Modeling the Truck Appointment System as a Multi-Player Game

<i>Background:</i> Random truck arrivals at maritime container terminals are one of the primary reasons for gate congestion. Gate congestion negatively affects the terminal’s and drayage firms’ productivity and the surrounding communities in terms of air pollution and noise. To alleviate...

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Main Authors: Mohammad Torkjazi, Nathan Huynh, Ali Asadabadi
Format: Article
Language:English
Published: MDPI AG 2022-07-01
Series:Logistics
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Online Access:https://www.mdpi.com/2305-6290/6/3/53
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author Mohammad Torkjazi
Nathan Huynh
Ali Asadabadi
author_facet Mohammad Torkjazi
Nathan Huynh
Ali Asadabadi
author_sort Mohammad Torkjazi
collection DOAJ
description <i>Background:</i> Random truck arrivals at maritime container terminals are one of the primary reasons for gate congestion. Gate congestion negatively affects the terminal’s and drayage firms’ productivity and the surrounding communities in terms of air pollution and noise. To alleviate gate congestion, more and more terminals in the USA are utilizing a truck appointment system (TAS). <i>Methods:</i> This paper proposes a novel approach to modeling the truck appointment system problem. Unlike previous studies which largely treated this problem as a single-player game, this study explicitly models the interplay between the terminal and drayage firms with regard to appointments. A multi-player bi-level programming model is proposed, where the terminal functions as the leader at the upper-level and the drayage firms function as followers at the lower-level. The objective of the leader (the terminal) is to minimize the gate waiting cost of trucks by spreading out the truck arrivals, and the objective of the followers (drayage firms) is to minimize their own drayage cost. To make the model tractable, the bi-level model is transformed to a single-level problem by replacing the lower-level problem with its equivalent Karush–Kuhn–Tucker (KKT) conditions and the model is solved by finding the Stackelberg equilibrium in one-shot simultaneous-moves among players. For comparison purposes, a single-player version of the TAS model is also developed. <i>Results:</i> Experimental results indicate that the proposed multi-player model yields a lower gate-waiting cost compared to the single-player model, and that it yields higher cost savings for the drayage firms as the number of appointments per truck increases. Moreover, the solution of the multi-player model is not dependent on the objective function coefficients, unlike the single player model. <i>Conclusions:</i> This study demonstrates that a TAS is more effective if it considers how the assigned appointment slot affects a truck’s drayage cost. It is recommended that terminal operators and port authorities initiate conversations with their TAS providers about incorporating this element into their TAS.
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spelling doaj-art-4fefe9f2606b428088c413eeadf19e302025-08-20T02:52:38ZengMDPI AGLogistics2305-62902022-07-01635310.3390/logistics6030053Modeling the Truck Appointment System as a Multi-Player GameMohammad Torkjazi0Nathan Huynh1Ali Asadabadi2Civil & Environmental Engineering, University of South Carolina, Columbia, SC 29208, USACivil & Environmental Engineering, University of South Carolina, Columbia, SC 29208, USASupply Chain Analytics, Nestlé USA, Arlington, VA 22209, USA<i>Background:</i> Random truck arrivals at maritime container terminals are one of the primary reasons for gate congestion. Gate congestion negatively affects the terminal’s and drayage firms’ productivity and the surrounding communities in terms of air pollution and noise. To alleviate gate congestion, more and more terminals in the USA are utilizing a truck appointment system (TAS). <i>Methods:</i> This paper proposes a novel approach to modeling the truck appointment system problem. Unlike previous studies which largely treated this problem as a single-player game, this study explicitly models the interplay between the terminal and drayage firms with regard to appointments. A multi-player bi-level programming model is proposed, where the terminal functions as the leader at the upper-level and the drayage firms function as followers at the lower-level. The objective of the leader (the terminal) is to minimize the gate waiting cost of trucks by spreading out the truck arrivals, and the objective of the followers (drayage firms) is to minimize their own drayage cost. To make the model tractable, the bi-level model is transformed to a single-level problem by replacing the lower-level problem with its equivalent Karush–Kuhn–Tucker (KKT) conditions and the model is solved by finding the Stackelberg equilibrium in one-shot simultaneous-moves among players. For comparison purposes, a single-player version of the TAS model is also developed. <i>Results:</i> Experimental results indicate that the proposed multi-player model yields a lower gate-waiting cost compared to the single-player model, and that it yields higher cost savings for the drayage firms as the number of appointments per truck increases. Moreover, the solution of the multi-player model is not dependent on the objective function coefficients, unlike the single player model. <i>Conclusions:</i> This study demonstrates that a TAS is more effective if it considers how the assigned appointment slot affects a truck’s drayage cost. It is recommended that terminal operators and port authorities initiate conversations with their TAS providers about incorporating this element into their TAS.https://www.mdpi.com/2305-6290/6/3/53maritime container terminaltruck appointment systemgame theorymulti-player optimizationbi-level mathematical programport congestion
spellingShingle Mohammad Torkjazi
Nathan Huynh
Ali Asadabadi
Modeling the Truck Appointment System as a Multi-Player Game
Logistics
maritime container terminal
truck appointment system
game theory
multi-player optimization
bi-level mathematical program
port congestion
title Modeling the Truck Appointment System as a Multi-Player Game
title_full Modeling the Truck Appointment System as a Multi-Player Game
title_fullStr Modeling the Truck Appointment System as a Multi-Player Game
title_full_unstemmed Modeling the Truck Appointment System as a Multi-Player Game
title_short Modeling the Truck Appointment System as a Multi-Player Game
title_sort modeling the truck appointment system as a multi player game
topic maritime container terminal
truck appointment system
game theory
multi-player optimization
bi-level mathematical program
port congestion
url https://www.mdpi.com/2305-6290/6/3/53
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