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Improved Decentral Task Allocation for AGV Systems based on Karis Pro

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In this paper, our aim was to extend an existing decentralised method for allocating tasks to AGVs, by additionally considering vehicles which already are assigned to a task. This was achieved by also taking into account the opportunity costs arising from a vehicle passing a current task to another vehicle and subsequently accepting a new task. By means of simulation, our findings confirm the notion that our extended method – namely Karis Pro Plus – leads to lower traffic density and higher flexibility, both of which are important KPIs for large-scale transport vehicle systems.
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Improved Decentral Task Allocation for
Autonomous Guided Vehicle Systems
based on Karis Pro
Maximilian Selmair
BMW Group
80788 Munich, Germany
maximilian.selmair@bmw.de
Klaus-J¨
urgen Meier
University of Applied Sciences Munich
80335 Munich, Germany
klaus-juergen.meier@hm.edu
KeywordsTask Allocation; AGV; Karis Pro
Abstract—In this paper, we extended an existing decentralised
method for allocating tasks to AGVs, by additionally considering
vehicles which already are assigned to a task. This was achieved
by also considering the opportunity costs arising from a vehicle
passing a current task to another vehicle and subsequently
accepting a new task. This loosened restriction is enabling the
vehicle fleet for a higher flexibility, which can be used for
improving the efficiency of the overall system. By means of
simulation, our findings confirm the notion that our extended
method – namely Karis Pro+ (KP+) – leads to lower traffic density
and higher flexibility, both of which are important KPIs for large-
scale transport vehicle systems.
LIS T OF ABBREVIATIONS
AGV Automated Guided Vehicle
BMBF Bundesministerium f¨
ur Bildung und Forschung
(English: German Federal Ministry of Education and
Research)
FCFS first-come-first-serve
KIT Karsruhe Institute of Technology
KP Karis Pro
KP+ Karis Pro+
KPI Key Performance Indicator
MRPD Multi-robot Task Allocation for Pickup and Delivery
MRS Multi-robot System
MRTA Multi-robot Task Allocation
TeSSI Temporal Sequential Single-item Auction
VIidle vehicles
VPvehicles in pickup
VDvehicles in delivery
RAassigned transportation requests
RUunassigned transportation requests
I. INTRODUCTION
Greater efficiency, higher productivity and more flexibility
are some of the key objectives that govern today’s production
operations (Dorri et al. 2018). Consequently, these objectives
are the focus of strategic efforts regardless of company’s
industrial branch. Production and logistics have been identified
as the two areas in manufacturing companies that are especially
subject to meet these demands, which entails the necessity
for continuous innovation and improvements (Dorri et al.
2018). The main driving forces behind these objectives and
the associated requirements are the competitive pressure of the
market as well as customer demands for greater customisation
and individualisation (Leupold et al. 2018; Jazdi 2014). In
order to meet these requirements and to maintain a competitive
edge in its industry, new technologies for handling material
are in demand. Conventional material flow systems, seemingly
rigid in terms of layout and throughput, are therefore con-
tinuously becoming less suitable to meet industry standards.
The constantly rising demand for flexibility drives the de-
velopment of autonomous floor-bound vehicle systems. One
of these vehicle systems is the result of the research project
Karis Pro, introduced by Colling et al. (2016) as a ”modular,
decentralised controlled automated guided vehicle system”.
This task allocation system harnesses both, a decentralised job
creation system and a decentralised job allocation system. Due
to its flexible application, the developers state this system can
be employed with ease by the customer and without the need
for infrastructural adjustments. The decentralised control and
the autonomous nature of each vehicle forms a reliable system
that caters to the requirements of modern industrial processes
(Colling et al. 2016).
Karis Pro (KP) has been utilised in two industrial settings
under real-life conditions. An industrial pilot study, set in the
production lines, was successfully performed in corporation
with Bosch and Audi (see Figure 1). The use cases of au-
tonomous transport systems in this environment are driven
by the principles of lean production, in order to reduce the
produced and transported lot sizes as well as to increase the
frequency of arrivals and departures without having to increase
the number of required personnel (Trenkle 2016).
Particularly large-scale vehicle systems depend on highly
efficient organisation to avoid traffic jams and delays (Versteegt
and Verbraeck 2002). A means of achieving this may be to
allocate scarce resources, such as the number of available
vehicles, as efficiently as possible. Our developed method aims
to improve the established method of Colling et al. (2016) to
enhance the performance and efficiency significantly.
This paper is divided into the following sections. Section II
provides a review of the relevant literature, followed by an
introduction of the extended version of Karis Pro, namely
Karis Pro+ and an outline of the associated development ratio-
Fig. 1. Karis Pro AGV in an Industrial Use Case; Illustration from
amplify.pepperl-fuchs.com/de/inhalte/121/wo-die-dinge-ins-schwaermen-
geraten
nale. A description of a subsequent simulation study to validate
the improvements in Section IV precedes the conclusion in
Section V.
II. RE LATE D LITERATURE
In academia, the issue of task allocation to agents is known
as the Multi-robot Task Allocation (MRTA) problem or, more
specific to the use-case of this study, the Multi-robot Task
Allocation for Pickup and Delivery (MRPD) problem. The
MRPD defines an extension of the widely studied MRTA
problem which assumes each task as a single location to
visit (Heap and Pagnucco 2013). By definition, a Multi-robot
System (MRS) describes a group of agents that are assigned
to perform a collective behaviour (Khamis, Hussein, et al.
2015). Due to its high industrial academic relevance, one of
the major topics of research in the area is the multi-robot
task allocation problem. That is the problem of dividing tasks
across robots so that some objective of interest is optimised
(Nunes, Manner, et al. 2017). Referring to Gerkey and Matari´
c
(2004), this particular MRPD problem can be described as
ST-SR-IA (single-task robots, single-robot tasks, instantaneous
assignment).
Contributions around MRTA are utilised in many different
industries, such as for fleets of cooperated unmanned aerial
vehicles (Moon et al. 2015; Bellingham et al. 2003; Innocenti
et al. 2010), maritime industry (B˘
adic˘
a et al. 2018), manufac-
turing automation (McIntire et al. 2016), robots for refinery
inspections (Liu and Kroll 2012) and areas where it is either
too expensive or dangerous for humans to work (Nagarajan and
Thondiyath 2013; Khamis and ElGindy 2012). In order to find
a suitable solution for the task allocation problem, the literature
proposes several different concepts. The review of the literature
indicates that the most used and state-of-the-art solution for a
large-scale decentralised system in order to achieve satisfactory
performance is the agent-based auction mechanism. Auctions,
in any form, have been used in societies throughout history to
allocate scarce resources among interested parties (Gerkey and
Matari´
c 2002). Consequently, auctions have received a great
deal of attention from economists, and a rich body of theory
exists regarding their properties, especially their ability to deal
with uncertainty (Akerlof 1970; Holt 1979).
For common industrial applications, agents such as robots
or vehicles, bids on tasks by calculating the amount of effort
needed to perform them. In most cases, the effort depends on
the distance between the agent location and the task location
plus any additional cost for doing the task itself, such as
resources consumed (e. g. time spent) in doing the task (Nunes
and Gini 2015). The agents act as bidders and stations as
sellers. Thereupon, the agents submit their bids and, depending
on this, receive an acceptance or refusal (Schwarz et al. 2013).
The smart coordination of groups of robots is an important
topic in this context, as significant amount of resources can
be saved when robots work together. While this does not
necessarily mean that the robots conduct their tasks together
in teams, but they do adjust their actions to each other (Gerkey
and Matari´
c 2002).
One should also pay attention to spatial and temporal con-
straints, as many tasks have to be executed in a specified time
window in industrial practice, as well. For this reason, the Tem-
poral Sequential Single-item Auction (TeSSI) algorithm was
developed (Nunes and Gini 2015; Nunes, Manner, et al. 2017).
In addition, B˘
adic˘
a et al. (2018) proposed an “intelligent”
freight broker agent which uses a mathematical optimisation
service to compute the optimal schedule of vehicles fulfilling
customer requirements.
Using heuristic-based task allocation algorithms is another
strategy to solve such a task allocation problem (Jennings
et al. 2001; Windelinckx and Strens 2004; Nagarajan and
Thondiyath 2013). Such static approaches usually require that
the announced tasks and the available vehicles are known prior
to the actual calculation and scheduling phase. As this is not
the case for a decentralised control setting, these approaches
are of no interest for this research (Schwarz 2014).
Summarised, agent-based methods like negotiations (e. g.
auctions) are an appropriate and established method for proac-
tive allocation of tasks to vehicles (Lagoudakis et al. 2004;
Tovey et al. 2005). One showcase project for a decentral
task allocation will be presented in detail in the next section.
Furthermore, Karis Pro will be enabled for the idea of differ-
ent traveller assignment strategies, presented by Hyland and
Mahmassani (2018).
III. KAR IS PRO A ND THE TRAVELL ER AS SI GN ME NT
STR ATEG IE S
Karis Pro is a research project of the Karsruhe Institute
of Technology (KIT), which was carried out between 2013
and 2016 with the support of the German Federal Ministry of
Education and Research (BMBF).
As opposed to the centralised methods, the process of
allocating tasks to vehicles within the Karis Pro system takes
place without the involvement of a central control unit. Instead,
the vehicles carry out auctions in order to determine which
vehicle should handle which task (Trenkle 2016). After a task
is generated, it is automatically entered into a list that ranks
all tasks according to a specific priority. The tasks with the
highest priority can be found at the top of the list. As Colling
et al. (2016) has not specified which priority was used in
their approach, different criteria for the priority rule could be
selected depending on the underlying specifications. Possible
examples of these priorities are:
Date of task generation, i. e. according to the first-come,
first-served rule, the oldest tasks have the highest priority
Deadline when a task has to be fulfilled, i. e. tasks closer
to the deadline have a higher priority
Distance between origin (source) and destination (sink),
i. e. shorter distances have a higher priority or vice versa
Pre-determined rules, i. e. certain source-sink relations are
more critical and have thus a higher priority
The tasks are assigned to vehicles just before their execu-
tion, which means that each vehicle receives only one task at
a time. The task allocation process begins when one of two
events takes place. Either a vehicle has just finished its task and
there are tasks left on the list, or a vehicle is idle and a new task
appears on the list. In both instances the vehicle chooses the
task with the highest priority and begins the auction process.
During the first step of the auction, the vehicle that started
the auction calculates its own bid. Subsequently, it contacts
all other vehicles and asks them to submit their bids. These
vehicles can be categorised as follows:
1) Idle: Without a task
2) Pickup: Vehicle is currently driving to a source to pick
up a task. This can also be described as an ”empty drive”
as it is not adding value
3) Delivery, without reservation: Vehicle is currently trans-
porting a task to its sink and is not reserved for a
subsequent task.
4) Delivery, with reservation: Vehicle is currently transport-
ing a task to its sink and is reserved for a subsequent
task.
Under the constraints of Karis Pro, vehicles from Cate-
gory 1 (Idle) and Category 3 (Delivery, without reservation)
will respond with a bid to the auctioning vehicle. The bid
itself is given in number of seconds and is either appraised or
calculated by adding the following values:
1) The expected remaining time required to fulfil the current
task (only for vehicles of Category 3)
2) The expected time to reach the source of the new task
(for vehicles of Categories 1 and 3)
Therefore, the bid is the amount of time it would take
each vehicle to reach the source of the new task. After having
received all bids, the auctioning vehicle determines the most
efficient vehicle, which can lead to either one of two outcomes.
The vehicle itself is the most suitable for the task (i. e. the
lowest bid) or another vehicle is more favourable. In the first
case, the auctioning vehicle immediately begins to execute the
task and informs the other vehicles that it was awarded with
the task. In the second case, the auctioning vehicle informs the
winner that it has won the auction. Subsequently, it chooses
the next task on the list and commences a new auction. The
auctioning vehicle continues to repeat the auctioning process
until it either wins an auction, there are no more tasks left on
the list or no other vehicles remain to participate in auctions.
The upcoming presented contribution deals with assign-
ment strategies, which are a substantial part of task allocation
methods (Nunes, Manner, et al. 2017). Hyland and Mahmas-
sani (2018) have compared different assignment strategies for a
share-use autonomous vehicle mobility service. In this setting,
the vehicles are controlled by a central unit. This information
0 20 40 60 80 100
0
500
1,000
1,500
2,000
2,500
vehicles (vehicle / task ratio 1 : 1)
average number of bids per auction
Origin KP KP+ v1 KP+ v2
Fig. 2. Average Number of Bids per Auction (5,000 Samples)
hub provides a direct origin-to-destination service to travellers
who request a ride, or, if one were to apply this to the
environment of our research, for a source-to-sink service of
a load carrier.
Table I summarises the different strategies compared by
Hyland and Mahmassani (2018). The first two assignment
strategies are basic first-come-first-serve (FCFS) strategies
with different objectives, to either minimise waiting time
or travelling distance. Here, unassigned travellers (RU) are
assigned to idle vehicles (VI). The other four optimisation
strategies consider different combinations of idle vehicles,
vehicles in pickup (VP) and vehicles in delivery (VD) as well
as the variables unassigned or assigned travellers (RA). In
order to generate the most efficient outcome in light of the
given objectives, a mathematical solver is used to identify
the most suitable allocation. The optimisation-based strategies,
especially those that involve the reassignment of already
assigned travellers (RA), significantly outperform both FCFS
assignment strategies.
More specifically, the results of their simulation study
indicate that Strategy 6 unambiguously outperforms all other
strategies in terms of empty fleet miles in all of the examined
scenarios. In terms of traveller waiting times, Strategy 6 is
deemed to be more efficient when the fleet size is small
relative to the demand rate. For large fleet sizes like 200+
vehicles, Strategy 3 and Strategy 4 outperform Strategy 5 and
Strategy 6 in terms of traveller waiting times. It is proposed
that Strategy 5 in Table I corresponds to the current Karis Pro
method.
IV. METHODOLOGY
The basic methodology to achieve this research’s objective,
is to compare the existing method of Colling et al. (2016) with
our extended version, namely Karis Pro+. This comparison is
accomplished by means of a simulation study in which the
agent-based modelling paradigm is used.
The software AnyLogic is chosen for this purpose, as it
supports the paradigms of agent-based modelling and thus
TABLE I. OVE RVIE W OF TR AVELL ER AS SI GNM EN T STR ATEGI ES ( HY LA ND AN D MAH MA SSA NI 2018)
∑∑
−+
dx γwx φpxmin ( )
xiR jV
ij ij i ij jij
ij (13)
4.6. Strategy 6
In the sixth and nal strategy, unassigned and assigned travelers ( =∪
i
RRR{}
UA
) as well as all AVs (idle, en-route pickup, and
en-route drop-o,
=∪
j
VVVV{}
IPD
) are considered in the assignment problem. Strategy 6 combines the valuable additions in
Strategy 4 (traveler reassignment and AV diversions) and Strategy 5 (inclusion of en-route drop-oAVs in AV-traveler assignment
problem) to the base optimization-based assignment strategy, Strategy 3. The AV-traveler mathematical programming formulation
associated with Strategy 6 includes the constraints in Eqs. (10) and (11) as well as the additional terms in Eqs. (12) and (13).
The right side of Fig. 7 shows the results of allowing AV diversions (AV 5is diverted from traveler 2to traveler 3), traveler
reassignment (traveler 2is reassigned from AV 5to AV 4), and two-person schedules (AV 1is assigned to pick up traveler 4, as it is en-
route to drop otraveler 1). For this problem instance, the total eet mileage associated with Strategy 6 is 5.4 miles.
Table 1 distinguishes between the six AV-traveler assignment strategies. Section 6compares these six AV-traveler assignment
strategies on much larger problem instances. As the problem is dynamic and stochastic, it is not possible to guarantee any other
strategy will perform the best. Hence, a variety of scenarios are presented in the computational results section, to empirically
compare the six strategies.
5. Agent-Based simulation framework
This section briey describes the agent-based simulation framework developed to model the dynamic system of AVs, travelers,
and intelligent SAMS eet operator. The simulation is coded in Python 3.5.1 (Python, 2017). The Gurobi 7.0.2 optimization solver
(Gurobi, 2017) is embedded in the Python simulation model and is used to solve the AV-traveler assignment problem for Strategy 3
through Strategy 6. Gurobi is a state-of-the-art mathematical programming solver; however, the assignment problem is a relatively
easy problem to solve.
5.1. Inputs
The analyst denes the area size, length of the analysis period (
T
), and spatial-temporal demand rate of traveler requests (
λ
). With
this information, a random number generator is employed to generate traveler origin locations (
i
), destination locations (
d
i), and
request times (
r
i
) for each traveler
iR
.
In this paper, AVs travel on a Manhattan network (i.e. a grid-based network with omnipresent streets), which is an abstraction of
an urban road network. The AVs travel at a constant speed (v)dened by the analyst. The locations of the AVs, and travelers in the
AVs, are updated every time step (
t
Δ
). Smaller
t
Δ
values better represent continuous time; however, they increase the computer
simulation time. The analyst must also set traveler drop-otimes (c
d
) and pickup times (
c
p
).
In a single simulation run, to model the SAMS eet operator, it is necessary to choose an inter-assignment time (
h
), one of the AV-
traveler assignment strategies presented in Section 4, the SAMS eet size, and several parameters in the AV-traveler assignment
problem. These parameters include the weight of elapsed wait time relative to travel distance (
γ
), the penalty for assigning a traveler
to an en-route drop-oAV (
φ
), and the penalty for assigning a traveler to an en-route pickup AV (
δ
). Additionally, the analyst needs
to provide the start location of each AV; this study assumes the AVs start in the middle of the service region.
5.2. Simulator
The agent-based simulation tool models the dynamic behavior of and interactions between travelers, AVs, and the SAMS eet
operator. The SAMS eet operator is the only intelligentagent in the simulation; it makes decisions to assign AVs to travelers.
Fig. 8 displays an overview of how the simulation model updates the positions and states of travelers. The simulation is time-
driven; at each time step (
t
Δ
), the simulation updates the position and state of travelers. The simulation rst updates the position of
in-vehicle travelers (
R
IV
) by moving each traveler
i
R
IV
one step ( ×tv
Δ
) towards her destination
d
i. After moving traveler
i
, the
Table 1
Overview of AV-traveler assignment strategies.
Strategy Travelers (R)Vehicles (
V
)Sequential/Simultaneous Traveler Reassignment? En-Route Drop-off
1 First-Come-Frist-Serve RU
V
I
Sequential No No
2 First-Come-First-Serve RU
V
I
Sequential No No
3 Optimization RU
V
I
Simultaneous No No
4 Optimization U RRA
V V
IP Simultaneous Yes No
5 Optimization RUVI VDSimultaneous No Yes
6 Optimization URRAVIPVVDSimultaneous Yes Yes
M. Hyland, H.S. Mahmassani Transportation Research Part C 92 (2018) 278–297
288
KP KP+ v1 KP+ v2
0
500
1,000
1,500
2,000
2,500
allocation method
number of bids per auction
Fig. 3. Bid Requests for a large-scale Scenario of 100 Vehicles / 100 Tasks
(5.000 Samples)
the architecture of a multi-agent system. With its ability to
combine several simulation methods (discrete-event,agent-
based and system dynamics), it fulfils, as the only software
that features multi-method simulation modelling, the basic pre-
requisites for this research project. A combination of discrete-
event and agent-based methods is proposed for the simulation
study, as the performance of both methods can be examined
in a risk-free environment.
The limitations of AnyLogic are of a general nature. As
the software is proprietary and not open-source, the project
depended on the provision by the AnyLogic Company. Fur-
thermore, the project is bound to Java implementations for
database applications or extensions (e. g. algorithms or model
implementations). It is unlikely that either of these limitations
will influence the feasibility of this project. General limita-
tions that apply to the discrete-event simulation and agent-
based modelling, relate to the level of detail with which the
simulation is constructed (Mes et al. 2008; Heger and Voss
2018).
V. DR AF T OF KARIS PRO+
Motivated by the informative simulation study of Hyland
and Mahmassani (2018), our goal was to extend the Karis Pro
task allocation method by permitting the reassignment of
already allocated tasks. That is, vehicles that are currently
driving to collect a load have to be able to diverge towards
a new task and pass the one currently assigned to another
vehicle to ensure that this task won’t be late or forgotten. Also,
vehicles already carrying a load have to be able to change their
reservation for the subsequent task if this is beneficial for the
objective in the overall system.
The main difficulty is the decision when to reallocate an
already assigned, but not initiated, task on to another vehicle,
while allocating the new task to the formerly assigned vehicle
so that the overall system benefits from this change. For this
purpose, it is important to determine the opportunity costs, the
costs accrued due to a reallocation, from an overall perspective.
These costs in combination with the potential effort, more
specifically time or distance a vehicle needs to travel, are
used to formulate a key performance indicator to support the
decision-making process.
A. Opportunity Costs
Opportunity costs have to be considered whenever a vehicle
has to pass an assigned task on to another vehicle. In our case,
two potential outcomes may arise when a new task is auctioned
and is subsequently assigned to one of the following vehicles:
1) A vehicle which is currently driving to pick up its
assigned task (pick up task). This pick up task can be
passed on to another vehicle and is then substituted by
the new task.
2) A vehicle with a loaded task (delivery task) and a subse-
quent reservation (reservation task). Here, the reservation
task can be passed on to another vehicle.
Due to the decentralised organisation, an increased flow
of information is required between the vehicles in order to
determine the opportunity costs: A vehicle, that intends to
determine the opportunity costs of a currently assigned task,
has to query all other vehicles for bids in an effort to determine
which vehicle is going to perform the task. Due to the nature
of this process, the process chain may well end in an infinity
loop. That is, in order to ascertain these costs, the query is
going to include vehicles that also have to calculate opportunity
costs and therefore also have to query other vehicles. At this
point, it is necessary to include only those vehicles in the
calculation of opportunity costs that can provide an answer
without again considering opportunity costs, i. e. vehicles in
an idle state or a delivery state without reservations. Figure 2
shows the resulting bids of Version 1 of Karis Pro+ in red. The
method can therefore be classified as not scalable (Lirkov and
Margenov 2018). More than 1,600 bid calculations per tasks
are required in a system with 80 vehicles in the system, in
some cases even more.
Consequent to the primary feasibility assessment of Ver-
sion 1 of Karis Pro+ described above, KP+ was adapted
Vehicle
(delivering 1)
Source
1
Sink
1
Source
2
Sink
2
Time-based effort
Way-based effort
Fig. 4. Illustration of the time-based and the way-based Calculation of Effort
to Version 2 in order to reduce the number of necessary
bid calculations. In Version 2 the opportunity costs are only
determined if the best bidder has to determine the opportunity
costs to establish the total costs for the system, i. e. pickup
mode or delivery mode with no reservation. The reduction of
the number of bid calculations from and KP+ v1 to KP+ v2
are substantial as is illustrated in Figure 2 and Figure 3.
B. Priorities and Calculation of Effort
In the following simulation study, which was performed
as a case study in the automotive sector, schedules play
an important role. To ensure that all tasks are delivered on
time, while utilising the temporal flexibility of each task in
the planning process, Karis Pro+ operates with two types of
priorities (priority and no priority). Whenever a task is in
danger of being delayed, it will receive a priority flag, which
will position it on the first ranks of the task list.
Furthermore, the calculation of the effort required for a ve-
hicle to fulfil a specific task depends on its priority status. That
is, all calculations for priority tasks are time-based, whereas
the effort for no priority tasks is based on the distance a vehicle
has to travel. This important differentiation ensures that priority
tasks will be performed as fast as possible regardless of the
distance it would need to travel. Both calculation methods are
depicted in Figure 4. The time-based effort is measured in
seconds from the present to the estimated time of arrival at
the new task source (Source 2 of Figure 4). However, the way-
based effort is measured in meters from the current task’s sink
(Sink 1) to the new task’s source (Source 2). Both calculation
methods ensure that tasks without priority are delivered with
the least traffic possible and tasks with priority as fast as
possible.
Depending on this priority setting, each vehicle calculates
its own effort in seconds or meters and – if requested – the
opportunity costs. Table II illustrates the bid composition for
different priority combinations for the newly auctioned task
and the currently assigned task of the vehicle.
VI. SIMULATION STUDY
The following section describes the simulation study, which
was carried out to compare the performance of KP and KP+.
The software AnyLogic version 8.6, was used to model the
environment and all processes. In the upcoming subsections,
TABLE II. COMPOSITION OF BIDS REGARDING NEW TAS KS A ND
CURRENT TASK SPRIORITY
New Mission Current Mission Bid Composition
(auction)
(pickup / delivery
with reservation)
Only own Effort (time-based)
Own Effort + Opporunity Costs
(both way-based)
Own Effort + Opporunity Costs
(both time-based)
No bid calculated
Priority
the simulation setup, the parameters and the results will be
presented in detail.
A. Setup and Parameters
Tasks were carried out by a predetermined number of
vehicles. All vehicles were positioned at an initial location
at a random point beside the road network, also referred
to as fit-point. Tasks appeared at random fit-points, however
parameters were set to avoid clustering of such. Each task
was assigned to a sink at a random free fit-point with a
minimum linear distance of 1
/3of the total layout dimensions.
The total number of tasks in the system was also limited by
the parameter Task Pool for each simulation run. Therefore,
whenever a task was completed, a new task appeared at another
random fit-point. This logic ensured a constant utilisation of
the vehicles, adjustable by the ratio between two parameters:
number of vehicles and size task pool. When a task appeared,
a random deadline between 20 and 30 minutes was set. This
parameter was chosen to have a meaningful pressure on the
system. Seven minutes prior to this deadline, a task was
prioritised if had not already been collected by a vehicle.
Priority tasks were collected by the closest vehicle and not,
as is the case for non-prioritised tasks, by the vehicle with the
least way–based effort. This parameter was chosen through
preliminary studies in the same layout and ensures that tasks
are not delayed.
B. Scenarios
The study compares the Karis Pro and Karis Pro+ methods
in scenarios incorporating a variety of scale and utilisation
levels. We selected scenarios with 5, 30, 80 and 100 vehicles,
thus providing differing scale levels and combined these with
differently sized task pools to generate varying load factors.
Three alternative task pools were chosen and applied to each
vehicle pool size: one with the same number of tasks as number
of vehicles, one with 20 % fewer and one with 20 % more
tasks than vehicles. Each described scenario was calculated
with both methods KP and KP+ and 5,000 tasks.
C. Results and Discussion
The results of the simulation study are presented in the
following section. The statistics are utilised to compare the task
allocation methods Karis Pro and Karis Pro+ for the differently
scaled scenarios.
Figure 5 illustrates the average utilisation for both alloca-
tion methods and the three different workload ratios. A vehicle
is said to be utilised when it is either collecting a load or
delivering a load. For all scenarios, KP+ has a lower utilisation
1 : 0.8 1 : 1 1 : 1.2
0
20
40
60
80
100
workload ratio [vehicles / tasks]
avg. utilisation [%]
Origin KP KP+ v2
Fig. 5. Average Utilisation for each Workload and Allocation Method
5 30 50 80 100
0
50
100
vehicles (vehicle / task ratio 1 : 1)
avg. bids per task
Origin KP KP+ v2
Fig. 6. Average Bids per Task for a Vehicle/ Task Ratio of 1 : 1 (5,000
Samples)
0 20 40 60 80 100
0
500
1,000
1,500
2,000
vehicles (vehicle / tasks ratio 1 : 1)
throughput [tasks / h]
Origin KP KP+ v2
Fig. 7. Throughput measured in Tasks per Hour for KP and KP+v2 (5,000
Samples)
than KP. No tasks were delayed, and all requirements were
met in all of the scenarios. The lower utilisation rate can be
explained by the fact that KP+ allocates tasks in advance.
That is, vehicles already underway can be scheduled for a
subsequent task, instead of activating an idle vehicle which
would be associated with greater effort.
Corresponding with the lower utilisation of KP+, the
throughput, given in tasks per hour, is also lower for KP+
than KP (see Figure 7). As all requirements are met in all
KP+ scenarios, this finding can deem to be of secondary
importance. KP+ makes use of the temporal flexibility of each
task’s deadline to execute it with the least necessary effort in
terms of meters travelled per task. This finding is represented
in Figure 8. The original KP method has a significant higher
way-based effort to process tasks than KP+ (between 7 % and
23 %).
The required communication effort, represented by bid
requests per task, was also evaluated. It might seem self-
evident that KP+ should require more communication between
the vehicles than KP, since vehicles bid in every mode and not
only in idle or delivery mode. For a vehicle / task ratio of 1 : 1,
the communication effort is illustrated in Figure 6.
VII. CONCLUSION
Motivated by the contribution from Hyland and Mahmas-
sani (2018), this study has introduced an alternative decen-
tralised task allocation method based on Karis Pro (Colling
et al. 2016), which has been proven to be superior, namely
Karis Pro+. When auctioning a task, this version also considers
vehicles that are either already performing a task or are re-
served as a potential resource for a subsequent one. The aim of
this study was to determinate opportunity costs for the overall
system and use them to make better decisions for reaching
the objective. By using the same bidding system as Karis Pro,
every vehicle is able calculate the effort required for passing a
task on to another vehicle. This feature improves the flexibility
of the system by a substantial margin. The presented simulation
0 20 40 60 80 100
0
20
40
60
80
100
vehicles (vehicle / tasks ratio 1 : 1)
average pickup meters per task [m]
Origin KP KP+ v2
Fig. 8. Average Number of driven Pickup Meters per Task for a Vehicle / Task
Ratio of 1 : 1 (5,000 Samples)
study supports the notion that using Karis Pro+ instead of
Karis Pro leads to less empty drives and subsequently to a
higher efficiency of the vehicle fleet. Consequently, it is sug-
gested that a larger capacity buffer, resulting from this higher
efficiency, may lead to higher flexibility for task peaks. This
is turn may prevent traffic issues in large scale applications
as the same goals may be achieved with lower traffic density,
in comparison to the original allocation method of Karis Pro.
Accordingly, the communication effort to reach this outcome
is much higher than for the original method. Nevertheless, the
developed simulation study demonstrated that Karis Pro+ in
its final version can be considered to be a scalable method.
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AUTHOR BIOGRAPHIES
Maximilian Selmair is a doctoral student at the University
of Plymouth. Recently employed at the SimPlan AG, he was
in charge of projects in the area of material flow simulation.
He is currently working on his doctoral thesis as a part
of a fellowship of the BMW Group. His email address is:
maximilian.selmair@bmw.de and his website can be found at
maximilian.selmair.de.
Prof. Dr. Klaus-J¨
urgen Meier holds the professorship for
production planning and logistic systems in the Department
of Engineering and Management at the University of Applied
Sciences, Munich, and he is the head of the Institute for Pro-
duction Management and Logistics (IPL). His email address
is: klaus-juergen.meier@hm.edu.
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