974 Part F Industrial Automation
tion; those authors transform this nonlinear function
to a piecewise-linear function to make the problem
tractable. Lau and Zhao [55.4] study a joint job schedul-
ing problem for the automated air cargo terminal at
Hong Kong, which is mainly composed of AGV sys-
tems, AS/RSs, cargo hoists, and conveyors. In the
model, activities between different AMHSs are trig-
gered by communication between the systems. The
scheduling algorithm constructs a cooperative sequen-
tial job served by different AMHSs, employing the
maximum matching algorithm of the bipartite graph.
A task for an AGV is assigned or matched to an stacker
crane (SC) to reduce the SC delay time. A similar prob-
lem is solved by Meersmans and Wagelmans [55.5].
Their research focuses on the scheduling problem of the
IAMHS in seaport terminals employing a local beam
search algorithm. The nodes explored in the search al-
gorithm are represented by a sequence of container IDs
to be processed by different AMHSs, and the nodes in
branches are cutbased onthe beam widthdetermined by
an evaluation function. Those authors prove that there
existsan optimalsequence of tasks forone AMHS when
the sequence is assigned to the other AMHS.
Sujono and Lashkari [55.52] study another inte-
grating method allocating a part type to a processing
machine and material handling (MH) equipment type
simultaneously in a flexible manufacturing system
(FMS). In that research, there are nine different types
of the material handling systems in the experimental
model. The method improves the algorithms proposed
by Paulo et al. [55.53]andLashkari et al. [55.54]and
uses a 0/1 mixed integer programming model. Two ob-
jective functions are modeled: one minimizes operating
costs related to machine operations, setup, and MH
operations; the other maximizes the compatibility of
the part types using MH equipment types. To measure
compatibility, parameters are quantified from the sub-
jective factors defined by Ayres [55.55]. Some of the
constraints are: balance equations between parts and
process plans, machines and process plan, processing
machines, and MH equipment types. The other impor-
tant constraint sets are capacity constraints: the total
load of the allocated tasks for an MH equipment type
cannot exceed its capacity, and a machine cannot be
allocated more than its capacity. A test problem con-
sisting of 1356 constraints and 3036 binary variables
was solved in about 9.2s by using LINGO in a Pen-
tium 4 PC. Since this model considers many details of
the practical factors in the FMS, and showed a suc-
cessful calculation result, it can be used for many other
practical applications.
In addition to the examples shown above, large-
scale optimization problems such as the vehicle routing
problem (VRP), vehicle scheduling problem (VSP), and
integrated scheduling problem of IAMHS
with con-
sideration of processing machines have been modeled
to increase MHA efficiency. However, to be used for
actual applications and thereby achieve a higher-level
MHA, shorter computation times are urgently required.
In a complicated IAMHS, integrating software pack-
ages such as the MMS need sophisticated algorithms;
however, it also needs high reliability in a dynamic en-
vironment. For most tasks, real-time decision-making
that requires response times within a few seconds is
a precondition for IAMHS algorithms.
MMS-related Issues
The MMS is a key component to integrate different
AMHSsinanIAMHS. Destination allocation, routing
algorithm, and prioritizing algorithm are essential roles
of the MMS, among others. Graph theory is popularly
used to represent components and relationships in the
IAMHS.InFig.55.6, nodes represent the AMHSsand
their subcomponents, such as load/unload ports. Edges
represent the connection and distance between nodes.
As mentioned above, this graph is stored in database
tables using the adjacency and incidence matrices. The
shortest-path algorithm isthe mostimportant and funda-
mental algorithmfor an MMS since it is usedfor several
purposes in the system such as destination assignment
and best routing determination. Dijkstra’s algorithm is
popularly used [55.56]. The Bellman–Ford algorithm
can be used if there are negative weights of the edges.
To determine the final destination of a unit load,
the MMS has to evaluate various factors on the same
scale. More specifically, to determine an AS/RS as the
final destination among several alternatives, the shortest
distance is generally the most important criterion; how-
ever, the full rates of the AS/RSs are sometimes also
important to make the loads balanced between different
AS/RSs. There are two applicable ways to standard-
ize different scales of factors on the same scale. First,
different weight values can be applied for each factor
to find the best alternatives. Second, a priority and its
threshold value can be givento each factor, and the most
important alternativeis selectedif it is within the thresh-
old, otherwise the next alternative will be considered.
Determining the best route from a source to desti-
nation location via several AMHSs is relatively simple
when compared with the vehicle routing problem(VRP)
or vehicle schedulingproblem (VSP), becausethe graph
generally has a smaller number of nodes than those of
Part F 55.3