Heuristic-Based Hybrid Algorithm for Value Stream Design with Milk-
Run Approach
SAFIYE TURGAY, CANBERK ÇOBAN
Department of Industrial Engineering,
Sakarya University,
54187, Esentepe Campus Serdivan-Sakarya,
TURKEY
Abstract: - In this study, a heuristic algorithm has been developed for the Milk-Run related to the vehicle
routing problem. It aimed to supply in the right place and at the right time in a short time with the internal
logistics system approach. Since the proposed problem formulation is NP-hard, we suggested a heuristic-based
hybrid genetic algorithm method to solve the problem. Real life problem is solved with a milk run approach
inspired by vehicle routing problems. Firstly the model was developed with mixed integer linear programming
then the problem was solved with the proposed hybrid genetic algorithm. The aim reduce the total
transportation cost in the network and the number of vehicles required by using an efficient vehicle routing
strategy. It explains the change in the existing distribution and collection systems of a logistics service
company. The response of variables such as time, weight, volume, and pallet was measured under various
scenarios with cost and time savings by applying Milk-Run optimization. The deterministic model and the
proposed heuristic algorithm compared the previews and outputs of the paths. Accordingly, 30% and 50%
discounts were made on restrictions for six different scenarios.
Key-Words: - Milk-run Systems, Vehicle Routing Problem, Integer Programming; Genetic Algorithm, Stream
Design, Optimization, Heuristic Algorithm.
Received: August 9, 2023. Revised: March 11, 2024. Accepted: May 1, 2024. Published: May 17, 2024.
1 Introduction
The milk-run system provides cyclical deliveries of
smaller lot sizes with short lead times and low
inventory at points of use, especially during short
distance, low inventory, and short time supply
processes. It is a repetition event with iterative
rounds of short duration. However, the time, the
place of delivery, and the product quantity
information are uncertain. Our aim formulate and
schedule iterative tours in a fixed order and
according to a fixed schedule with fixed arrival
times. The main goal is for an optimal periodic
distribution policy, which determines who will be
served, how much will be delivered, and which
routes will be repeated regularly to travel with
which fleet of vehicles. Milk run routing and timing
issues are NP-hard, it can be solved using heuristics.
Solutions can be derived, for example, from milk
distribution policy when determining whether tours
are scheduled cyclically in the Milk-Run approach.
Before a product is delivered to the procurement
note, it may stop at more than one supplier point.
The changing orders may also cause an instant
dynamic in the product quantities at the supply
points. Before a product is delivered to a customer
or a consolidation center, it passes through multiple
suppliers. The order-and-repeat system reduces the
variability of processes and transport costs with the
Milk Run. It allows the transfer of less product with
frequent cyclic dispensing, time, and more frequent
turnover compared to point-to-point transfer which
is another advantage. Field guidance services,
shorter transfer times, and a more transparent
process until delivery to the customer positively
affects quality is the comparable benefits. Which
product will be delivered in how much, to which
point, and with which vehicle in the Vehicle
Routing Problem (VRP). The problem of NP-hard
routing and scheduling creates a service plan that
specifies how much a given fleet of vehicles should
deliver and what cyclical routes vehicles must
follow to deliver the required materials on time. A
heuristic approach was proposed for solving the
VRP, NP-hard vehicle routing and scheduling
problem. While low volume and short delivery time
cargoes are distributed with the milk run approach,
which we call bound logistics, the cargoes collected
at the collection centers are shipped with larger
vehicles for large volume cargoes. The mixed
integer linear programming model and heuristic
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1262
Volume 21, 2024
algorithm are proposed for the optimization process
of the problem. To achieve this goal, we are
designing a new model that combines low-volume
loads through cross-docking and/or dairy logistics
and allows high-volume loads to be shipped directly
from parts suppliers to assembly plants. In effect,
this model decides how to route and consolidate
each supplier's load to each assembly facility in the
network, minimizing the need for vehicles to
perform the transport. Therefore, a proposed integer
programming model has been addressed to the
problem, but its complexity and NP-complete nature
require a combination of heuristic and meta-
heuristic optimization algorithms to solve it, which
is performed with a hybrid genetic algorithm (GA)
in this study.
The stocks of the supply units will be reduced
and this may increase the chance of competition
among the competitors by affecting the sales prices
due to its cost with this method. The main
contributions of this study can be summarized as
follows:
1) A real milk run problem in Istanbul has been
solved by taking into account the milk run approach
and vehicle route structure.
2) We proposed a mixed integer linear programming
(MILP) model with a hybrid genetic algorithm that
discusses the milk run approach in detail.
3) Contrary to generally accepted assumptions,
transport processes have a deterministic structure.
To evaluate the effectiveness of the variants, the
relevant delivery times are taken into account and
more realistic results are obtained with the help of
the proposed model.
4) We suggested a hybrid genetic algorithm to solve
the MilkRun model. The proposed approach has
taken into account the structure of large and small
truck fleets. While the small trucks perform the
rotation process in the cycle consisting of more
frequent points, the large trucks perform the product
purchase process in order not to interrupt the cycle
process at the point where the small truck completes
the cycle. A large truck begins and ends its journey
at the factory, while a small truck performs the cycle
process to perform intermediate stock and
distribution operations.
The remainder of the paper is structured as
follows: section 2 presents a literature review of
relevant milk collection issues. Section 3 gives
details about the specific milk transport issue
associated with collection centers. Section 4 shows
the MILP model and a sequential three-step solution
approach. Section 5 illustrates the main components
of the ILS approach. Section 6 explains the
conclusions. Finally, Chapter 7 demonstrates the
results and develops some ideas for future research.
2 Literature Survey
VRPs are combinatorial optimization problems that
distribute goods or services to various destinations
as a Traveling Salesman Problem. Indeed, in VRPs,
a set of vehicles must serve a set of pickup/delivery
points and meet predefined constraints that allow
the possibility of minimizing various targets such as
cost, distance or time. Therefore, VRPs are often
NP-hard problems for which no effective solution
has been found so far, [1], [2]. In this study, the
evaluation of loading and unloading points by time
criteria, will provide a solution to the constraint-
based vehicle routing and scheduling problem, [3],
[4].
In the milk-run system, routes, timetables, and
the type and number of parts to be transported are
assigned to different logistics trucks. Therefore,
trucks can collect orders from different suppliers,
[5], [6], [7]. The benefits of using this type of
system include increased efficiency of the overall
logistics system and significant potential savings in
the environment and human resources, as well as
significant cost reductions associated with inventory
and shipping, [8], [9]. We can give some examples,
such as the optimization of routes with the
Enhanced C-W algorithm with the Time Windows
structure [10]; the collaborative milk run model
considering supply and demand situations [11];
simulated in-plant milk run routing model [12]; the
time window milk run model with a dynamic
structure [13]; the milk run model for a factory
supplying high-volume parts [14]; demand
situations in the agent-based collaborative milk run
model [15]; and the in-factory milk run model.
Especially in the automotive industry, they preferred
this method in the process of supplying materials
between warehouses and the number and variety of
parts [16].
There are many approaches to operations
research, linear programming, MLP, Integer
programming as well as heuristics and artificial
intelligence methods for vehicle routing, [17], [18],
[19]. In this study, the milk run structure was
modeled with Integer linear programming, and a
hybrid genetic algorithm structure was developed at
the same time. Various studies have been conducted
on this subject. As an example, integer
programming with local search algorithm was used
as a heuristic algorithm for a milk collection system
using fleets of different types of trucks, [20], [21].
Which are, a hybrid heuristic algorithm for network
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1263
Volume 21, 2024
optimization with cross-docking and heuristic
algorithm, with a harmony algorithm and simulated
annealing [22]; the transition strategies in the cross
dock structure by aiming to reduce the delivery time
with a hybrid metaheuristic algorithm consisting of
particle swarm optimization and simulation
annealing [23]; to solve the crossdock
transportation problem with ant colony algorithm
[24]; examined heuristic algorithms used in solving
cross dock [25].
During logistics, simultaneous demands can
only be met with a good planning system. Analysis
of potential deadlock systems prevents bottlenecks
in the system. Distribution networks and cyclical
realization of transactions and flows can be
achieved through the milkrun method, [26], [27]. As
a result, suppliers may reduce their safety stocks,
which in the long run will affect part price declines.
With the effect of this situation, logistics service
providers can reduce their transportation costs in the
medium term by balancing the empty cycles they
have to make. The proposed model contributed to
the literature in this study.
3 Milk Run Approach
The Milk-Run serves supplier relations. It has a
fixed route, serves at least one supplier, and takes
place in circular tours. It preferred to facilitate
transportation in daily relations between
neighboring suppliers. Volumes are determined
daily within an order policy and the Milk-Run
system planned by the buyer and delivered to the
suppliers. It may involve one or more transfers
(Figure 1).
Our mathematical model includes the below
assumptions:
(1) The loads to be sent from each supplier to each
facility are known and are assumed to be less than
the truck capacity. Otherwise, the solution is trivial
as the truck would have to go directly from the
supplier to the plant for this flow.
(2) Trucks are always available when needed.
(3) Trucks are in two categories, small tucks, and
big trucks
(4) The loads shipped have the same cross-sections
that can use the entire front section of the truck.
The parameters and definitions used in the model
are as follows:
I distribution point
i transfer node number, i=1,2,3…,l
L number of total vehicle, L=1,2,…,n
L th vehicle volume
f the volume of the ordered product
to be transport
minimum travel distance between the node
i and the node j
i. unit move fee to node
M set of potential sites to locate depots
F set of depots
N set of all nodes of the network: N = M F
{0}
i. unit move fee to node
fixed vehicle usage fee
flow from i point to j point;
SF F set of small depots
BF F set of big depots
NF F set of depots: NF = M SF.
L set of big trucks
L set of small trucks
L. the amount of load loaded on the vehicle
i. load volume to be delivered to the node
i. volume of cargo to be received from the
node
i. the amount of freight to be delivered to
the node
i. the amount of freight to be received from
the node
maximum volume that tool k can hold
maximum payload that vehicle k can take
transportation cost for big trucks with i ,
j
transportation cost for small trucks, i,
j
capacity for each truck k
capacity for each truck k
Decision Variables
(1)
(2)
(3)
(4)
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1264
Volume 21, 2024
(5)
(6)
(7)
(8)
(9)
(10)
Fig. 1: Milk run concept
The model aims to minimize the overall
distance and costs in Eq(1). Eq(2) refers to the
calling agent at each node, and a node can be visited
by a maximum of one vehicle. Eq.(3) indicates
suitable routes for trucks. Eq.(4) expresses vehicle
arrivals. It describes the delivery or pick-up of the
car that has reached a node. Eq. (5) explains that
when a vehicle completes its task, it must return to
the distribution point. Eq.(6) and (7) cover quantity
and volume restrictions. (8) indicates the maximum
capacity for all large trucks. Each node must have
an intermediary, but this may change while the
model is being solved. Eq. (9,10) undesired sub-
tours. The model assumed that each node is serviced
by a vehicle. It does not cover the possibility that
the service vehicle is not fully loaded or that the
load to be loaded is more than its capacity. If the
load to be loaded is more than the vehicle's capacity,
it causes the vehicle to return to the distribution
point. However, in this model, the number of
vehicles serving the nodes is not limited to one,
[28], [29], [30], [31], [32], [33]. This section is
divided into two subsections: the first presents the
mathematical model of the three-stage supply chain,
while the second delves into the permutation-based
genetic algorithm.
The development and application of a heuristic-
based hybrid algorithm for Value Stream Design
(VSD) with a Milk-Run approach can significantly
contribute to and promote research in the field of
supply chain management, logistics, and lean
manufacturing. Consider a manufacturing facility
where various products undergo different processes.
The plan targets the main processes including
manufacturing and materials supply chain cut off
the stressed time and lessen redundant work. The
complexity-based hybrid algorithm presents an
individual method of evaluating various value
stream schemes and determining optimal ones based
on factors like production technological processes,
materials movement, and customer demand. This
provides a way of developing the concept, as well as
a means of taking optimization of value chains
which is used for achieving higher efficiency and
resource utilization. The confusing wholesale
industry of multiple suppliers and distribution points
in which the shipment can be optimized to cut the
transportation costs and improve logistics efficiency
through the Milk-Run concept.
The integration of the Milk-Run approach in a
heuristic-based algorithm will address the problems
associated with the efficient movement of the
storage and transportation concerning
materials. Besides, it does not only generate savings
but also an eco-friendly philosophy which is
achieved by minimizing the environmental
impact. Scientists will continue to unearth the ability
of the algorithm in the Milk-Run route and schedule
optimization, consequently driving progress toward
a sustainable supply chain. Market demand coupled
with production processes causes variations from
time to time. The software should enable
adjustments in light of fluctuations in demand,
production process alterations, or any other input.
According to the research, changes in dynamic
adapt organisms by using heuristic-based
method. Researchers can study an algorithm's ability
to adapt to the ever-changing world and analyze
how it holds up and performs in unpredictable
conditions serving as a basis for insights on
adaptation and consistency. This subtlety increases
the chain's agility and resistance to rapid changes in
the corporate world of this day. Through lean
manufacturing, one of the key objectives is to
expedite the lead times and the work-in-progress
inventory. The rule requires an algorithm to focus
on the procedure speeding and cutting out the
useless delay. The scheme moves forward with
heuristics while it gives a chance to decrease lead
time and optimize work in progress. Regarding the
achievement of key findings, researchers may find
out how the algorithm relates to the crucial
performance measures, such as cycle time and
process flow. First and foremost, priorities of
stakeholders like cost reduction, service
improvements and eco-friendly may differ from one
company to another. Such preferences of the
algorithm add value to the algorithm while it makes
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1265
Volume 21, 2024
the optimized design of the production
sequence. What is involved in the heuristic-based
method has both purposes and contraindications The
researchers can conduct the fact-finding on the
algorithm that is negotiating different stakeholder
needs to have frameworks for decision-making in
the design of the supply chain that entails a wider
range of issues. Besides, they can tie up with
business partners to do actual on-ground case
studies to apply the heuristic-based hybrid algorithm
in reality. Researchers can verify the efficiency of
the algorithm on true experiences in real problems
by using empirical evidence from real-world
applications and experimentations. Case studies
contribute to the base of knowledge by showing
approaches to the most relevant metrics and
shedding light on the institutional factors.
Some of the examples are:
- Dynamic Production Environment
A production site often finds itself in a situation
where there's a variety of products and a fluctuation
in demand. The algorithm hybrid of heuristics,
which is adaptive to changes will dynamically
modify the production layout to adjust to different
production needs. Such testing can measure the
reaction time of the algorithm towards changing
demand patterns by the algorithm and also by
evaluating its ability to reduce setup times and
transition easily between different production
setups. This as well allows us to assess the dexterity
of the algorithm in the dynamic production areas.
- Multi-Site Manufacturing Network
A company runs several manufacturing sites across
the country whereby each site houses different
production processes and suppliers. Integrating the
MILK-RUN transportation approach to the
algorithm is done to optimize the transportation of
materials by consolidating deliveries across various
sites. The research within this context would
concentrate on the algorithm’s fitting degree in
harmonizing Milk-Run planning across different
manufacturing sites. These insights may help
measure better the algorithm's efficiency for the
inter-site material flow, the transport costs, and the
collaborative practices in the multi-site
manufacturing networks.
- Environmental Sustainability
An organization tries to adhere to the green
principles and puts a limit on greenhouse gas
emissions. The algorithm is sustainability-based,
including route optimization features which are to
decrease fuel consumption and emission. Research
can serve as the key to identifying the role of
algorithms in the entire transport system including
the environmentally favorable effects. Among such
measures are the quantification of carbon emission
reductions, assessment of the algorithm’s
involvement toward sustainability of the supply
chain, and provision of knowledge that can lead
businesses to align their operations with
environmental goals.
- Supplier Collaboration
An industry comprises interaction including various
sub-suppliers which participate at every stage by
equipping the production process with different
components. The algorithm evaluates suppliers'
location in terms of the Milk-Run optimization
resulting in a coordinated operation and the smooth
flow of material from a supplier to a given
manufacturing plant. The studies can deepen into
how the algorithms help you create fruitful
collaboration with suppliers, lead times optimization
and reduction as well as rationalization of material
flows. Besides, it might help build awareness of the
algorithm in terms of deeper supplier relations and
more resilient supply chains.
- Customization and Product Variability
A company offers a configurable product line,
through which the products can be ordered with
customized options and a selection of different
features. The ability of the algorithm to adapt to
product demand no matter the variant means the
optimization of the value stream can be easily done
for all the products regardless of their
customizations. Research can approve the algorithm
while being customization task considered, it can be
evaluated how the algorithm can minimize
changeover time and create utilization at best. This
therefore helps to realize, the applicability of the
algorithm in the industrial setting with high product
variation.
- Real-time Decision Support
An industrial setting that faces particular cases of
unforeseen disturbance, which requires
instantaneous response and apt actions. The
heuristic feature inherent in the application makes
responses to unforeseen circumstances unmatched
in any other app easy and in real time. Therefore,
the examination may involve looking at how the
algorithm works in a decision support function in
real time, or its capability to change just in case any
disruptions that occur in the manufacturing or
supply fields. It causes the development of
interactive and in-motion value mapping practice.
In order, the third party, the heuristic-based hybrid
algorithm for Value Stream Design and the Milk-
RUN approach is proposed for the application in the
production management and supply chain. It
directly relates to how value chains can be set up in
a changing environment as well as how they can
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1266
Volume 21, 2024
support sustainability practices, and will finally help
to create decision-support tools for the industry
practitioners. The algorithm's adaptiveness,
productivity gains, and ability to address issues
relevant to the real world are the main features that
make it an imperative instrument in the spectrum of
research activities aimed at increasing the
effectiveness of modern supply chains.
4 Improved Hybrid Fit Genetic
Algorithm
The genetic algorithm evaluates the best probability
population with the heuristic approach and makes
the best use of biological natural selection and
randomness. It combines individual solution
populations with heuristic optima and leads to the
most suitable solution. New solutions are created by
combining pairs of individuals in the population.
This coupling operation is not centered, and local
optima are less frequent totally in the best available
solution. In the appropriate harmonic fit genetic
algorithm, the inner loop process of the system
works in finding the most suitable solution in
repetitive operations and in iteration times [34],
[35]. Crossover combines a pair of "main" solutions
and then produces parent vectors at the same point,
a pair of “children” and recombining the first part of
a parent solution with the second part of the other
and vice versa. The single best solution ever
encountered will always be part of the population.
(in the variant discussed here), but each generation
is also another solution. Ideally, anything will be
possible, and some may be nearly as good objective
function as best. Others may have rather poor
solution values. New solutions are created by
combining pairs of individuals in the population.
Because this coupling operation is not centered,
local optima are less frequent totally in the best
available solution. The standard genetic algorithm
method for combining population solutions is
known as crossover. Many variations on the basic
genetic algorithm strategy have been used
successfully.
The only requirement is that better solutions
have more chances. We consider only one elite
population method to manage. Each new generation
will be made up of a combination of elite,
migratory, mutated, and cross-solutions.
The most outstanding strategy for implementing
genetic algorithms creates each new generation as a
mix of best solutions from the past. The previous
generation was added arbitrarily to migratory
solutions to increase diversity, random mutation of
other solutions, and children of crossover operations
on non-overlapping pairs of solutions in the
previous population (Table 1).
Table 1. Steps of the Genetic Algorithm
Maintaining the best solutions from the previous
generation, the finest known solutions so far will
remain in the population and have more
opportunities to produce offspring. Adding new
migratory solutions and random mutations are
existing ones that help maintain equality as
solutions combined (Table 2).
Table 2. Steps of the hybrid genetic algorithm
Collective new solutions are allowed to act as
parents, which will be the product of crossovers
with elites in the previous population. The hybrid
genetic algorithm processing steps above are applied
to the following heuristic steps (Table 2 and Figure
2).
5 Case Study
A logistics firm with a warehouse located in Gebze
serves nine different locations in Istanbul. It
provides collection and delivery services, and wants
to change its distribution systems to add one more
stop to its current route and save on costs in the
locations where the company provides service,
which are located in Kartal, Başakşehir, Üsküdar,
Kadıköy, Sarıyer,Sultanbeyli,Büyükçekmece,
Küçükçekmece, Çekmeköy. The location to be
added is a customer located in Beylikdüzü. The
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1267
Volume 21, 2024
company has three vehicles in use and the available
ways are in Figure 3 and Table 3.
Fig. 2: Illustration of the hybrid fit genetic algorithm
steps
The features of the vehicles available to the
company are listed in Table 4. It includes the
average speed of the cars, the distance they can
travel, their maximum capacity on a pallet-volume-
weight basis, and various fixed costs.
Fig. 3: Current Route Preview
Stage 1: Inclusion of the New Location in the
System
The location planned to be added is located in
Beylikdüzü and delivery is planned to this point.
The weight of the product to be delivered, its
volume, the amount of pallets, the starting and
delivery time intervals, and other costs are given in
Table 5.
Table 3. Current Route Preview Outputs
Table 4. Vehicle Features
Table 5. New Location Delivery Information
Stage 2: Implementation of Milk-Run Algorithm
With the new location included in the system,
delivery/collection services will be offered to ten
different locations, and these points and zip codes
are listed in Table 6. Table 7 also includes the
details of the planned deliveries.
Table 6. Location Postal Codes
By transferring the tables containing the
location information to the Log-Hub plugin, the
outputs in Table 8 are obtained.
Based on the Table 8 information, the vehicle
departing from Gebze Warehouse at 05:23 visits the
Kartal location, which is the first visit point, at
06:00 and provides collection service. After this
process, which takes 20 minutes, it departs for
Kadıköy at 06.20, arrives at 06.37, and provides a
30-minute delivery service. The vehicle, which
departs for Çekmeköy point at 07.07, arrives at this
point at 07.32 and provides a collection service that
takes 30 minutes. Leaving the Çekmeköy point at
08.02, the vehicle departs for its fourth planned
point, Sarıyer, and arrives at this point at 08.32 and
provides a 25-minute delivery service. The vehicle
leaves Sarıyer at 08.57, arrives at Başakşehir at
09.32, and provides a delivery service that takes 15
minutes.
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1268
Volume 21, 2024
Table 7. Delivery/Collection Information of
Locations
Table 8. Route-Time Breakdown
The vehicle sets off for Büyükçekmece at 09.47,
arrives at this point at 10.09, and makes a delivery
that takes 40 minutes. The vehicle, which is ready to
depart for the Beylikdüzü point at 10.49, arrives at
this point at 11.10 and will provide a 15-minute
pick-up service. The vehicle leaves Beylikdüzü at
11.25, arrives at Küçükçekmece at 11.43 and will
provide the delivery service that will take 25
minutes. The vehicle, which will be ready to depart
at 12.08, will arrive at Üsküdar at 12.42 and will
provide a 20-minute pick-up service. The vehicle,
which will depart for Sultanbeyli point at 13.02,
arrives at this location at 13.31 and will provide a
collection service that will take 30 minutes. Having
completed its delivery/transport duties at 14.01, the
vehicle will depart for the Gebze warehouse and
arrive at 14.36 (Figure 4). Figure 5 shows the chart
of Time Distribution in Planned Route.
Fig. 4: Route Preview after Milk-Run Application
Fig. 5: Gantt Chart with Time Distribution of
Planned Route
The "Loading Meter" graphic in the third
graphic in Figure 6 is the standard unit of
measurement used for transport by truck. It is used
as a unit of calculation for goods that need to be
transported but cannot be stored. LDM truck length
is considered equal to one meter of loading area but
may vary between regions.
Fig. 6: Changes in Weight, Volume, and Load Size*
of the Delivery/Distribution Vehicle over Time
Stage 3: Achieved Results
Table 3 is examined, the total cost is 1306,2229
currency units, the total distance traveled is 431.87
kilometers, the travel time between the points is 520
minutes and the total elapsed time is 755 minutes.
The total carried weight was 7670 weight units and
24 pallets were used. The outputs obtained after the
Milk-Run application are shown in Table 9. From
this point of view, the total cost is 750.6563
currency units, the total distance is 251.89 km, the
travel time between points is 303 minutes and the
total elapsed time is 553 minutes. The total
transported weight is 5333 weight units, and 16
pallets are used.
Table 9. Condition Table After Milk-Run
Application
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1269
Volume 21, 2024
Stage 4: Possible Scenario Outcomes When
Constraints Change
Scenario 1: Visit Point Constraint Change
(30%↓)
As mentioned in the introduction part of the
problem, the current vehicle capacities are given in
the Table 10. In addition to the given capacities,
vehicles can visit 10 different points. Considering a
scenario where the visiting point capacity drops by
30%, the outputs are as follows (Figure 7).
Fig. 7: Route Preview after Visit Point Constraint
Change (30%↓)
While the outputs for Route 0, the first Blue-
colored Milk-Run cycle, are in the first row of Table
10, the outputs for Route 1, that is, the second Milk-
Run cycle in green, are in the second row. Based on
the table, the total cost is 986,1034 currency units,
the total distance is 321.02 kilometers, the travel
time between points is 386 minutes and the total
elapsed time is 636 minutes. The total transported
weight was 6136 weight units and 19 pallets were
used.
Table 10. Milk-Run Outputs After Visiting Point
Constraint Change (30%↓)
Scenario 2: Visit Point Constraint Change (50%↓)
Considering a situation where the visiting point
capacity drops by 50%, the outputs are as follows
(Figure 8 and Table 11).
Fig. 8: Route Preview after Visit Point Constraint
Change (50%↓)
Table 11. Milk-Run Outputs After the Visitation
Point Constraint Change (50%↓)
While the outputs for Route 0, the first Blue-
colored Milk-Run cycle, are in the first row of Table
11, the outputs for Route 1, the green-colored
second Milk-Run cycle, are on the second line.
Based on the table, the total cost is found to be
1014.4934 currency units, the total distance is
338.02 kilometers, the travel time between points is
405 minutes and the total elapsed time is 655
minutes. The total weight carried was 7657 weight
units and 25 pallets were used.
Scenario 3: Transit Time Constraint Change
(30%↓)
As shown in Table 12 and Figure 9, each
vehicle can travel for a maximum of 600 minutes in
each Milk-Run cycle. Considering a scenario where
the Transport Time capacity decreases by 30%, the
outputs are as follows.
Fig. 9: Route Preview after Move Time Constraint
Change (30%↓)
Table 12. Milk-Run Outputs After Transport Time
Constraint Change (30%↓)
Route 0, the first Blue-colored Milk-Run cycle
outputs, is in the first row of Table 13, while Route
1, the second Green-colored Milk-Run cycle
outputs, is in the second row.
Based on the table, the total cost is found to be
1002,5362 currency units, the total distance is
330,86 kilometers, the travel time between points is
398 minutes and the total elapsed time is 650
minutes. The total transported weight was 6854
weight units and 22 pallets were used.
Scenario 4: Transit Time Constraint Change
(50%↓)
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1270
Volume 21, 2024
Considering a scenario where the Transport
Time capacity decreases by 50%, the outputs are as
follows (Figure 10 and Table 13).
Fig. 10: Route Preview after Move Time Constraint
Change (50%↓)
Route 0, the first Blue-colored Milk-Run cycle
outputs, are located in the first line of Table 14,
Route 1, that is, the second Milk-Run cycle outputs
in green, are located in the second line, and finally
Route 2, the third Milk-Run cycle in red. -Run loop
is in the last line.
Table 13. Milk-Run Outputs After Transport Time
Constraint Change (50%↓)
Based on the table, the total cost is 1467,899
currency units, the total distance is 519.7 kilometers,
the time between points is 624 minutes and the total
elapsed time is 874 minutes. Total transported
weight was 7657 weight units and 25 pallets were
used.
Scenario 5: Transported Volume Constraint Change
(30%↓)
As shown in Table 10, each vehicle can carry a
maximum of 15 volumes of cargo. Considering a
scenario where the transported volume capacity
decreases by 30%, the outputs are as follows (Figure
11 and Table 14).
Fig. 11: Route Preview after Moved Volume
Constraint Change (30%↓)
Table 14. Milk-Run Outputs After Conveyed
Volume Constraint Change (30%↓)
As shown in blue in Figure 10, the outputs of
the Milk-Run cycle were found to be 781.9453
currency units with total cost, total distance 288.59
kilometers, travel time between points 346 minutes
and total elapsed time 596 minutes. While the total
transported weight was 3980 weight units, 12 pallets
were used.
Scenario 6. Transported Volume Constraint Change
(50%↓)
As in the previous scenario, each vehicle can
carry a maximum of 15 volumes of cargo.
Considering a scenario where the transported
volume capacity decreases by 50%, the outputs are
as follows (Figure 12 and Table 15).
Fig. 12: Route Preview after Transported Volume
Constraint Change ( 50%)
Table 15. Milk-Run Outputs (50%↓) After
Transported Volume Constraint Change (%50)
As shown in blue in Figure 11. Route 0 outputs
are in the first row of Table 16, and Route 1 outputs,
shown in green, are in the second row of the table.
Based on the table, the total cost is 1114.0755
currency units, the total distance is 397.65
kilometers, the travel time between points is 477
minutes and the total elapsed time is 727 minutes.
The total transported weight is 5308 weight units
and 16 pallets are used.
5.1 Statistical Analysis
Cost is one of the most important criteria in Milk-
Run optimization processes and other outputs were
compared with Total Cost output and their
relationships were investigated. For the analysis, the
IBM SPSS program was used and Pearson
Correlation measures were used for the analysis to
compare significant differences among total cost,
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1271
Volume 21, 2024
total distance, and total carried weight. As stated in
Table 16, there is a positive and significant
correlation at the level of 0.01 between Total Cost
and Total Distance. There is a positive and
significant correlation at the level of 0.05 between
Total Cost and Total Carried Weight. A sufficient
relationship between Total Distance and Total
Carried Weight could not be determined.
Table 16. Total Cost, Total Distance, and Total
Weight Carried Relationship
When Table 17 was analyzed, there was a
positive significant correlation at the level of 0.01
between Total Cost and Total Time. A positive
significant correlation was found at 0.01 level
between Total Cost and Time Between Points. In
addition, it was determined that there is a positive
and significant correlation at the level of 0.01
between the Total Time and the Time Between
Points.
Table 17. Total Cost, Total Time, and Time
Between Points Relationship
As stated in Table 18 is a positive correlation of
0.05 levels between Total Cost and Total Volume. A
positive correlation of 0.05 levels was found
between Total Cost and Total Number of Pallets.
There is a positive correlation at the level of 0.01
between the Total Volume and the Total Number of
Pallets.
Table 18. Relationship Table between Total Cost,
Total Volume, and Total Pallet
6 Conclusion
As a result, of the implementation of Milk-Run
optimization, the total cost decreased from
1306.2229 currency units to 720.6563 currency
units, the total distance decreased from 431.87
kilometers to 251.89 kilometers and the time
between points decreased from 520 minutes to 303
minutes with the inclusion of the new location in the
current situation. Afterward, by reducing the vehicle
capacities by 30% and 50% has positive effect on
the behaviour in the system that observed and
obtained the outputs.
The first situation and the optimal state after
Milk-Run with the constraint changes and the
scenario outputs obtained are compared and
illustrated in Figure 13. For each situation and
scenario, total cost, total distance, time between
points, total elapsed, time, total weight carried, total
volume and number of pallets changes are given
separately in Figure 14.
Fig. 13: Table of Changes Due to Scenarios
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1272
Volume 21, 2024
Fig. 14: Parameter Results for different scenarios
The optimization study will save the company a
great deal in the short and long term, and it will
provide a preview of the actions that can be taken in
case the vehicle constraints change due to various
reasons. The scenarios created express these
possible changes and will protect the company
against possible risks. In this way, the company will
have efficiency in itself by directing the surplus
resources it holds to the necessary areas.
References:
[1] Bocewicz, G., Nielsen, P., & Zbigniew, B.
(2019). Milk-run routing and scheduling
subject to different pick-up/delivery profiles
and congestion-avoidance
constraints. IFAC-PapersOnLine, 52(8),
313-320.
[2] Hormes F, Siala A, Lieb C, Fottner J
(2020). Fleet Sizing of Dynamically Routed
In-plant Milk-run Vehicles Based on a
Genetic Algorithm. Logistics Journal:
Proceedings, Vol. 2020. (urn:nbn:de:0009-
14-51420).
[3] Bocewicz G., Nielsen I., Zbigniew B., A
decision support model for prototyping in-
plant milk-run traffic systems, (2019)
IFAC-PapersOnLine, 52 (13) , pp. 814-819.
[4] Bocewicz, G., Banaszak, Z.A., Rudnik, K.,
Witczak, M., Smutnicki, C., Wikarek,
J.,Milk-run Routing and Scheduling Subject
to Fuzzy Pickup and Delivery Time
Constraints: An Ordered Fuzzy Numbers
Approach,2020 IEEE International
Conference on Fuzzy Systems (FUZZ-
IEEE), 2020,pp.1-10.
[5] Kilic HS, Durmusoglu MB. “A
mathematical model and a heuristic
approach for periodic material delivery in
lean production environment”. The
International Journal of Advanced
Manufacturing Technology, 69(5-8), 977-
92, 2013.
[6] Kilic HS, Durmusoglu MB, Baskak M.
“Classification and modeling for in-plant
milk-run distribution systems”. The
International Journal of Advanced
Manufacturing Technology, (2012) 62(9-
12), 1135-1146.
[7] Gotthardt, S., Hulla, M., Eder, M., Karre,
H., Ramsauer, C., Digitalized milk-run
system for a learning factory assembly line,
Procedia Manufacturing, Vol. 31, 2019,
PP.175-179, ISSN: 2351-9789.
[8] De Moura D.A., Botter R.C. Delivery and
pick-up problem transportation – milk run
or conventional systems. Independent
Journal of Management & Production
(IJM&P), (2016), vol. 7 (3), 746-770.
[9] Meyer A., Milk Run Design (Definitions,
Concepts and Solution Approaches), PhD
thesis, Institute of Technology. (2015)
Fakultät für Maschinenbau, KIT Scientific
Publishing, Karlsruhe.
[10] Mei, H., Jingshuai, Y., Teng, M., Xiuli, L.,
Ting, W., The Modeling of Milk-run
Vehicle Routing Problem Based on
Improved C-W Algorithm that Joined Time
Window, Transportation Research
Procedia, Volume 25, 2017, pp.716-728,
ISSN: 2352-1465.
[11] Lou, Z., Li, Z., Luo, L., Dai, X., Study on
Multi-Depot Collaborative Transportation
Problem of Milk-Run Pattern, MATEC Web
Conf., 81 (2016) Lucerne, Switzerland,
01004,
https://doi.org/10.1051/matecconf/2016810
1004.
[12] Sipahioğlu, A., Altın, İ., A mathematical
model for in-plant Milk-Run routing,
Journal of Pamukkale Univ Engineering
Science, (2019) 25(9), 1050-1055.
[13] Adriano, D.D.; Montez, C.; Novaes,
A.G.N.; Wangham, M. DMRVR: Dynamic
Milk-Run Vehicle Routing Solution Using
Fog-Based Vehicular Ad Hoc Networks,
Electronics, 2020, 9, 2010
[14] Vilda, F.G., Yague-Fabra,J.A., Torrents,
A.S., An in-plant milk-run design method
for improving surface occupation and
optimizing mizusumashi work time, CIRP
Annals - Manufacturing Technology, 69
(2020), p.405-408.
[15] Aragao, D.P., Antonio Galvao, A., Novaes,
N., Lunac, M. M. M,, An agent-based
approach to evaluate collaborative strategies
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1273
Volume 21, 2024
in milk-run OEM operations, Computers &
Industrial Engineering, 129 (2019), p. 545–
55.
[16] Klenk, E., Galka, S., Günthner, W.A.,
Operating Strategies for In-Plant Milk-Run
Systems, IFAC-PapersOnLine, 48-3,
(2015), pp.1882–1887.
[17] Sahar, G. S., Okba, K., Abdelkader, L.,
Amine, Y. M., Euler, R., Bounceur, A.,
Hammoudeh, M., An Optimized Scalable
Multi-ant Colony System for Multi-depot
Vehicle Routing Problems Using a Reactive
Multi-agent System, WSEAS Transactions
on Systems, (2021), vol. 20, pp. 249-259,
https://doi.org/10.37394/23202.2021.20.28.
[18] Turgay, S., Streamlined Supply Chain
Operations: Leveraging Permutation-Based
Genetic Algorithms for Production and
Distribution, WSEAS Transactions on
Information Science and Applications,
(2024) Vol. 21, pp. 23-32,
https://doi.org/10.37394/23209.2024.21.3.
[19] Rardin, RL (2000) Optimization in
Operations Research, Prentive Hall, April
[20] ParedesBelmar, G., Marianov, V.,
Bronfman, A., Obreque, C. and Lüer-
villagra, A. (2016), “A milk collection
problem with blending, Transportation
Research Part E: Logistics and
Transportation Review, Vol. 94, pp. 26-43,
doi: 10.1016/j.tre.2016.07.006.
[21] Paredes-Belmar, G. Montero, E.,
Leonardini, O., A milk transportation
problem with milk collection centers and
vehicle routing, ISA Transactions, Vol. 122,
2022, pp.294-311,
https://doi.org/10.1016/j.isatra.2021.04.020
[22] Hosseini, S.D., Shirazi, M.A:, Karimi, B.,
Cross-docking and milk run logistics in a
consolidation network: A hybrid of
harmony search and simulated annealing
approach, Journal of Manufacturing
Systems, Vol. 33, Issue 4, 2014, pp.567-577,
https://doi.org/10.1016/j.jmsy.2014.05.004.
[23] Vahdani, B., Tavakkoli-Moghaddam, R.,
Zandieh, M., Razmi, J., Vehicle routing
scheduling using an enhanced hybrid
optimization approach, J Intell Manuf.
2012) 2 759-774, doi: 10.1007/s10845-010-
0427.
[24] Musa, R., Arnaout, J.P., Jung, H., Ant
colony optimiza tion algorithm to solve for
the transportation problem of cross-docking
network, Computers & Industrial
Engineering, Vol. 59, Issue 1, 2010, pp.85-
92.
[25] Goodarzi A, H., Zegordi S.H. (2016) A
location-routing problem for cross-docking
networks: a biogeography-based
optimization algorithm. Computers &
Industrial Engineering, 102:132–146.
[26] Urru, A., Bonini, M., & Echelmeyer, W.
(2018). Planning and dimensioning of a
milk-run transportation system considering
the actual line consumption. IFAC-
PapersOnLine, 51, 404-409.
[27] Klenk, E., Galka,S., Analysis of real-time
tour building and scheduling strategies for
in-plant milk-run systems with volatile
transportation demand, IFAC-
PapersOnLine, Vol. 52, Issue 13, 2019,
pp.2110-2115.
[28] You, Z., Jiao, Y., Development and
Application of Milk-Run Distribution
Systems in the Express Industry Based on
Saving Algorithm", Mathematical Problems
in Engineering, vol. 2014, Article ID:
536459, 6 pages, 2014.
[29] Mao, Z., Huang, D., Fang, K., Wang, C., &
Lu, D. (2019), Milk-run routing problem
with progress-lane in the collection of
automobile parts. Annals of Operations
Research 26, 1-28.
[30] Turgay, S., Yaşar, Ö., Aydın, A., A Multi-
objective Framework for Dairy Products
Supply Chain Network with Benders
Decomposition, Industrial Engineering and
Innovation Management, (2023), Vol. 6
Num. 5.
[31] Meyer, A. (2017). Milk run design:
Definitions, concepts and solution
approaches, (Vol. 88). KIT Scientific
Publishing.
[32] Hižak, J.; Logožar, R., An Overview Of The
Genetic Algorithm And Its Use For Finding
Extrema ─ With Implementations In
Matlab, Tehnički glasnik 10, 3-4(2016),
pp.55-70.
[33] Turgay, S., Aydın, A., An Effective
Heuristic Algorithm for Flexible Flow Shop
Scheduling Problems with Parallel Batch
Processing. Manufacturing and Service
Operations Management (2023) Vol. 4,
pp.62-70.
[34] Meilinda F. Maghfiroh, N. , Darmawan, A.,
Yu, V.F., Genetic Algorithm for Job Shop
Scheduling Problem: A Case Study,
International Journal of Innovation,
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1274
Volume 21, 2024
Management and Technology, Vol. 4, No.
1, February 2013.
[35] Süer, G.A., Yang, X., Alhawari, O.I.,
Santos, J., Vazquez, R., A Genetic
Algorithm Approach for Minimizing Total
Tardiness in Single Machine Scheduling,
International Journal of Industrial
Engineering and Management (IJIEM),
(2012) Vol. 3 No 3, pp.163-171.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- S. Turgay - investigation,
- C. Coban - validation,
- S. Turgay - writing & editing
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The author has no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on BUSINESS and ECONOMICS
DOI: 10.37394/23207.2024.21.103
Safiye Turgay, Canberk Çoban
E-ISSN: 2224-2899
1275
Volume 21, 2024
