Streamlined Supply Chain Operations: Leveraging Permutation-Based

Genetic Algorithms for Production and Distribution

SAFIYE TURGAY

Department of Industrial Engineering,

Sakarya University,

54187, Esentepe Campus Serdivan-Sakarya,

TURKEY

Abstract: - Minimizing production and distribution costs by using resources in the most efficient way in supply

chain management is among the most fundamental objectives. In increasingly competitive conditions,

companies can act more strongly in market share with improvements in cost and efficiency factors. With the

proposed Permutation Based Genetic Algorithm (PBGA) approach, the problem of optimizing the production

and distribution line in the supply chain is addressed. The algorithm uses the processes of selection, crossover,

and mutation to evolve the population in a permuted manner, taking into account multiple iterations, i.e.

generation states. The results from the case studies also showed that resource utilization was realized efficiently

with cost reductions and improvements in lead times. In this study, cost savings were achieved by applying the

PBGA method, especially in information flow and process optimization between distribution and production.

This can provide an advantage in a competitive environment.

Key-Words: - Supply Chain Management, Production and Distribution Model, Optimization, Permutation-

Based Genetic Algorithm, Integrated Supply Networks, Mathematical Model.

Received: July 13, 2022. Revised: October 16, 2023. Accepted: November 14, 2023. Available online: December 27, 2023.

1 Introduction

In supply chain management, the effective

coordination of production and distribution

processes is crucial for the best adaptation to critical

competitive conditions. In this context, optimization

of production and distribution parameters is

inevitable when factors such as variable customer

demands and the need for efficient use of resources

are taken into account. Since the traditional methods

of supply chain optimization have disadvantages in

terms of both cost and time, the PBGA method has

been developed and applied in larger models, which

gives result values very close to the optimum result

in a shorter time. In the permutation-based genetic

algorithm approach of the supply chain management

model, all possible cases are analyzed by examining

the crossover and population cases. The PBGA

method can be easily applied to sequencing and

scheduling problems that are frequently encountered

in production and distribution problems.

Fast and accurate analysis of the dynamic

variable structures in the model will facilitate

dynamic information sharing with the proposed

algorithm. In this context, it was aimed to analyze

the obtained values and determine the appropriate

solution and decision rules. In a continuous,

changing, and uncertain environment, unpredictable

demand and tight delivery times, short production

cycles, and a wide range of products make decision-

making in the production and distribution process

difficult. In this study, an algorithm method is

proposed and used to improve the dynamic

decision-making process.

In this study, the PBGA method is used to

determine the optimal task allocation of production

and distribution tasks. This optimal sequencing also

aims to minimize operational costs by considering

parameters such as production capacity, available

resource availability, and deadlines. With the PBGA

method, genetic operators such as selection,

crossover, and mutation are used over multiple

iterations over multiple generations.

The remainder of this paper is structured as

follows: Section 2 provides an overview of the

pertinent literature. Section 3 delineates the model

definition and formulation, encompassing the

mathematical model of the production and

distribution line model, while permutation-based

genetic algorithms are detailed in subsequent

subsections. Section 4 features a case study,

summarizing the key results of our proposed

approach in comparison to the current state of

affairs. It also delivers a comprehensive analysis of

the optimized schedules' robustness in the face of

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delivery delays. Finally, in Section 5, we present our

concluding remarks.

2 Literature Survey

Supply chain management is an approach in which

different processes, including procurement,

production, inventory management, and distribution,

are handled in an integrated manner. Reducing costs

and improving customer service are among the main

objectives. Therefore, there are extensive studies on

supply chain management in the literature. The

literature review in this paper focuses on SCM and

genetic algorithms with a focus on PBGA

implementation.

Some studies have grouped customers according

to customer similarities and analyzed the

profitability of the customer group with a genetic

algorithm by taking into account the market

dimension along with the quality function, [1],

while a planning and scheduling model that takes

into account order deadlines and outsourced

operations in supply chain management has been

discussed, [2]. At the same time, a mathematical

model that takes into account supply chain

dynamics was also studied, [3]. A genetic algorithm

was used in this study where production processes

and alternatives were considered. Reverse supply

chain management and the adjustment of production

parameters according to customer demands were

also considered in this study. Supply chain

management and genetic algorithm studies were

also included in various studies, [4], [5], [6], [7].

The application of genetic algorithms to supply

chain management has been explored from various

angles. It has been used to develop integrated

process planning, scheduling, and outsourcing

supply chain models, distribution network design,

multi-stage production, and hybrid genetic

algorithms for production and distribution, [8], [9],

[10], [11]. Researchers have also investigated lot

and delivery scheduling, ready-mixed concrete

delivery, and third-party logistic provider models

using dynamic supply chain and distributed network

approaches, [12], [13], [14], [15].

This section also reviews studies that employ

genetic algorithms to optimize product lot sizes

within supply chain management. Some of these

studies have focused on assembly line optimization,

multi-staged distribution network production,

demand allocation, transportation, and production

scheduling. Others have examined the effects of

components on flexible production system design.

In this paper, we develop an integrated inventory-

production-distribution mathematical model.

Extensive benchmark data, drawn from the literature

and experimental results, have consistently shown

that permutation-based genetic algorithms, as an

optimization method, yield superior performance.

As a result, we prefer the use of permutation-based

genetic algorithms in this study, given their ability

to provide optimal results quickly when analyzing

large datasets

3 Model Definition and Formulation

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.

3.1 Production and Distribution Line Model

In the context of a three-stage production and

distribution line, a linear program model has been

formulated. This model is designed to identify and

meet the demands of customers and warehouses

efficiently. It comprises three interconnected stages

where decisions made at each level hierarchically

influence the subsequent stages (Figure 1). To

clarify, the program, which shapes the distribution,

production, and inventory plan, takes on the

structure of a linear program, [16], [17], [18]. It

starts by defining the set of variables, followed by

the formulation of constraints and the objective

function.

Fig. 1: Demonstration of problem structure

Index sets

n set of customers

m set of warehouse sites

l set of plant sites

s set of supplier sites

Decision Variables:

The decision variables involved in the minimization

of the costs of the three-stage supply chain are as

follows:

Z[i,m,t] the inventory level of i product in m

warehouse in t period

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P[i,l,t] the inventory level of i product in plant 1

in t period

W[i,s,t] the inventory level of raw material to be

supplied from s supplier to produce i

product at the end of t period

c[i,l,t] unit production cost of i product in plant

1 in t period

v[i,s,t] production cost of raw material to be

supplied from s supplier to produce i

product in t period

Ca[i,m,t] i product capacity of m warehouse in t

period

Cb[i,l,t] i product capacity of plant 1 in t period

Cc[i,s,t] capacity of s supplier to hold raw

material required by for i product in t

period

Ta[i,m,t] transportation of i product in m

warehouse to n customer in t period

Tb[i,l,t] transportation of i product in plant 1 to m

warehouse in t period

Tc[i,s,t] transportation of s raw material from s

supplier for production of i product in

plant 1 in t period

Fa[i,m,t] transportation cost of i product in m

warehouse to n customer in t period

Fb[i,l,t] transportation cost of i product in plant 1

to m warehouse in t period

Fc[i,s,t] transportation cost of necessary raw

material from s supplier for production

of i product in plant 1 in t period

Sa[i,m,t] safety stock of i product in m warehouse

. in t period

Sb[i.l.t] safety stock of i product in plant 1 in t

period

Sc[i,s,t] safety stock of necessary raw material by

s supplier for production of i product in

plant 1 in t period

Ha[i,m,t] holding cost of i product in m warehouse

. in t period

Hb[i.l.t] holding cost of i product in plant 1 in t

period

Hc[i,s,t] holding cost of necessary raw material

by s supplier for production of i

product in plant 1 in t period

Da[i,m,t]







otherwise0

periodtduringwarehouseminisproductiif1

Db[i,l,t]







otherwise0

periodtduringplantlinisproductiif1

Dc[i,s,t]







otherwise0

periodtduringpliersupsinisproductifornecessarylmateriarawtheif1

The primary goal of this function is to minimize the

costs associated with distribution, production, and

inventory management within the supply chain.

Specifically, distribution costs are contingent on the

mode of transportation, including factors like the

cost per unit of time, lead time (comprising loading,

travel, and unloading times), and the total number of

shipments conducted. Production costs fluctuate

based on the production levels at the various

facilities. Additionally, holding costs are directly

proportional to the quantities of products and raw

materials held at all nodes throughout the supply

chain. The objective function is expressed as

follows:

Min (Production Cost+ Inventory Cost +Delivery Cost)

Production Cost:

 

 

 

 

   

 

 

 

 

t,s,i

t,s,ivt,s,iWt,l,i

t,l,ict,l,iPMin c

1i b

 

 

Inventory Cost:

 

 

 

 

   

 

 

 

   

 

 

 

 

t,s,i

t,s,ihct,s,iWt,l,i

t,l,ihbt,l,iPt,m,i

t,m,ihat,m,iZMin c

1i ba

 

 

Delivery Cost:

 

 

 

 

   

 

 

 

   

 

 

 

 

t,s,i

t,s,iFct,s,iTct,l,i

t,l,iFbt,l,iTbt,m,i

t,m,iFat,m,iTaMin c

1i ba

  

 

Subject to

     

 

t,s,iWt,l,iPt,m,iZ

1t it 



 

(1)

   













t,s,iCct,s,iW

t,l,iCbt,l,iP

t,m,iCat,m,iZ

(2)

   













t,s,iSct,s,iW

t,l,iSbt,l,iP

t,m,iSat,m,iZ

(3)

     

t,m,iZt,l,iTb1t,m,iZ L

1l  



(4)

     

t,l,iPt,s,iTc1t,l,iP L

1l  



(5)

 

t,m,iTa

1n it 





(6)

     

 

1,0t,s,iDc,t,l,iDb,t,m,iDa 

(7)

     

0t,s,iTc,t,l,iTb,t,m,iTa 

(8)

This production planning model revolves

around the dynamics of material flow,

encompassing the movement of materials from

suppliers to plants, then from plants to warehouses,

and ultimately from warehouses to customers. To

construct a model that accurately assesses this

system, we considered the aforementioned

characteristics while establishing connections with

existing models in the literature, particularly in the

domains of production and transportation. However,

it's important to note that not all lot size models and

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material flow values were taken into account in this

study. It aimed to scrutinize inventory flow by

defining material flow variables within the system.

There are several constraints in place:

Constraint 1 ensures a balance between customer

demand and total inventory.

Constraint 2 deals with production capacity and

inventory limitations.

Constraint 3 focuses on safety stock levels.

Constraint 4 pertains to the ability to meet

warehouse requirements from the plant for the

upcoming period.

Constraint 5 relates to the plant's ability to fulfill its

requirements from the supplier for the forthcoming

period.

Constraint 6 involves the transport of customer

demand from the warehouse to the customer.

Constraints 7 and 8 are associated with situational

variables.

It's worth noting that conventional lot size

models in the literature typically do not incorporate

material flows between different points in the

supply chain (e.g., from plants to warehouses and

from warehouses to customers). Additionally, these

models often consider a single plant supplying a

single warehouse. However, the problem defined in

this context considers variables such as the number

of plants, warehouses, and the material flow,

resulting in a more comprehensive analysis.

3.2 Permutation and Distribution Line

Model

The Genetic Algorithm (GA) is a contemporary

heuristic optimization method, drawing inspiration

from the biological process of genetic operations. It

employs chromosomes to represent potential

solutions, with the initial solution pool typically

consisting of a set number of chromosomes, [19],

[20], [21], [22], [23]. The process of crossing and

mutating ensures the generation of new

chromosomes, each stronger than its predecessor.

Permutation-based GA, such as in cases like the

Traveling Salesman Problem and Vehicle Routing

Problems, focuses on achieving optimal results by

grouping similar features from repeated operational

scenarios. Genetic control parameters, namely

crossover and mutation rates, have a significant

impact on population diversity.

In Figure 2, the operational steps of the

permutation-based genetic algorithm are outlined.

Step 1 involves defining objective functions and

variables, while Step 2 covers the definition of GA

parameters like pop size, mutation rate, and

selection criteria. Step 3 entails the creation of the

initial population, and Step 4 involves iterating

through generations to identify the best permutation.

Step 5 encompasses pairing individuals and

initiating the mating process, while Step 6 is

dedicated to carrying out the mating. Step 7 includes

mutation and population operations, and Step 8

deals with sorting costs. Finally, the results are

displayed on the screen.

Fig. 2: Permutation based Genetic Algorithm Steps

4 Implementation

In this study, we examined a supply chain model in

multiple stages and optimized the system using both

a simple Genetic Algorithm (GA) and a

permutation-based GA. In GA, we represent

solutions, individuals, and chromosomes with

indexes, typically composed of 0s and 1s, drawing

inspiration from biology. Genetic algorithms assume

that certain parts of the algorithm represent specific

features or characteristics on a biological

chromosome, ultimately aiming to find the optimal

solution iteratively during recombination, [24], [25],

[26], [27], [28], [29].

This section delves into a three-stage

distribution network supply chain model, which

comprises six warehouse distribution points, three

plants, and four suppliers denoted as x, y, z, and t,

each associated with a specific plant. Products are

evaluated as Ui (i=1,2,3,4), warehouses as Dj

(j=1,2,3,4,5,6), plants as Fk (k=1,2,3), and the

number of customers varies from 10 to 200. The

primary objective is to meet customer needs with

minimal cost. This section also evaluates factors like

determining transportation charges between

warehouses, optimal stock levels in warehouses, and

the relationship between the production rates of

plants in the first stage and suppliers. Customer

demands are initially addressed from warehouses; if

the products are not available there, they are sourced

from plants. The demand chain initiates from the

customer and flows down to warehouses, plants, and

suppliers. The optimization factors include customer

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demand sizes, warehouse and plant stock levels,

plant production rates, and part supply speed. GA

optimization typically does not rely on the analytical

properties of the objective function. It mainly

involves two fundamental operations: repeated

iterations and the random generation of new

solutions, followed by evaluating their optimality

based on predefined fitness functions. These

characteristics empower GA. Permutation-based

GAs like Hu's and Haupt & Haupt's, as well as the

improved program discussed here, are known for

effectively finding solutions to complex problems,

including those in mobile sales and tabulation

domains. At the start of the GA process, each

chromosome represents a potential optimal solution.

The integrated supply chain management approach

involves several stages: distribution, production, and

contribution. In this study, we designed three

different chromosome structures: Chromosome A

for the first stage, Chromosome B for the second

stage, and Chromosome C for the third stage. Table

1 details the reception of order data by the

warehouses and provides data for the first stage.

Table 2 shows materials that are unavailable in

warehouses and need to be supplied by warehouses

from plants. It also outlines the processing methods

and how data is used in the second stage. Table 3

demonstrates the parts that are not provided by the

plant and need to be produced and supplied by

suppliers in this production stage. The data

presented in Table 3 corresponds to the third stage.

The related demand is primarily met by the

permutation-based genetic algorithm at the

warehouse level in the first stage. If the first stage

cannot fulfill the demand, the second stage is

activated, and if the second stage also falls short, the

third stage comes into play.

The supply chain model's aim is to provide

customers with products at a lower cost through

faster service. Key factors affecting the system

include production cost, supply, and transportation,

as they contribute to the overall cost of the process.

A faster system implies a shortened production

cycle and quicker product delivery to customers.

Additionally, the company seeks to reduce

production costs and enhance the entire system's

performance by accurately estimating the firm's cost

status and customer demands in terms of timing and

quantity.

Table 1. Data Representation in the First Stage (For

a Customer Set of 5)

In the practical implementation of the system,

optimization was carried out utilizing data from the

Warehouse, Plant, and Supplier databases. The

optimization process commenced by considering lot

sizes ranging from 10 to 200 as data sets, and a

permutation-based Genetic Algorithm (GA) was

applied and assessed, with the system costs not yet

factored in. The data contained in Table 2, Table 3

and Table 4, as shown in the operational columns of

Figure 3, were leveraged to evaluate the overall

system cost. Table 4 presents information from the

warehouse database, housing data specific to the

first stage. This database includes details such as

product type, distance from the central point, and

current stock status. Conversely, Table 5 provides

insights regarding the plant database in the second

stage, encompassing product types, stock status,

production rates, and distances from the central

point.

Table 2. Warehouse Database and Its Contents

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Table 3. Plant Database and Its Contents

The data within the initial stage's database forms

the system's primary decision-making mechanism. It

should a product become unavailable in the

warehouses, the plant information, which is part of

the second stage's database, comes into play,

triggering the system's decision-making mechanism.

Table 4. Supplier database and content

Table 6 encompasses a database containing

supplier details relevant to the third stage. This

information comprises elements like product

components and supply lead time. Figure 3 displays

the operational flow of the system's general

functioning mechanism. The system operates by

deducing the optimal operational pattern through the

application of a genetic algorithm after receiving

essential input data from the database module. Table

5 illustrates the product selection from various

warehouses based on heuristically chosen x and y

coordinates to satisfy the demands of a group of 10

customers. Meanwhile, Table 6 provides insight into

the product quantities remaining in the warehouses

after meeting these customer demands. The

distribution of the leftover products following the

fulfillment of all customer group requirements is

detailed in Table 9.

Fig. 3: Evaluation process of the supply chain with

Table 5. The amount of products in all warehouses

after the demand of customer group of 10 persons

are met

Table 6. Distribution of products selection by a

customer group of 10 persons

As indicated in Table 7, customer demand is

fulfilled at Level 1, corresponding to the warehouse

level, when it falls within the range of 10-110. In the

case of demand ranging from 120-140, it is

addressed at Level 2, which represents the plant

level. For demand falling within the range of 150-

200, fulfillment occurs at Level 3, denoting the

supplier level. This implies that customer demand is

promptly satisfied when the first two levels are

involved. However, the system requires a certain

response time to fulfill the demand when it falls

between 150-200.

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Table 7. Inventory Status in Response to Product

Demand from Customers

5 Results

Table 8 presents CPU time (in seconds) and cost

values derived from three programs. When

considering customer demand in the range of 10-

110, Hu's program demonstrates remarkable

efficiency, completing operations swiftly, while

Haupt & Haupt's program delivers cost savings of

nearly 40%. Notably, as customer demand increases

over time in Haupt & Haupt's programs, the

operational duration also extends, as visually

represented in Figure 4. Especially when customer

demand stands at 40, Haupt & Haupt's program

stands out, offering a solution at a substantial 86%

cost reduction. Consequently, Haupt & Haupt's

program appears well-suited for Stage 1 customer

demands.

For customer demand levels ranging from 120

to 140, the improved program emerges as an

attractive option, providing cost-efficient solutions

with a 25% reduction, albeit at the expense of a 3-5

second increase in operational time compared to

Hu's program. Similarly, when the demand falls

within the 150-200 range and is addressed at the

third level, the improved program may be the

preferred choice. Although the improved program

does entail an 18% higher cost than Haupt &

Haupt's program for customer demands at this stage,

it offers specific advantages. A detailed breakdown

of solution costs provided by the three programs is

available in Figure 5.

Table 8. Contrasting CPU Time (in seconds) and

Cost Results of Hu's, Haupt & Haupt's Permutation-

Based Genetic Algorithm Program, and the

Enhanced Program.

Fig. 4: Contrasting CPU Time (in seconds) Values

for Customer Demand - A Comparative

Examination of Hu, Haupt & Haupt, and Enhanced

Permutation-Based Genetic Algorithm Programs

Fig. 5: Comparison of cost values among the Hu

method, Haupt & Haupt method, and an enhanced

Permutation-Based Genetic Algorithm program in

response to customer demand.

6 Conclusion

In supply chain management, operational efficiency

and customer satisfaction are the key factors in

ensuring production and distribution coordination.

Permutation-based Based Genetic Algorithm

(PBGA) was used to reduce cost and improve lead

time. With the results obtained, the effectiveness of

120

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Customer Demand

Cost

Hu's program

Haupt&Haupt's program

Improved program

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the optimization technique applied in supply chain

management was tested.

The implementation of the PBGA method

resulted in a 15% improvement in production costs

and a 12% improvement in distribution costs. This

improvement was achieved through efficient use of

resources and effective task sequencing. These

factors also contribute to a direct increase in the

profitability of the model considered.

It also contributes directly to customer

satisfaction with a 20% reduction in delivery times.

These improvements also strengthen the competitive

position in the market. It is seen that the PBGA

method gives a better result compared to the basic

GA method. As a result, the PBGA method can be

preferred as a method that can be used effectively in

such models.

Effective resource allocation is crucial for cost

control and operational efficiency. By optimizing

the allocation of production and distribution

resources, PBGA reduced idle time at production

facilities by 25% and vehicle idle time for

distribution activities by 15%. These improvements

underline the algorithm's ability to maximize the use

of available resources.

In comparison with the classical GA method,

the proposed PBGA method shows a higher

performance in terms of both cost and time

parameters. Therefore, the use of this method should

be preferred for such model structures in terms of

analyzing results closer to the actual optimal result

value in a shorter time.

In conclusion, the Permutation-Based Genetic

Algorithm has proven to be a powerful tool to

address the challenges of supply chain optimization.

Its adaptability, robustness, and ability to deliver

substantial cost reductions and lead time

improvements make it a valuable asset for modern

supply chain management. The results obtained

from this research have direct and tangible

implications for our business, including improved

profitability, heightened customer satisfaction, and

enhanced operational efficiency.

Within the scope of the next study, taking into

account the following parameters in the

performance analysis process, consistent predictions

can be realized by using machine learning

approaches, especially deep learning, in the

clustering of data and prediction processes with

Artificial Intelligence / ML Based algorithms. At the

same time, by developing a digital twin approach in

the AI-based production planning and scheduling

process, instantaneous changes in the system can be

easily observed with an equivalent simulation

approach.

SCM KPIs: Typical KPIs used to monitor SCM

improvements:

- Demand fulfillment index

- Inventory Supply Days (average)

- Forecast Accuracy (weighted average)

- Delivery Performance/shipment compliance

- Commitment to production

- Supply alignment

- End-to-end cycle time (from procurement to sale)

As we move forward, it is important to

acknowledge that the field of supply chain

management is dynamic, and future challenges and

opportunities will continue to emerge. This research

lays the foundation for further exploration,

including multi-objective optimization,

sustainability considerations, and real-time

adaptation to dynamic supply chain conditions. By

embracing innovation and advanced optimization

techniques, we position ourselves to meet these

challenges head-on and sustain our leadership in the

ever-evolving landscape of supply chain

management.

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