Robust door assignment in less-than-truckload terminals

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Abstract

The assignment of incoming trailers to strip doors is one of the critical decisions that affect the performance of cross docking operations in less-than-truckload terminals. This paper introduces a mixed integer quadratic model with the objective of generating trailer-to-door assignments that equally distribute idle times at doors to accommodate operational level uncertainty encountered in truck arrival times. A door assignment heuristic is presented. The performance of the heuristic is compared with optimal solutions to small problems. The effectiveness of the proposed heuristic is studied under a variety of circumstances and terminal sizes. The simulation results show that the proposed heuristic is applicable to realistic-size terminals, and it is effective when variability in truck arrival and service times is considered.

Highlights

► The trailer assignments are dynamic based on truck arrival and service times. ► The heuristic evenly distributes the idle times at doors to absorb operational level uncertainties. ► A customer oriented percent making cut-off metric is used to evaluate the heuristic.

Introduction

In less-than-truckload (LTL) freight transportation, for every origin–destination pair of traffic demand, the corresponding freight is shipped either directly or indirectly through intermediate nodes where the traffic is consolidated and re-routed. Most models for freight routing are defined over a network whose nodes represent origins, destinations and intermediate transfer points, and the arcs of the network represent channels of transport e.g. highways. One then distinguishes between local problems involving only a node (terminal) or an arc of the network, and global problems involving multiple entities.

The travel time of freight from its origin to its destination consists of the time spent between the nodes and time spent at the nodes. Since the distances between the nodes are fixed, substantial decrease in these times is less likely than a decrease in the time spent in the terminals and, in some cases, the variance and the duration of time spent at the nodes is considerably higher than the time spent transferring freight between nodes.

In an LTL terminal, freight from arriving trailers flows through the terminal to departing trailers in a cross docking environment without accumulating significant inventories. Freight is unloaded from trucks and reloaded onto another vehicle by means of individual transportation units such as forklifts. The number of doors in an LTL terminal typically ranges from 10 to 200 or more. The two types of doors in LTL terminals are strip doors for receiving (unloading), and stack doors for shipping (loading) to destinations as depicted in Fig. 1. The assignment of arriving and departing trailers to a door, the door assignment problem (DAP), is one of the critical decision factors that affect the performance of LTL terminals.

Section snippets

Literature review and motivation

A recent survey by Agustina, Lee, and Piplani (2010) presents a comprehensive review of mathematical models for cross dock planning. The review compiles and categorizes over 50 articles according to operational, tactical and strategic planning decisions considered in the referenced work. The door assignment problem considered in this paper falls under the category of operational level decision making problems along with the truck scheduling problem.

The truck scheduling problem which determines

Problem formulation

Considering the unavoidable variability associated with truck arrival and service times, schedules with appropriately built in slack should provide a more workable and robust schedule for operational activities. A delayed truck arrival will not disrupt the subsequent operations at a door if the subsequent idle time before the next trailer to be serviced in that door can accommodate this delay. Therefore, trailers should be assigned to doors in a manner which maximizes the idle time subsequent

Door assignment heuristic

The assignment of trailers to doors is similar to the parallel machine scheduling problem frequently encountered in manufacturing (Li, Lim, & Rodrigues, 2004). The proposed Door Assignment Heuristic (DAH) minimizes the makespan on M doors to maximize idle times at each door. The total idle time at each door is then evenly distributed between the trailers assigned to that door. The heuristic is described below using the example problem of Section 3. The steps of the DAH are as follows:

Input: The

Terminal performance using DAH

A simulation model with 200 trailers and 20 strip doors is built using Arena Simulation v7.01 (Rockwell Software, 2003). The data input to the simulation model are the truck arrival times Aj, the scheduled trailer service time Gj, and the enter times and door assignment Ej,k .

Conclusions

In this paper we present a new approach for the solution of the door assignment problem in LTL terminals. The trailer assignments to doors are based on truck arrival times and service times rather than static allocation of trailers to doors based on their origin and destination as pursued in previous approaches. The introduced heuristic evenly distributes the idle times at doors between trailer service times to absorb operational level uncertainties such as truck arrival lateness. In addition,

References (25)

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  • Cited by (19)

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      Except for the origins or destinations information, many other factors are subsequently investigated in the assignment problems of automatic sorting systems. Acar et al. (2012) take the arrival times and service times of incoming trucks into consideration in the assignment of incoming trucks to unload docks. Van Belle et al. (2013) consider the time window constraints in the assignment of trucks to both inbound and outbound docks.

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      Larbi, Alpan, & Penz (2009) also discuss different dynamic scheduling methods when there is partial or no information about truck arrivals. Acar, Yalcin, & Yankov (2012) suggest using idle times in scheduling trucks, which might have delays. These studies do not consider rescheduling concepts.

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      Thereafter, just a few proposals have been performed in this sense. We may cite Acar et al. (2012) where the authors have considered uncertainty on truck arrival and departure time as well as freight flow. They have introduced a new mixed-integer quadratic formulation for the problem and have proposed to solve it using a Door Assignment Heuristic (DAH) that distributes the idle times at doors between trailer service times to absorb uncertainty.

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      Acar et al. (2012) and Konur and Golias (2013a,b) assume random arrival times of inbound trucks. Therefore, in their objective function, Acar et al. (2012) focus on evenly distributing the idle times between processing inbound trucks assigned to strip doors. In contrast, Konur and Golias (2013a,b) and Heidari, Zegordi, and Tavakkoli-Moghaddam (2018) focus on minimizing waiting times at the yard (i.e., the time between arrival at the yard and entering the dock door).

    • Robust cross-dock scheduling with time windows

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      Redundancy-based techniques. Time redundancy techniques are only used in the cross-dock operations context by Acar et al. (2012). They aim at minimizing the variance of the doors’ idle times, in order to spread the inbound trucks on a given dock as evenly as possible and thus create buffer times between trucks.

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