Public-transit frequency setting using minimum-cost approach with stochastic demand and travel time

Common practice in public-transit planning is to determine the frequency of service based on accumulated hourly passenger counts, average travel time, given vehicle capacity, and the standard of minimum frequency by time of day. With the increased usage of automatic vehicle location (AVL) and automatic passenger counting (APC) systems, it is possible to construct the statistical distributions of passenger demand and travel time by time of day. This can give rise to improve the accuracy of the frequencies determined. This study presents a new approach of frequency setting by enabling the use of stochastic properties of the collected data and its associated costs within a supply chain optimization model. An optimization framework is constructed based on two main cost elements: (a) empty-seat driven (unproductive cost) and (b) overload and un-served demand (increased user cost). The objective function is to minimize the total cost incurred with decision variables of either frequency or vehicle capacity (vehicle size). That is, from the operator perspective it is desirable to utilize efficiently the fleet of vehicles which is related to the decisions of the vehicle size. From the authority perspective, the concern is to provide an adequate level of service in terms of frequency. The study contains sensitivity analysis of the cost elements involved for economic evaluation

A logit-based model for facility placement planning in supply chain management

The facility placement in supply chain management entails suppliers and consumers along with the terminals in between for distributing commodities. This study seeks to find the best terminal placement by taking into consideration the costs for both transportation and terminal construction. We call this a supplier-terminal-consumer (STC) problem and show that the STC is an NP-hard quadratic assignment problem. The NP-hard problems in real-size are proven to be intractable; hence, we develop a two-fold heuristic method for solving the STC problems. First, we identify the commodity flow by using a logit-based mathematical programming (Logit-MP) methodology based on the demand for the commodity and the locations of the candidate-terminals. We apply Logit-MP in an iterative process and specify the maximum utilisation of the candidate-terminals. Second, the best possible locations for the terminals are identified by analysing the utilisation rates in a geographic information system interface and using an interpolation method for converting the point-based utilisation rates into spatial data. We present numerical results of a large-size transportation case study for the city of Chicago where the commodity, terminals and consumers are interpreted as wheat, silos and bakeries, respectively