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In this model, the GBS Construction Materials Company provides steel structural materials to industrial contractors. GBS recently did a survey of price, delivery performance, and quality in order to get an assessment of how it compares with its four major competitors. The results of the survey, with the names of all companies disguised, appears in the following table:
Vendors A, B, and D are clearly competitive, based on Price, Delivery Time, and Quality, respectively. For example, a customer for whom quality is paramount will choose D. A customer for whom delivery time is important will choose B. Are C and E competitive? Imagine a customer who uses a linear weighting system to identify the best bid (e.g., score=WQ * Quality + WT * (Delivery time) + WP * Price. Is there a set of weights (all nonnegative) so that Score (C) < Score(i), for i=A,B,D,E? Likewise for E?
Company Quality Delivery Time Price A 1.8 14 $21 B 4.1 1 $26 C 3.2 3 $25 D 1.2 5 $23 E 2.4 7 $22