22-Mec-B4 Integrated Manufacturing Systems · December 2017
Question 4 of 7: Plant location by weighted factor rating
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper format. 16-Mec-B4 Integrated Manufacturing Systems,
December 2017 — a three-hour open-book examination; any non-communicating
calculator is permitted. The cover page states “Any five (5) questions constitute a complete
paper. Only the first five (5) questions as they appear in your answer book will be marked”
and “All questions are of equal value”, so each of the seven printed
questions carries 20 marks against a 100-mark paper. Note 1 invites the candidate to submit a clear
statement of any assumptions made where a question is open to interpretation; this paper needs that
licence twice, and both places are flagged below. All seven questions are worked here, because this
set is a study resource rather than a timed sitting.
Reference texts. E. S. Buffa and R. K. Sarin, Modern Production /
Operations Management, 8th ed. (requirements-schedule lot sizing, economic order interval,
part-period balancing, plant location, machine coupling and the man-machine chart);
R. B. Chase, F. R. Jacobs and N. J. Aquilano, Operations and Supply Chain Management,
16th ed. (aggregate planning strategies, categories of forecasting technique, weighted factor
rating for facility location); M. P. Groover, Automation, Production Systems, and
Computer-Integrated Manufacturing, 5th ed. (CAD geometric transformations, computer-aided
process planning, routing sheets, group technology); D. C. Montgomery, Introduction to
Statistical Quality Control, 8th ed. (Shewhart constants, process capability indices);
A. J. Duncan, Quality Control and Industrial Statistics, 5th ed. (natural tolerance versus
specification); C. E. Ebeling, An Introduction to Reliability and Maintainability
Engineering, 3rd ed. (when preventive maintenance pays).
Question 4: Plant location by weighted factor rating (20 marks)
Given. Three candidate sites whose transportation and processing costs are
essentially equal, so the decision rests entirely on five weighted qualitative factors:
Factor weights and committee scores (5-point scale, 5 = excellent)
Factor
Weight
Location A
Location B
Location C
Labour supply
0.02
5
4
4
Labour relations
0.03
3
4
5
Supporting services
0.25
5
3
3
Waste disposal
0.15
4
4
4
Community attitude
0.10
5
4
3
Sum of weights
0.55
—
—
—
Find. The weighted score of each location, and hence the site the committee
should select.
Check: the printed weights sum to 0.55, not 1.00. A weighted factor rating
requires the weights to be a partition of the decision, and the first two entries as printed
(0.02 and 0.03) are almost certainly typographical slips for 0.20 and 0.30 — with 0.20 and 0.30 the weights would be 0.20, 0.30, 0.25, 0.15, 0.10, which do sum to 1.00. Both readings are worked below. Location A is selected under either
one, so the slip does not change the recommendation; it changes only which site is runner
up. The answer is presented on the weights as printed, per Note 1, with the alternative shown
alongside.
Approach. Multiply each site's score by the factor weight, sum down the column
to obtain the weighted score, and compare; then repeat with the corrected weights to confirm that
the ranking does not depend on the discrepancy.
State the weighted factor rating model. With $w_i$ the weight of factor $i$
and $s_{ij}$ the committee's score for factor $i$ at location $j$, the composite score is
$$S_j=\sum_{i=1}^{n} w_i\,s_{ij}$$
and the location with the largest $S_j$ is preferred. The model is a simple additive-value
function: it presumes the factors are independent and that a point of score is worth the same
anywhere on the scale, which is why the scoring guide (5 = excellent) must be written down before
the committee scores anything.
Evaluate location A on the weights as printed. Taking the column term by
term,
$$S_A = 0.02(5)+0.03(3)+0.25(5)+0.15(4)+0.10(5)$$
$$S_A = 0.10+0.09+1.25+0.60+0.50 = \boxed{2.54}$$
Supporting services dominates the total, contributing 1.25 of the 2.54 — a direct consequence
of its being the heaviest single weight and A's being the only site to score 5 on it.
Evaluate locations B and C the same way. For B,
$$S_B = 0.02(4)+0.03(4)+0.25(3)+0.15(4)+0.10(4) = 0.08+0.12+0.75+0.60+0.40 = 1.95$$
and for C,
$$S_C = 0.02(4)+0.03(5)+0.25(3)+0.15(4)+0.10(3) = 0.08+0.15+0.75+0.60+0.30 = 1.88$$
so the ranking is $\boxed{S_A = 2.54 > S_B = 1.95 > S_C = 1.88}$ and Location A is
selected. Because the weights total 0.55 rather than 1.00 these totals are not on the
original 5-point scale; dividing by 0.55 restores comparability and gives 4.62, 3.55 and 3.42 out
of 5, which is the form worth quoting to a committee.
Repeat with the corrected weights as a check. Using 0.20, 0.30, 0.25, 0.15 and
0.10, which sum to unity,
$$S_A = 1.00+0.90+1.25+0.60+0.50 = 4.25,\quad
S_B = 0.80+1.20+0.75+0.60+0.40 = 3.75,\quad
S_C = 0.80+1.50+0.75+0.60+0.30 = 3.95$$
Location A still wins, now by 0.30 over C, and the runner-up changes from B to C because the
labour-relations weight rises tenfold and C is the strongest site on that factor. The decision is
therefore robust to the printing error, but the second and third places are not.
Interpret the margin before recommending. On the printed weights A leads B by
0.59 out of a 2.75 maximum, a margin of more than one full scale point on the dominant factor
— large enough to be safe against one committee member's disagreement about a single score.
The recommendation should nevertheless be stated conditionally: the model presumes the
transportation and processing costs really are equal, and a cost difference of even a few per cent
of annual operating cost would outweigh a qualitative gap of this size. The committee should also
be told that supporting services carries nearly half the printed weight, so the choice of A is in
substance a judgement that access to supporting services matters most.
