Minimizing fleet operating costs for a container transportation company

doi:10.1016/j.ejor.2004.09.005

European Journal of Operational Research

Volume 171, Issue 3, 16 June 2006, Pages 776-786

https://doi.org/10.1016/j.ejor.2004.09.005 Get rights and content

Abstract

This paper focuses on a fleet management problem that arises in container trucking industry. From the container transportation company perspective, the present and future operating costs to minimize can be divided in three components: the routing costs, the resource (i.e., driver and truck) assignment costs and the container repositioning costs (i.e., the costs of restoring a given container fleet distribution over the serviced territory, as requested by the shippers that own the containers).

This real-world problem has been modeled as an integer programming problem. The proposed solution approach is based on the decomposition of this problem in three simpler sub-problems associated to each of the costs considered above.

Numerical experiments on randomly generated instances, as well as on a real-world data set of an Italian container trucking company, are presented.

Section snippets

Introduction and problem statement

A core problem faced by container trucking companies deals with a set of transportation orders at minimum cost. The essential decisions to be taken are: how to partition the set of transportation orders so that each subset can be executed by a single driver; to whom to assign such subsets of orders; how to reduce the misplacement of containers produced by the two previous operations; see, e.g., Crainic and Laporte (1997) and Powell et al. (1995).

This paper addresses the problem that a container

Mathematical formulation and solution approach

In this section an approximate solution approach for Problem 1 is proposed.

From a mathematical point of view, Problem 1 could be formulated as: $J^{*} = \min_{u_{0}, \dots, u_{H}} E {J_{0} (I_{0}, u_{0}, \dots, u_{H}, S_{0}, \dots, S_{H})},$ where J₀ represents the overall cost, function of the initial state, the decisions taken and the orders to execute; expectation of J₀ is evaluated, since future transportation orders can only be estimated.

We are interested in dynamically solving (1), i.e., at each day t, we aim at determining the optimal decisions u_t

Solution of the single day problem

Problem (4a), (4b), (4c), (4d), (4e), (4f), (4g), (4h) is too difficult to be solved exactly for typical real-world instances (with hundreds of transportation orders and, consequently, tens of thousands of pairings). Hence, we decided to decompose it by separating the different decisions that the fleet manager has to take (i.e., which pairings to execute, which resources to use, and which containers to reposition). In order to perform this decomposition, constraints (4d), (4e), (4g) have been

Lower and upper bounds

In this section, a lower and an upper bound of Problem (4a), (4b), (4c), (4d), (4e), (4f), (4g), (4h) are presented.

Implementation details

The test algorithm (in the following also referred to as Ctr_opt module) was coded in ANSI C programming language, with calls to Cplex Callable Library (Cplex Linear Optimizer 4.0.7). Ctr_opt module was implemented on a COMPAQ AlphaServer DS20e running HP Tru64 Unix V4.0F operating system.

Fig. 4 shows a high level flow chart of the test algorithm. During the subgradient iterations, all the Lagrangian multipliers involved (vectors λ, μ and α) have been updated using a scalar stepsize that has

Summary and conclusions

This paper describes and tackles a fleet management problem that arises in container transportation industry. We have focused on the minimization of the present and future operating costs incurred by the container carrier. By means of Lagrangian relaxation, the integer programming model has been decomposed into three sub-problems.

We have set up numerical experiments using randomized data sets as well as a real-world data set of an Italian container transportation company, in order to assess the

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^☆: The research described in this paper has been partially supported by C.N.R. (National Research Council of Italy) contracts 00.00333.ST74 and 00.00339.ST74, and by “Fondo Trieste-Progetti di ricerca scientifica e tecnologica-Anno 1998”.

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Minimizing fleet operating costs for a container transportation company☆

Abstract

Section snippets

Introduction and problem statement

Mathematical formulation and solution approach

Solution of the single day problem

Lower and upper bounds

Implementation details

Summary and conclusions

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

Transportation Research E

Transportation Research E