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The Method of Logistic Optimization in E-commerce

Robert Bucki

(The College of Informatics and Management in Bielsko-Biała

Bielsko-Biała, Poland

rbucki@wsi.edu.pl)

Petr Suchánek

(Silesian University in Opava, School of Business Administration in Karviná

Karviná, Czech Republic

suchanek@opf.slu.cz)

Abstract: Rapidly changing business environment requires new approaches and methods for

supporting management systems in all types of companies. Modern companies doing business

use e-commerce systems by default. One of the key areas of e-commerce systems is logistics

and the supply chain. The optimal way to ensure the success of logistics and supply chains is to

use the methods of modeling and simulation based on appropriate models and especially its

mathematical representation. In this paper, authors highlight the customer-oriented model of the

e-commerce system and deal with logistic optimization and simulations. As an example,

a sample logistic structure which requires the adequate control approach is presented. This is

realized by means of heuristic algorithms which are responsible for meeting the set criterion.

Moreover, the criteria to either maximize the production output or minimize the lost flow

capacity of the logistic system or minimize the tool replacement criterion are introduced.

Equations of state are given in order to represent the flow of material through the logistic

system.

Keywords: e-commerce system, logistics, simulation, logistic process, production

maximization criterion.

Categories: C.4, H.1.1, H.4.2, I.6.8

1 Introduction

E-commerce development has acquired great importance in the contemporary

business. It has helped business organizations, businessmen and end users to

overcome the barriers of time and distance to sell, buy and carry out other business

transactions across the globe. The development of e-commerce makes it necessary to

search for new management methods and techniques designed to optimize the entire

e-commerce system. The emergence of e-commerce has changed the relationship

between customers and retailers and created a new need to restructure the entire

supply chain and logistic system. The main objective remains the maximization of the

whole system effectiveness which is to be achieved at the lowest possible costs. E-

commerce systems are by their nature considered as systems with low operating costs.

This must be provided by means of the adequate optimization approach. The area,

which could significantly affect the costs associated with running an e-commerce

system, is either logistics or the supply chain (SC). The initial point for the

Journal of Universal Computer Science, vol. 18, no. 10 (2012), 1238-1258

submitted: 30/6/11, accepted: 25/5/12, appeared: 28/5/12 © J.UCS

implementation of all types of systems is a suitable model with its own architecture

and mathematical description. Different types of models in conjunction with

a suitable mathematical representation allow us to perform the simulation process

whose outputs can help managers make suitable decisions. The major support of

simulation is provided by advanced computer systems. In this context, we often talk

about the so-called computational logistics. Computational logistics involves planning

and implementation of large and complex tasks using computations and higher

mathematics. Computational logistics is implemented in many areas, including the

flow and storage of goods, services, and related information from their point of origin

to the point of consumption. In computational logistics, optimization models and

algorithms must be developed and verified for the plan and execution of complex

logistics and supply chain systems. The main objective of this paper which emerges

from the above discussion is to present the importance of logistic optimization in

customer-oriented e-commerce systems as well as a sample logistic structure which

requires the adequately specified control approach. These days it is evident that

production activities are treated as sub-processes of trade processes. Should it be

thought that an e-commerce system is directly oriented on the order of the specified

product e.g. furniture, it is necessary to properly emphasize the problem of order

realization as well as supply of a ready product. Moreover, it is also indispensable to

optimize logistics within realizing the determined products. The main goal of the

paper is to present how the order manufacturing process is controlled by means of

heuristic algorithms while implementing the required criterion.

2 E-commerce system

The structural model describes an e-commerce system as a set of functionally

connected components (Figure 1). The main basic components of e-commerce

systems are:

customers and generally business environment,

the Internet,

the web server,

LAN (Local Area Network),

CRM (Customer Relationship Management) characterized among others in

[Pradeep, 10],

ERP (Enterprise Resource Planning) [Bredford, 09],

payment system [White, 08],

delivery of goods [Chopra, 09],

after-delivery (after-sales) services,

information systems (CRM/ERP) of cooperating suppliers.

Important and integral parts of the whole system are hardware, software, people,

co-operative suppliers, legislation and generally information and communication

technologies (ICT). All shown parts of e-commerce systems are supported and

controlled by the management at all control levels (tactical, operational, strategic).

Most important for control and support functions are SCM - Supply Chain

Management, FRM - Financial Resource Management, HRM - Human Resource

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Bucki R., Suchanek P.: The Method of Logistic Optimization ...

Management, IBP – Integrated Business Planning and Information

system/Information technology administration (IS/ICT management).

Figure 1: Basic structure of e-commerce system Source: after [Suchánek, 10]

3 Customer-oriented e-commerce system

The e-commerce system should be seen as the part of a complete business

environment. Here, the main decisive part of the environment is understood as the

customer whose orientation is one of the main prerequisites of an effective

management system.

Based on its own research, Simulation Systems Ltd. [Simulation Systems, 11]

presented the fundamental definition and description of customer-oriented systems.

They say that each customer-oriented system results from the individual work with

the client taking into account specific details of his business processes. The customer-

oriented system is made according to the principle emphasizing the well-known truth

which reads that the system must be created for the user, avoiding the need to adjust

the user for the system.

The development of customer-oriented systems includes the full cycle of tasks,

such as: collection and analysis of data needed for automation, definition of the

requirements, designing, implementation, introducing, testing and maintenance of the

system. The specific features of the approach to designing of customer-oriented IS are

formulated as follow:

1240 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

fundamental analysis of the customer’s business as a base for working out the

solutions corresponding to the actual goals and problems of the customer;

detail elaboration and coordination with the customer of all stages of the project

development, control points and required resources;

support of the convenient mode of maintenance, modification and extension of the

system;

provision of openness, mobility and scalability of the system.

Customer-oriented functionalities of e-commerce comprise business-to-customer

(B2C) applications such as remote shopping, banking and infotainment-on-demand.

To study the possibilities of e-commerce functionality improvement, the structure

model presented in Figure 1 does not seem to be sufficient. Any company strives to

accomplish its business strategy. Following the business strategy, long-term and

short-term objectives and targets are set.

After measuring the results achieved in a certain period of time, the differences

from the target values are evaluated and corrective actions for the next term are

specified by the company management. Thus, in a very general way, any business

system can be looked upon as a specific form of a control loop (Figure 2). In our

opinion, this holds true also for e-commerce systems.

Let us set an example in which a customer faces a billboard showing a car. Then

the customer decides to buy this car immediately. There is a credit card in his pocket

with the necessary financial coverage and the telephone number of the seller on the

billboard. The customer contacts the dealer and tells him he wants to buy a car

immediately specifying required parameters and the geographical localization (the

customer does not have to call, but he can use the Internet via his mobile phone or

another mobile device). The dealer should be able to determine immediately where

the desired car is available and how long it will take them to deliver the car to the

customer. Let us suppose that using the information system the dealer determines that

the car can be delivered to the customer’s destination in e.g. half an hour and

subsequently makes a quote. If the customer agrees, he can sit on a bench next to the

billboard and wait. Within this period of time, a responsible person will bring him the

required car. The customer makes a payment by means of a mobile credit card reader

and takes over the car. This example presents another possible direction of e-

commerce development. The scheme in Figure 3 fully complies with the need of

direct orientation to the customer. However, it requires to solve a wide range of

technical, personnel and legal issues. The discussed model seems to be realistic. In

order to make this model fully operational in the real environment, the following

conditions have to be met:

ensuring unambiguous identification of the customer (the customer who has made

the order);

defining the legal framework for this type of business in particular;

defining principles of the legal protection of the dealers (for example it is

necessary to ensure that the customer could not deny the ordered goods – click-

wrap and browse-wrap contracts);

ensuring technical support of the mobile credit card readers;

defining and implementing the logistic system (especially the supply chain).

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Bucki R., Suchanek P.: The Method of Logistic Optimization ...

Figure 2: Generic e-Commerce model Source: after [Suchánek, 11]

The controlled subsystem consists of the actual e-Commerce system itself. The

inputs constitute the management decisions on the e-Commerce parameters like

prices, investments, marketing decisions, safety rules etc. The outputs include sales

value, profits and margins, return on investment (ROI), stability, security and other

key performance factors. The outputs are measured in the measuring element and

compared with the targets in the differential component.

There is a general rule on the basis of which the customer wants to find products

quickly and easily and get products in the shortest time as well as to pay for goods in

the selected way and to have the longest possible warranty. One way of meeting this

rule is to accept the basic philosophy of orientation on the customer and use all

available technologies and business and management practices in company

operations. The general business pattern following the stated conditions can be

presented as transformation of Figure 1 into Figure 3. Using the pattern shown in

Figure 3, it is possible to advance much further in the considerations.

1242 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

Figure 3: Main activities focused on the customer

4 Logistic and supply chain and its optimization in e-commerce

For the discussed purpose, namely the area of electronic commerce, logistics is

defined as a business planning framework for the management of material, goods,

services, information and capital flows. It includes the increasingly complex

information, communication and control systems required in today's business

environment [Logistics, 96], [Langevin, 10]. Especially, in business, the logistics has

the meaning of the way of the supply of goods by which the customers’ requirements

can be solved. It determines the path of transporting goods and a lot of important

information exchanged between the consumer, production or source points. It has the

special term production logistics which means that the supply of the high quality

products in time along with the security must be assured (for tax related products: like

iphone, iPod, etc. which are for sale). Logistics and the entire system must be

controlled. In this context, we are talking about the management of logistics and

supply chain management.

Logistics management is that part of the Supply Chain Management process

which is responsible for planning, implementing and controlling the efficient,

effective forwarding and reversing the flow and storage of goods, services, and

related information between the point of origin and the point of consumption in order

to meet customers' requirements. Supply Chain Management (SCM) encompasses the

planning and management of all activities involved in sourcing and procurement,

conversion, and all Logistics Management activities. Importantly, it also includes

coordination and collaboration with channel partners which can be suppliers,

intermediaries, third-party service providers and customers. In essence, Supply Chain

Management integrates supply and demand management within and across companies

[Cantrell, 04].

One of the key areas of e-commerce system is to optimize the whole e-commerce

system. It is clear that to be optimized, the entire e-commerce system and all of its

subsystems must be optimized. The rules defined by [Ratliff, 03] as the general

principles of logistic (as a subsystem of the e-commerce system) optimization can be

1243

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

adopted:

Objectives - must be quantified and measurable;

Models - must faithfully represent required logistic processes;

Variability - must be explicitly considered;

Data - must be accurate, timely, and comprehensive;

Integration - must support fully automated data transfer;

Delivery - must provide results in a form that facilitates execution, management

and control;

Algorithms - must intelligently exploit individual problem structure;

People - must have the domain and technology expertise required to support the

models, data, and optimization engines;

Process - must support optimization and have the ability to continuously improve;

Return on Investment (ROI) - must be provable considering the total cost of

technology, people and operations.

Optimization is a highly timely topic in the field of manufacturing and supply

chain management. Optimal control of a substitutable inventory system, structured

assemble-to-order systems and the impact of advance demand information on various

production-inventory control mechanisms are the key factors which must be taken

into account while planning order realization procedures [Shanthikumar, 03].

A deterministic system does not involve any randomness in the development of

subsequent states of the logistic system. Therefore, such a model will always produce

the same output from a given initial state. Stochastic ordering is a fundamental guide

for decision making under uncertainty. It is also an essential tool in the study of

structural properties of complex stochastic systems [Shaked, 07]. Supply chain

optimization is the application of processes and tools to ensure the optimal operation

of a manufacturing and distribution supply chain. This includes the optimal placement

of inventory within the supply chain, minimizing operating costs (including

manufacturing costs, transportation costs, and distribution costs). This often involves

the application of mathematical modelling techniques using computer software.

The general objective is to find optimal logistic network design. In the logistic

network design problem (LNDP), decisions must be made regarding the selection of

suppliers, the location of plants and warehouses, the assignment of activities to these

facilities, and the flows of raw materials and finished products in the network

[Cordeau, 08]. Optimal network design/redesign minimizes inventory carrying,

warehousing, and transportation costs while satisfying customer response-time

requirements. Specifics include the network’s distribution levels and centers, location

and mission of each facility, assignment of supplier and customer locations to each

center, and inventory deployment [Frazelle, 06]. To create an optimal network

design/redesign, Frazelle recommends a 10-step of logistics network design process

shown in the Table 1 (analogous approach can be found for example in [Groothedde,

11]).

1244 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

10-step of logistic network design process

1. Assess/evaluate the current network

2. Design and populate the network optimization database.

3. Create network design alternatives such as more or fewer hierarchies,

multi-commodity flows, pooling opportunities, merge-in-transit, direct

shipping, cross docking, and supply-flow optimization concepts.

4. Develop a network optimization model.

5. Choose a network optimization tool.

6. Implement the network model in the chosen tool.

7. Evaluate alternative network designs.

8. “Practicalize” the recommended network structure.

9. Compute the reconfiguration cost.

10. Make a go/no-go decision.

Table 1: The 10-step of logistic network design process

Simulations can be effectively used in order to support optimization procedures in

the state of uncertainty. Simulations are based on modelling and in particular

mathematical models. Computer simulations are used extensively as models of real

systems to evaluate output responses. Applications of simulation are widely found in

many areas including supply chain management, finance, manufacturing, engineering

design and medical treatment [Fu, 95], [Kim, 05], [Semini, 06]. Supply chain

simulations [Chang, 03]:

help to understand the overall supply chain processes and characteristics by

graphics and/or animation;

are able to capture system dynamics: using probability distribution, user can

model unexpected events in certain areas and understand the impact of these

events on the supply chain.

could dramatically minimize the risk of changes in planning process: By what-if

simulation, user can test various alternatives before changing plan.

Traditionally, the formal modelling of systems has been carried out by means of

a mathematical model which attempts to find analytical solutions to problems which

enable the prediction of the system behaviour on the basis of the set of parameters and

initial conditions. There are many methods for the purposes of simulation and

especially simulation-based optimization techniques. Kleijnen claims that supply

chain simulations can be carried out by means of the use of spreadsheet simulation

methods, system dynamics, discrete event simulation and/or business games

[Kleijnen, 03]. E-commerce systems can be classified into the category of intelligent

systems. Evolutionary optimization can be effectively used for the optimization of

intelligent systems. Evolutionary optimization is becoming an omnipresent technique

in almost every process of intelligent system design. Just to name few, engineering,

control, economics and forecasting are some of the scientific fields that take

advantage of an evolutionary computational process that supports engineering

systems with intelligent behavior [Nedjah, 08]. Detailed breakdown of the simulation-

1245

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

based optimization techniques is presented in Table 2 [Ashram, 96], [Silva, 05].

Simulation-based Optimization Techniques

Deterministic search techniques

Heuristic search technique

Complete enumeration and

random choice

Response surface search

Pattern search techniques

Conjugate direction search

Steepest ascent (descent)

Tabu search technique

Hooke and Jeeves type

techniques

Simplex-based techniques

Probabilistic search techniques

Random search

Pure adaptive and hit-and-run

search

Evolutionary Techniques

Simulated annealing

Genetic techniques

A short comparison

References and Further

Readings

Stochastic approximation techniques

Kiefer-Wolfowitz type

techniques

Robbins-Monro type

techniques

Gradient surface method

Post-solution analysis Rare Event Simulation

Table 2: Simulation-based Optimization Techniques

For the purpose of presenting a sample logistic manufacturing system,

deterministic search techniques and especially heuristic search techniques are

implemented. Professor Ashram further states that the heuristic search technique is

probably most commonly used in optimizing response surfaces. It is also the least

sophisticated scheme from the mathematical point of view and it can be thought of as

an intuitive and experimental approach. The analyst determines the starting point and

the stopping rule based on the previous experience with the system. Generally,

heuristic search methods generate and test algorithms in order to meet the set

manufacturing criteria.

In e-commerce, logistic optimization must be based upon business objectives to

find the schedule producing the product with the least cost or the shortest production

lead time. It all means that the planner ought to be presented with the best algorithm

enabling him to manufacture the best sequence of products. Traditionally simulation

models have been used effectively on a project-by-project basis to analyze changes to

a factory physical equipment. Simulation models contribute more effectively to the

design of new methods for production scheduling and new supply chain

configurations. By the nature of the control the simulation model is to assist with the

day-to-day scheduling of the company doing business.

Knowing that there is an order to be realized, we can easily find out in advance

what kind of charge will be necessary and what amount of it will be needed. In this

context we are talking about supply chain master planning presented, for example, in

1246 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

[Schröpfer, 09]. Running the simulation process for just a few hours, the results show

a completely different but more accurate story. This is why simulation is so important.

Simulation, and only simulation, takes into account the combined effect of variability,

uncertainty, and complex interdependencies between processes. Simulation is helping

companies improve their businesses and become more competitive. Increasingly

competitive markets bring new challenges and customers' demands are constantly

changing. As a result, manufacturers need to become more responsive, more quickly,

more efficiently, yet often within tighter budgets and timescales. Simulators are

helping them to visualize, analyze and optimize their processes to achieve these

business performance improvements [Bucki, 09].

Following the above remarks, in the next section we present the sample logistic

structure which requires the adequate control approach.

5 General assumptions of the sample logistic system

The problem itself consists in determining the sequence of elements of the order

vector which are to be realized subsequently. The proposed heuristic algorithms

choose the required element on which certain operations are carried out. The state of

orders decreases after each production decision which influences the state of the

whole logistic system at every stage. The given criteria are used on condition that

each of them is associated by adequate bounds. Assuming that the results of

calculations which are made for one chosen heuristic algorithm do not deliver

a satisfactory solution, there arises a need to test other algorithms.

Let us assume that the logistic system consists of I active logistic blocks arranged

in a series. Each logistic block is meant to carry out a production operation. There are

no buffer stores placed between logistic blocks in the discussed case. Each logistic

block consists of a certain number of production stands. If a production stand in the

logistic block does not have enough production capacity to accept all production flow,

another parallel stand carrying out the same production operation is activated in this

exact logistic block. If a production stand is not needed any more, it is deactivated in

the discussed logistic block [Bucki, 10].

Let us introduce the vector of charges:

l

wW , Ll ,...,1,

where: l

w - the l-th charge material.

Let us introduce the vector of orders:

n

zZ , Nn ,...,1

,

where: n

z - the n-th production order (given in units).

Having defined the vector of charges W as well as the vector of orders Z, the

assignment matrix of products to charges is proposed as follows:

ln,

, Nn ,...,1

, Ll ,...,1,

where: ln,

- the assignement of the n-th product to the l-th charge material.

Elements of the assignment matrix take the following values:

1247

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

0

1

,ln

if the n-th product is realized from the l-th charge,

otherwise.

The assignment matrix of products to charges is presented as follows:

We also assume that used charge vector elements are immediately supplemented,

which means that we treat them as the constant source of charge material. However,

for simplicity reasons, it is assumed that each n-th product is made from the universal

charge which enables realization of the given n-th product from any l-th charge

material element, Ll ,...,1. The determined charge material enters the production

system itself. Machines in each logistic block i

M, Ii ,...,1

in the production system

carry out autonomous operations on the specified material. The operations are

realized subsequently. If the logistic block i

M is able to accept the material from

which the n-th product is made, it is passed to this block and after carrying out the

adequate operation is passed to the block 1i

M. After leaving the I-th block, it fills

the elements of the order vector in the serial logistic system.

n

I

jI

JI

i

ji

Ji

j

J

lz

m

m

m

m

m

m

m

m

m

w

1,

,

,

1,

,

,

1,1

,1

,1

......

Let us introduce the vector of production stands corresponding with the logistic

blocks:

jii mM ,

, Jj ,...,1

,

where: ji

m, - the j-th production stand in the i-th logistic block.

The stage k, Kk ,...,1

is the moment at which the manufacturing process at any j-th

production stand in the i-th logistic block begins. We need to consider that decisions

are made at the stage 1k, Kk ,...,1.

It is assumed that operations in the stands in the system are realized subsequently.

The structure scheme of the serial logistic system is presented as follows:

1248 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

k

n

k

I

kjI

kJI

k

i

kji

kJi

k

kj

kJ

ln z

e

e

e

e

e

e

e

e

e

1,

,

,

1,

,

,

1,1

,1

,1

,.....

,

where: Ii,...,1,Jj ,...,1,Kk ,...,1,, Nn ,...,1

Ll ,...,1.

Elements representing production stands take the following values:

0

1

,

kji

e

if the n-th product is realized by the j-th production stand in

the i-th logistic block at the k-th stage,

otherwise.

Moreover, it is assume that 1

1,

k

i

ie

Having assumed the above, we can introduce the life vector of the logistic system

for a new brand set of tools:

in

gG ,

, Nn ,...,1

, Ii ,...,1

,

where: in

g,- the number of the n-th product units which can be realized in any

j-th production stand of the i-th logistic block before the tool in

this stand is completely worn out and requires an immediate

replacement.

The elements of the matrix G take the following values:

0

,

in

g

if the n-th product is realized in the j-th production stand

of the i-th logistic block,

,...,1

,

otherwise.

Moreover, we can assume that

in

Ii

g,

1

,

,...,1

.

If the number

is reached for the given n-th element of the vector Z in the j-th

production stand of the i-th logistic block, the tool in this exact stand has to be

replaced by a new one.

Let

1

,

1)( kji

k

nnsS be the matrix of state of the logistic system for the

n-th product realization at the stage 1

k where 1

,

)( kji

ns is the number of units of the

n-th product already realized in the j-th stand of the i-th logistic block with the use of

the installed tool. The matrix of state can be shown in the following extended form:

1249

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

1

1,

1

1,

1

1,1

1

,

1

,

1

,1

1

,

1

,

1

,1

1

)(...)(...)(

)(...)(...)(

)(...)(...)(

k

I

k

i

k

kjI

kji

kj

kJI

kJi

kJ

k

n

nsnsns

nsnsns

nsnsns

S

Let

1

,

1)( kji

k

nnpP be the matrix of the flow capacity of the logistic system

for the n-th product realization at the stage 1

k where 1

,

)( kji

np is the number of

units of the n-th product which still can be realized in the j-th stand of the i-th logistic

block.

The matrix of state can be shown in the following extended form:

1

1,

1

1,

1

1,1

1

,

1

,

1

,1

1

,

1

,

1

,1

1

)(...)(...)(

)(...)(...)(

)(...)(...)(

k

I

k

i

k

kjI

kji

kj

kJI

kJi

kJ

k

n

npnpnp

npnpnp

npnpnp

P

On the basis of the above assumptions we can determine the flow capacity of

the j-th production stand in the i-th logistic block for the n-th element of the order

vector Z at the stage 1k:

1

,,

1

,)()( kjijn

kji nsgnp

The manufacturing procedure consists in realizing orders in sequence

(manufacturing of the order may begin when the previously realized one leaves the

logistic system). Its disadvantage consists in the need of waiting for completing the

manufacturing process of a certain product before resuming it again for the next one.

This results in not using the available flow capacity of the whole production system.

Moreover, during the production course tools must be replaced. When another

element of the order vector Z enters the production system, the state of the system has

to be recalculated.

Let us define the production times for the n-th product, Nn ,...,1

in the j-th

production stand of the i-th logistic block in the matrix form:

prIN

priN

pr

N

pr

In

pr

in

pr

n

pr

I

pr

i

pr

pr

T

,,

1,

,

,

1,

,1,11,1

......

......

......

If the n-th product is not realized in the j-th production stand of the i-th logistic

block, then 0

,

pr

in

(in this case the implemented technology excludes production

operations in certain logistic blocks).

Let us define the vector of replacement times for the tools in the logistic system:

repl

I

repl

i

replrepl

T

......

1

,

1250 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

where: repl

i

- the replacement time of the tool in the j-th production stand of the i-th

logistic block.

If pr

in

pr

in 1,

,

, then the j-th production stand of the i-th logistic block becomes

blocked while manufacturing the n-th product so there is the need to activate the

production stand 1.1 ji

m which is based on the assumption that the number of active

production stands in the i-th logistic block is increased by 1 (not to block the

production process in the logistic block 1i

M) on condition that the number i

J is not

exceeded, where i

jis the number of the j-th production stand in the i-th logistic

block. It is justified by the fact that the production of the subsequent part of the n-th

order from the vector

Z

can be started instantly without having to await for

completing the current production operation in the logistic block i

M. The structure of

such a system guarantees continuing the production activity in any stand 1j in the

i-th logistic block if the stand i

j requires tool replacement.

Let us introduce the production rate vector

in

vV ,

. Its element in

v, is the

number of units of the n-th product made in the time unit.

Let us calculate the total manufacturing time of all elements from vector Z:

K

k

I

i

repl

i

k

i

pr

in

I

i

N

nyT 0

,

1

The coefficient k

i

y takes the following values:

0

1

k

i

y

if the replacement procedure of the tool in the i-th stand is carried out,

otherwise.

6 Production criteria

The criteria presented hereby are to either maximize the production output or

minimize the lost flow capacity of the production stands or minimize the tool

replacement time. Let us propose production criteria for the logistic system along with

the necessary bounds:

6.1 The production maximization criterion

Let us introduce the production maximization criterion:

max

11111

K

k

N

n

k

n

K

k

kxqQ ,

where: k

n

x - the number of units of the n-th element realized at the k-th stage.

The tool replacement bound: cy repl

i

I

i

k

i

1

,

where: c - the maximal allowable tool replacement time,

1251

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

repl

i

- the replacement time of the used tool in the j-th stand of the i-th logistic

block.

The flow capacity bound:

in

I

i

kin

k

igpy ,

1,

,

where: kin

p, - the lost flow capacity of the j-th stand of the i-th logistic block

at the k-th stage.

The production-maximizing criterion is reduced to the replacement time of tools

and flow capacity bounds.

6.2 The lost flow capacity criterion

Let us introduce the flow capacity criterion:

min

1,

11122

I

j

kin

K

k

I

i

k

i

K

k

kpyqQ

The tool replacement bound: cy repl

i

I

i

k

i

1

The order bound: n

N

n

k

nzx

1

The lost flow capacity criterion is reduced to the replacement time of tools and

order bounds.

6.3 The minimal tool replacement time criterion

Let us introduce the flow capacity criterion:

min

11

3

repl

i

K

k

I

i

k

i

yQ

The flow capacity bound: in

I

i

kin

k

igpy ,

1,

The order bound: n

N

n

k

nzx

1

The minimal tool replacement time criterion is reduced to the flow capacity

bound and the order bound.

7 Equations of state

The state of the discussed serial logistic system for the n-th element changes in the

production course as follows:

K

n

k

nnn SSSS ......

10

The state of the j-th production stand of the i-th logistic block in case of the n-th

product manufacturing changes consequently:

1252 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

Kji

kjijiji nsnsnsns ,,

1,

0

,)(...)(...)()(

which can be written in the following form:

k

n

kji

kji

kji xns

ns

ns

1

,

1

,

,

)(

)(

)(

if no n-th product is realized in the j-th stand of

the i-th logistic block at the k-1 stage,

otherwise.

Let i

be the tool to be replaced with a new one, I

i

1 . The state of the j-th

production stand of the i-th logistic block in case of replacement of tools changes in

the way shown below:

0

)(

)(

1

,

,

kin

kin ns

ns if

i at the stage k-1,

if

i at the stage k-1.

If tools in all stands are totally worn out, then GS

and they need an immediate

replacement procedure to resume the production process.

The order vector Z changes after every production decision:

Kk ZZZZ ......

10

The order vector is modified after every decision about production:

1

1

k

n

k

n

k

n

k

nz

xz

z if the number of units k

n

x of the n-th order is realized at the k-th stage,

otherwise.

8 Heuristics

In order to control the logistic process we need to implement heuristics for

determining elements from the vector Z for the production process. The following

control algorithms are put forward:

8.1 The algorithm of the maximal order

This algorithm chooses the biggest order vector element characterized by the biggest

coefficient 1k

n

in the state 1k

S.

To produce the element a, the following condition must be met:

1

1

1max

)( k

Nn

k

a

kn

aq

,

where: 11 k

n

k

nz

.

1253

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

The above approach is justified by avoiding excessive bringing the production

line to a standstill in order to change an element to be manufactured. If in state 1k

S

only minimal orders were chosen, in consequence the number of orders might be

reduced. Such control is favorable because the serial production line is blocked and

must be stopped only in order to replace the tools in certain stands (on condition that

the replacement process disturbs the flow of the material).

8.2 The algorithm of the minimal order

This algorithm chooses the smallest order vector element characterized by the

smallest coefficient 1k

n

in the state 1k

S.

To produce the element a, the following condition must be met:

1

1

1min

)( k

Nn

k

a

kn

aq

,

where: 11 k

n

k

nz

.

The above approach is justified by the need to eliminate the elements of the order

vector Z which could be sent to the customer just after the n-th product leaves the

production line on condition that the customer sets such a requirement.

8.3 The algorithm of the relative order

This algorithm chooses the order element characterized by the maximal relative order

coefficient 1k

n

in the state 1k

S.

To produce the element a, the following condition must be met:

1

1

1max

)( k

n

Nn

k

a

kaq

,

where: 0

1

1

n

k

n

k

nz

z

.

It is assumed that the orders are realized one after another that is to say each order

element zn in the state 1k

S is reduced partly. Such control is advantageous when

some parts of the order are needed earlier and the rest can be manufactured later.

9 The block diagram of the logistic process

In order to create the block diagram of the logistic manufacturing system (Figure 4)

criteria

Q, B,..,1

must be implemented where:

the production maximization criterion → 1

Q

the lost flow capacity criterion → 2

Q

the minimal tool replacement time criterion → 3

Q

1254 Bucki R., Suchanek P.: The Method of Logistic Optimization ...

Moreover, a heuristic algorithm

h,

,...,1

is responsible for choosing

the n-th element of the order vector where:

the algorithm of the maximal order → 1

h

the algorithm of the minimal order → 2

h

the algorithm of the relative order → 3

h

Figure 4: The block diagram of the discussed logistic manufacturing system

10 Conclusions

The problem presented in the paper discusses the issue of the serial production system

with no buffer stores. The system delivers ready products corresponding with the

elements of the order vector. The main goal is to fulfil the task by the set criteria.

There is also a possibility to implement a two- or three-criterion model. Such models

may lead to delivering a solution which would satisfy criteria included in the

discussed model only partly as there should be bounds added. Heuristic algorithms

1255

Bucki R., Suchanek P.: The Method of Logistic Optimization ...

proposed in the paper enable the operator to choose the satisfactory production

sequence on the basis of which a certain element of the order vector is determined to

be realized. The use of one specified algorithm does not mean that we will achieve the

result satisfying the given criterion. It is advisable to implement other algorithms and

decide which one minimizes the order realization time, the loss of residual capacity,

and the total replacement time or satisfies a hypothetical customer’s demand not

specified hereby. Another idea already used in available works is to simulate the

combination of heuristic algorithms. By means of this method, we are able to combine

two or more algorithms. It also seems reasonable to draw products for manufacturing.

To achieve a satisfactory result a big number of simulations must be carried out. In

conclusion, it must be admitted that a simulator imitating real environment should be

built to continue this work. Simulation experiments carried out in the synthetic

environment may deliver an answer which heuristic approach is the expected one for

a certain criterion. The idea of time scaling by means of the simulation method on

condition a satisfactory number of simulation experiments is carried out seems to able

to deliver the results minimizing the total order realization time.

In conclusion, we can say that the interactive software combines real-life images,

with a step-by-step immersion process, which successfully replicates the experience

of controlling a real system. By providing the user with both the flexibility to operate

the whole system and the support of the data files, which can be easily downloaded, it

is possible to fit the simulator into any given system. Although the approach is

flexible, it is far from being an easy option. The design of the simulator ensures its

reliability at every stage of the technological process. Even in situations where there

can immerse a dose of uncertainty, the user will be able to count on the intuitive

support of the program. By using a simulator there will be an impact on further

production performance. The advantages far outweigh the costs of building

a simulator in a very short period of time proving its market value, which will

increase with every production unit. Operators will gain self-confidence as well as

improve their communication skills and learn how to contribute more effectively in

a plant activity, which is required of them in return.

Acknowledgements

This paper was supported by project ,,Strengthening of Competitive Advantages in

Research and Development of Information Technology in the Moravian-Silesian

Region" Nr. CZ.1.07/2.3.00/09.0197 within the EU Operational Program Education

for Competitiveness.

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