Aims and Scope
This study proposes a bi-objective linear integer programming model for heterogeneous fleet VAP with emissions considerations. Profit maximization and emissions minimization objectives are employed to handle economic and environmental sustainability purposes.
Our literature survey shows that there is no model for the heterogeneous fleet VAP with emissions considerations that simultaneously consider vehicle heterogeneity, penalty costs for unmet demands, and emissions from transportation operations.
The model is employed to also make several scenario analyses on sustainable freight logistics management to understand the trade-offs among economic and environmental objectives. In freight transportation problems, decision-makers need to be able to maintain profitability and to reduce emissions.
In this study, a bi-objective linear integer programming model is proposed for a heterogeneous fleet Vehicle Allocation Problem (VAP) with emissions considerations encountered in the field of sustainable freight transportation.
In the numerical analyses, various practical assumptions that can be confronted by decision-makers in real life are discussed. In each analysis, total profit and emissions amounts are revealed along with several other KPIs. The results of the analyses provided in this study could also be useful in terms of understanding the relations among pillars of sustainability in VAPs.
It is thought that the proposed model has the potential to aid decision-making processes in sustainable logistics management.
In the base case analyses, the total profit obtained under profit maximization is about nine times higher than that obtained under emissions minimization. When the aim is to minimize emissions, the total emissions are found to be nearly one-tenth of that of profit maximization. Supported by also additional scenario analyses, it can be concluded that it might not economically viable to be environmentally-friendly for companies. Therefore, companies have to be encouraged or forced to take environmentally and socially responsible actions through legislation. The analyses demonstrated that various legislative policies on emissions may affect the transportation plans differently in such vehicle allocation systems.
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The road management agencies often prescribe very low-speed limits for exceptional vehicles transiting on the deck. These restrictions aim to reduce the dynamic effects due to the vehicle-bridge interaction because it is assumed that these effects increase with speed. However, sometimes, a reduction in speed increases the encounter probability of two exceptional vehicles travelling in opposite directions and this could compromise the safety of the bridge when the total masses of both vehicles exceed the bridge bearing capacity (or limit mass).
While the literature has investigated the encounter probability in a theoretical way and has investigated the vehicle-bridge interaction, especially in terms of dynamic load increment, to the best of our knowledge, no study has investigated the conjunction probability of encounters and of exceeding the limit mass also by using real data. This paper aims to cover this gap by proposing an integrated model that computes the “Annual Probability of Failure” of the bridge, defined as the likelihood to exceed the “Limit Mass" of the deck when two opposite exceptional vehicles encounter.
According to the probability theory, the “Annual Probability of Failure” can be obtained by multiplying the likelihood that during the reference year, at least once, two exceptional vehicles, travelling in two opposite directions (ascendant and descendant), will be simultaneously on the bridge deck (“Annual probability of encounter”) with the likelihood that the sum of the single masses of two exceptional vehicles randomly extracted from the sample, including the dynamic effects, exceeds the limit mass ml (“Probability of exceeding the limit mass”).
The results show that the probability of encounter increases with both the exceptional vehicles flow rate and the length of the span, whereas it decreases with the passing speed. The probability of exceeding the limit mass increases with speed. Nevertheless, by combining both the probabilities, these results suggest the existence of an “Optimal Speed”, which minimizes the “Annual Probability of Failure”.
The existence of an “Optimal Speed” should be considered when defining the exceptional vehicle transit rules on bridges as well as the speed limit.
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