Abstract
This paper studies the solution procedure of a bus transit system with a rectangular service area that had been cited more than two hundred times. We will point out that they applied relations suitable for continuous variables, which are not held for a discrete variable and will result in invalid results. We provide our solution procedure to the same example proposed by the original paper to illustrate that their results are less accurate. Our findings will help researchers understand this kind of bus transit system.
Highlights
The goal of this paper is to study a famous paper by Kocur and Hendrickson [1] that claimed that they obtained a formulated approximated optimal solution for a bus transit system with a rectangular service area
We find that the optimal solution for this bus transit system is as follows: three bus routes, n∗ = 3; headway, h∗ = 19.14 min; fare, f ∗ = 105.40 cents
We showed that a well-known relationship developed by Kocur and Hendrickson [1], which was accepted by many following papers related to bus transit system, is invalid
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The goal of this paper is to study a famous paper by Kocur and Hendrickson [1] that claimed that they obtained a formulated approximated optimal solution for a bus transit system with a rectangular service area. Kocur and Hendrickson [1] considered a bus transit model with a rectangular service area. Yang and Bell [7] provided a review paper for the network design problems to discuss model formulations, Braess’s paradoxes, and capacity improvement plans. Studied the second transit model of Imam [13] to point out that the solution procedure proposed by Imam [13] contained less accurate results, and Chen and Julian [14].
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