Bus Service Model with Rectangular Service Zone under Exponential Relation

Most researchers developed bus service models with a rectangular service zone that relations among different costs are related by a linear relation. A bus service model had been constructed with a rectangular service zone where costs are synthesized by an exponential relation. An accepted paper had point out that a previous model without capacity constraint is unreasonable. This paper examines another model with capacity constraint to show that previous formulated optimal solution contains questionable findings and then we provide our solution approach. The key feature of our paper is to point out that using the route width as a continuous variable will derive unreasonable results. Our improved approach is to use the partition number for the zone width as a discrete variable. A numerical example is provided to illustrate our proposed approach.