine type to obtain the total machine space requirement for the facility.

8. Apply an allowance factor. A percentage allowance is added for aisles not already captured in gangway space, structural columns, and planned future expansion, since the raw machine total understates the true floor area the facility must provide.

(ii) Determining the Amount of Space Per Machine

The space allocated to an individual machine is the sum of three components, each obtained the same way used in part (i): (1) the machine's static space — its physical footprint, taken directly from the manufacturer's equipment specification sheet or a to-scale plan/CAD template of the machine; (2) its operating space — the clearance the machine and its operator need while running, including the envelope swept by moving components (doors, tool changers, robot arms), the operator's standing/reach zone, and the space material occupies as it enters and leaves the machine during the work cycle; and (3) its maintenance space — clearance for access panels, lubrication points and service procedures that must be reachable without moving the machine or an adjacent one. In practice these are read directly from a manufacturer's footprint template or 2-D/3-D layout block when detailed data is available; where it is not, a planning-stage approximation applies a standard allowance multiplier (commonly on the order of 1.5–2× the static footprint area) to account for the operating and maintenance envelope, understanding that this is a rough planning figure to be replaced by actual clearance data as soon as it is available, not a substitute for it in the final detailed layout.

(iii) Line Balancing by the Ranked Positional Weight (RPW) Technique

Given. 14 task elements with times and immediate-predecessor precedence as tabulated above (total content time $\sum t_i=6.0$ min); required output $=65$ units/hr, produced on a single assembly line.

Find. The theoretical minimum and actual number of stations, the station assignment (schematic), and the resulting line efficiency.

Approach. Compute the required cycle time from the output rate, find the theoretical minimum station count, rank every element by its Ranked Positional Weight (own time + the time of every element that must follow it), then assign elements to stations in RPW-rank order — adding the highest-ranked precedence-ready element that still fits the station's remaining cycle time, and opening a new station only when no ready element fits — finally compute the resulting line efficiency.

1. Cycle time from the required output. $C=\dfrac{60\ \text{min/hr}}{65\ \text{units/hr}}=\boxed{0.9231\ \text{min/unit}}$ (55.4 s/unit).
2. Theoretical minimum number of stations. $N_{min}=\left\lceil\dfrac{\sum t_i}{C}\right\rceil=\left\lceil\dfrac{6.0}{0.9231}\right\rceil=\lceil 6.50\rceil=\boxed{7\ \text{stations}}$.
3. Ranked Positional Weight of every element. $RPW_i=t_i+\sum_{j\in\text{followers}(i)}t_j$ (own time plus every element, direct or indirect, that must come after it). Working from the precedence network:

   Element	1	3	6	5	2	9	11	4	10	13	7	8	12	14
   RPW (min)	6.0	4.6	2.3	2.2	1.8	1.4	1.4	1.4	1.2	0.9	0.9	0.9	0.7	0.6

   This ranking is itself already a valid precedence order (every element's predecessors carry a strictly higher RPW), so it can be assigned to stations directly.
4. Station assignment (largest-candidate rule). Working down the RPW list, add each precedence-ready element to the open station if it fits the remaining cycle time ($C=0.9231$ min); otherwise leave it for a later station and try the next-ranked ready element:

   Station	Elements (RPW order)	Station time (min)	Idle (min)
   1	1, 3	0.9	0.0231
   2	6, 10	0.9	0.0231
   3	5	0.8	0.1231
   4	2, 11	0.9	0.0231
   5	9	0.8	0.1231
   6	4, 13, 7	0.8	0.1231
   7	8, 12, 14	0.9	0.0231

   Every station time is $\le C=0.9231$ min and every precedence requirement is respected (e.g. element 13 needs 10 and 11, both assigned in earlier stations 2 and 4; element 14 needs 9, 12 and 13, all assigned in earlier stations). This uses exactly $N_{actual}=\boxed{7\ \text{stations}}$ — the theoretical minimum from Step 2 is achieved, so no further re-balancing can reduce the station count.
5. Line efficiency and balance delay. $$\text{Efficiency}=\frac{\sum t_i}{N_{actual}\cdot C}=\frac{6.0}{7(0.9231)}=\frac{6.0}{6.4615}=\boxed{92.9\%}$$ Balance delay $=100\%-92.9\%=\boxed{7.1\%}$ (the idle time built into the line by imperfect divisibility of element times into a common cycle). At $C=0.9231$ min/unit the line's actual output is $60/0.9231=65.0$ units/hr, meeting the required rate exactly.