Economies of Scale in Empty Freight Car Distribution in Scheduled Railways

Abstract

I n this paper, we consider empty freight car distribution in a scheduled railway system. We analyze the cost structure for the repositioning of empty cars, and conclude that the distribution cost shows an economyof-scale behavior. In addition to the cost proportional to the number of cars sent from origin to destination, there is a cost related to car-handling operations at yards, which depends on the number of car groups that are handled. Thus, if we can find a transportation pattern in which fewer but larger groups of cars are built, the total distribution cost can be decreased. The objective of the paper is to propose an optimization model that explicitly takes this economy-of-scale effect into account. We use a time-dependent network to describe the possible car movements in time and space, and show how this network can be transformed into a network with fixed costs on links representing movements of cars with identical origin and destination terminals. The resulting optimization model is a capacitated network design model, where each capacity constraint limits the flow on several arcs. We describe a tabu heuristic for solving the model, and present computational results.

Allotment Booking in Intermodal Transport

“…Forwarding free space is compatible with the Lowe as well as with Ballis and Golias (2004) concepts in which intermodality is assumed as a combined transport chain performance. A similar theory was developed by Joborn et al (2004).…”

A mixed integer programming approach for freight railcar distribution

“…Unlike the approach reported in this paper, the model proposed by Joborn et al (2004) considers the allocation process, the wagons individually. This fact leads to long time to search the solution and usually requires fast heuristics to provide the resolution.…”

“…Moreover, Joborn et al (2004) conducted studies related to operational problems in nature, which is considered the capacity of each train and cost of distributing groups of wagons to obtain economies of scale. The objective function of this model aims to determine the lowest cost related to movements OD (origin-destination) fleet of empty wagons in a given planning horizon.…”

Approximate dynamic programming in transportation and logistics: a unified framework

“…Reviews of this problem class can be found in Crainic & Gendreau (1993), Crainic & Laporte (1997) and Powell et al (1995). The most common models used in industry are myopic (see Gorman et al (2011) for a summary of car distribution models at two major railroads) or they use a deterministic lookahead (rolling horizon) policy (Joborn et al (2004)). A number of authors have experimented with various approximations of stochastic models (Jordan & Turnquist (1983), List et al (2003), , Lam et al (2007)).…”