Question 3 of 7: Assembly Line Balancing (RPW Technique) and Buffer Design

Question 3: Assembly Line Balancing (RPW Technique) and Buffer Design (20 marks: i–10, ii–5, iii–5)

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) 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.

(ii) Purpose of Buffer Design and Decoupling Techniques

The purpose of buffer design in flow lines is to protect the line's overall throughput from station-to-station variability and stoppages. Even a well-balanced line (like the 7-station line above) has stations whose actual cycle time varies (machine micro-stops, operator pace variation, quality rework) or that fail outright; without any buffer, every station is rigidly synchronous with every other, so a stoppage or slowdown at ANY one station immediately propagates and stops the entire line (the disadvantage noted in Question 2(iii)). A buffer — a small amount of work-in-process inventory held between stations — decouples the stations' short-term timing from one another, so that a downstream station can keep working from buffer stock while an upstream station is stopped (and an upstream station can keep producing into the buffer while a downstream station is stopped), preserving overall line throughput despite local disruptions.

The two buffering techniques that use decoupling for this purpose are: (1) in-line (inter-station) storage buffers — a small bank of work-in-process parts physically held in a queue or accumulating conveyor section between two adjacent stations, sized to bridge the expected duration of a typical short stoppage; and (2) parallel stations (redundant/duplicate workstations) — providing two or more stations in parallel to perform the same operation, so that if one fails or falls behind, the parallel station(s) continue processing and the line's overall capacity is not reduced to zero at that point. Both achieve the same decoupling objective — breaking the strict one-to-one timing dependency between adjacent operations — by different physical means: storage buffers decouple in TIME (absorbing a temporary rate mismatch), while parallel stations decouple in CAPACITY (providing redundant capacity so a single failure does not stop the flow).

(iii) Two Major Costs of Providing a Buffer

The two major costs involved in providing a buffer are: (1) the carrying cost of the work-in-process inventory held in the buffer — capital tied up in partially completed units sitting idle, plus the risk of damage, obsolescence or quality issues accumulating undetected across a larger in-process inventory; and (2) the cost of the space and equipment needed to hold the buffer — the floor space, conveyor/accumulation hardware, and (for the parallel-station technique) the capital cost of the duplicate station itself, all of which increase the facility's footprint and capital investment. Buffer sizing is therefore a genuine trade-off, not a free improvement: a larger buffer improves the line's resilience to station stoppages but at the direct cost of more work-in-process capital, more floor space, and (for parallel stations) more duplicated equipment — the buffer/decoupling decision in Question 3(ii) must be sized against these costs, not maximized without limit.