Jena Research Papers in
Business and Economics
Cross Dock Scheduling: Classification,
Literature Review and Research Agenda
Nils Boysen, Malte Fliedner
2/2009
Jenaer Schriften zur Wirtschaftswissenschaft
Working and Discussion Paper Series
School of Economics and Business Administration
Friedrich-Schiller-University Jena
ISSN 1864-3108
Publisher:
Wirtschaftswissenschaftliche Fakultät
Friedrich-Schiller-Universität Jena
Carl-Zeiß-Str. 3, D-07743 Jena
www.jbe.uni-jena.de
Editor:
Prof. Dr. Hans-Walter Lorenz
h.w.lorenz@wiwi.uni-jena.de
Prof. Dr. Armin Scholl
armin.scholl@wiwi.uni-jena.de
www.jbe.uni-jena.de
Cross Dock Scheduling: Classication,
Literature Review and Research Agenda
Nils Boysen, Malte Fliedner
Friedrich-Schiller-Universität Jena, Lehrstuhl für ABWL/ Operations Management,
Carl-Zeiÿ-Str. 3, D-07743 Jena, Germany,
{nils.boysen,malte.fliedner}@uni-jena.de
Abstract
At cross docking terminals incoming deliveries of inbound trucks are un-
loaded, sorted, moved across the dock and nally loaded onto outbound
trucks, which immediately leave the terminal towards their next destina-
tion in the distribution chain. Accordingly, a cross dock is a consolidation
point in a distribution network, where multiple smaller shipments can be
merged to full truck loads in order to realize economies in transportation. In
this context, the truck scheduling problem, which decides on the succession
of truck processing at the dock doors, is especially important to ensure a
rapid turnover and on-time deliveries. Due to its high real-world signicance,
several truck scheduling procedures have been introduced within the recent
years, which all treat specic cross dock settings. In order to structure and
promote scientic progress, the paper on hand introduces a classication of
deterministic truck scheduling. With the help of this classication, existing
literature is reviewed and future research needs are identied. Moreover, we
represent a yet unexplored class of truck scheduling problems which is highly
relevant in real-world distribution networks.
Keywords:
Logistics; Cross Docking; Scheduling; Classication
1 Introduction
A cross docking terminal is an intermediate node in a distribution network which is
exclusively dedicated to the transshipment of truck loads. In contrast to traditional
warehouses, a cross dock carries no or at least a considerably reduced amount of stock.
Whenever an incoming truck arrives at the yard of a cross dock, it is assigned to a
dock door, where inbound loads are unloaded and scanned to determine their intended
destinations. The loads are then sorted, moved across the dock and loaded onto outbound
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Figure 1: Schematic representation of a cross docking terminal
trucks for an immediate delivery elsewhere in the distribution system. Figure 1 gives a
schematic representation of a cross docking terminal.
The primary purpose of a cross dock is to enable a consolidation of dierently sized
shipments with the same destination to full truck loads, so that economies in transporta-
tion costs can be realized (Apte and Viswanathan, 2000). This advantage makes cross
docking an important logistics strategy receiving increased attention in today's global-
ized competition with its ever increasing volume of transported goods. Success stories on
cross docking which resulted to considerable competitive advantages are reported for sev-
eral industries with high proportions of distribution cost such as retail chains (Wal Mart;
Stalk et al., 1992), mailing companies (UPS; Forger, 1995), automobile manufacturers
(Toyota; Witt, 1998) and less-than-truckload logistics providers (Gue, 1999).
In contrast to traditional point-to-point deliveries, an additional transshipment of
goods at the cross docking terminal slows down the distribution process and generates a
signicant amount of double handling. Consequently, ecient transshipment processes
are required where inbound and outbound truckloads are synchronized, so that interme-
diate storage inside the terminal is kept low and on-time deliveries are ensured.
For this purpose, several scheduling procedures have been introduced within the recent
years, which aim at solving the so called truck scheduling problem. This problem decides
on the succession of inbound and outbound trucks at a given set of dock doors of the
terminal. On the basis of the truck schedule, each inbound and outbound truck arriving
at the yard is assigned to a specic dock door where shipments are processed. Obviously,
this elementary problem consecutively arises during the daily cross dock operations and
has vital inuence on a rapid transshipment processes.
Dierent organizational and technical implementations lead to a large variety of possi-
ble truck scheduling problems in real-world settings. As cross docking is a comparatively
new logistics strategy, there is not yet a massive body of academic literature on this
subject. In fact, dedicated research on the short-term truck scheduling problem was
published no earlier than 2005 (see McWilliams et al., 2005). Due to the immense
practical importance, there has been a considerable amount of follow-up research in the
meantime, however, and we strongly assume that this trend continues in the future. On
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the one hand, this shows that we are in a formidable position to structure the eld in an
early stage of exploration, so that future research can be more easily coordinated. On the
other hand, this means that the classication scheme needs to be easily adoptable and
extendable, so that problem settings which have not yet been discussed can be readily
considered. We therefore base our classication of deterministic truck scheduling prob-
lems on the very successful and widely accepted tupel notation for machine scheduling
(Graham et al., 1976), provide a concise review on existing solution procedures and use
the insights to identify important elds of interest for future research.
The remainder of the paper is organized as follows. Section 2 denes the scope of this
review by characterizing the truck scheduling problem and establishing the relationship
to interdependent decision problems. In Section 3 the truck scheduling classication is
presented which is employed to review existing optimization models and solution proce-
dures in Section 4. In Sections 5 and 6, future research needs are specied. In particular,
a yet unexplored class of truck scheduling problems is introduced, which is highly relevant
in real-world cross docking applications, before Section 7 concludes the paper.
2 Scope of review
In general, scheduling problems deal with the allocation of resources over time to perform
a set of tasks being part of some process (e.g., Blazewicz et al., 2007, p. 1). In the special
case of truck scheduling, the process of transshipment can be subdivided into the tasks
unloading inbound trucks and loading outbound trucks, which are typically separated by
a time lag for material handling inside the terminal, i.e., for scanning, sorting and moving
shipments across the dock. These two tasks are to be processed by the resources dock
doors, which can process one truck at a time and are assumed to be suciently equipped
with loading equipment (e.g., hand stackers or fork lifts) and workers. Typically, truck
scheduling uses a time related objective function in order to evaluate a given solution.
As with other (operational) scheduling problems, cost consequences of task processing,
e.g., delayed deliveries inuencing customer satisfaction, are hard to quantify accurately,
so that a time related surrogate objective often turns out to be the better (operational)
choice. To conclude, a dispatcher of a cross docking terminal who seeks to solve a
truck scheduling problem faces two interrelated decisions bound to some (time related)
objective function:
where
and
when
the trucks should be processed at the dock doors of
the terminal.
This (positive) denition of truck scheduling is now amended with a (negative) de-
marcation from related (and possibly interdependent) decision problems. The decision
problems to be solved during the life cycle of a cross docking terminal ordered from
strategic to operational are as follows:
(i) Location of cross docking terminal(s)
(ii) Layout of the terminal
(iii) Assignment of destinations to dock doors
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(iv) Vehicle routing
(v) Truck Scheduling
(vi) Resource scheduling inside the terminal
(vii) (Un-)Packing loads into (from) trucks
The strategic problem (i) of locating a single cross dock (or some other kind of interme-
diate warehouse) or a complete distribution network consisting of multiple cross docks
is vividly discussed in scientic literature. A good starting point into location theory
investigating intermediate nodes in a network of sites are the reviews on the hub location
problem provided, e.g., by Campbell (1994) or Klose and Drexl (2005). In relation to the
location problem, truck scheduling merely considers an isolated terminal with a given
location.
The layout problem (ii) of a cross dock is investigated by Bartholdi and Gue (2004).
Here, the number of dock doors and the shape of the terminal building (e.g., I, T or
X-shaped) are to be determined. For truck scheduling, we presuppose a given terminal,
so that the number of dock doors and their placement along the perimeter of the terminal
are known. Consequently, the distance between any pair of doors is given, so that the
time lag for material handling (at least the load-independent part) between any pair of
doors can be anticipated accurately.
Typically, the truck scheduling problem presupposes that the assignment decision of
trucks (and the destinations they serve) to dock doors is part of the short-term problem,
so that each door may serve multiple destinations in varying succession per day depending
on the actual truck schedule. However, the assignment of destinations to dock doors
(problem (iii)) can also be executed on a mid-term horizon, with the result of each
dock door exclusively serving a specic inbound or outbound destination for a longer
period of time (e.g., a month). On the one hand, such a xed assignment eases the
allocation of shipments to trucks, since workers can learn the topology of the terminal
and respective information systems become superuous. On the other hand, a xed
assignment of doors to destinations restricts the degrees of freedom for short-term truck
scheduling, because peak loads for single destinations cannot be absorbed by additional
dock doors. Consequently, such a xed assignment seems especially suited for steady
commodity ows with a reliable distribution among inbound and outbound destinations.
Tsui and Chang (1990, 1992) were the rst to tackle the mid-term problem of assigning
doors to destinations. On the basis of a representative distribution of shipments among
related sites they solve the problem as a quadratic assignment problem, which minimizes
the shipment ows between doors. Other contributions for this problem stem from Gue
(1999), Bartholdi and Gue (2000), Bermudez and Cole (2001), Oh et al. (2006) as well as
Bozer and Carlo (2008). If the decision of assigning doors to destinations is solved at an
early (mid-term) stage, the short-term truck scheduling problem reduces to sequencing
all trucks of equal destination at the respective dock door. However, in either case there
remains a short-term truck scheduling problem. Typically, we assume that inbound and
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