Page 1 of 11

European Journal of Business &

Social Sciences

Available at https://ejbss.org/

ISSN: 2235-767X

Volume 07 Issue 03

March 2019

Available online: https://ejbss.org/ P a g e | 884

A New Efficient Approach for Solving Multi-Objective

Transportation Problems

PREETI RANI

Extension Lecturer, Faculty of Mathematics,

SMGCW, Safidon (Jind)

ABSTRACT

Nowadays transportation plays an important role for economic growth of the country.

Combination of transportation and mobility are directly involved with growth of financial

system of the country and for that mature transportation infrastructure necessary. Not only

that, modification in basic mathematical structure of transportation is required like simple

objective function can be modified by multi objective function. This paper discusses multi- objective transportation problem, its different solution with limitation and provide better

Information Communication Technology (ICT) based solution to avoid some limitation of

multi-objective TP. It also discusses issues when multi-objective transportation associate with

technology and its solution.

Key Words: Multi-objective Transportation problem, Data Base, Knowledge Discovery IT

INTRODUCTION

Transportation is an essential part of modern society. It is not possible for each individual of

family to produce his own food, clothing, etc. Goods can be produced more efficiently in

factories, large farms, etc. but this necessitates the movement of both goods and people. The

whole structure of society involves a trade-off between the economies of scale and focusing

activities or groups of activities (factories, schools, office buildings, and cities) and the cost

of transporting people from home to work places and goods from factories to consumers thus,

the structure generates a problem known as Transportation Problem. The Transportation

Problem is a classic Operations Research Problem where the objective is to determine the

schedule for transporting goods from source to destination in a way that minimizes the

Page 2 of 11

European Journal of Business &

Social Sciences

Available at https://ejbss.org/

ISSN: 2235-767X

Volume 07 Issue 03

March 2019

Available online: https://ejbss.org/ P a g e | 885

shipping cost while satisfying supply and demand constraints. Although it can be solved as a

Linear Programming problem, other methods exist.

The Transportation Problem (TP) was first developed and proposed by F. L. Hitchcock since

1941[1], [2]. It usually aims to minimize the total transportation cost [3]-[7]. Other

objectives that can be set are a minimization of the total delivery time, a maximization of the

profit, etc. The Hitchcock-Koopman's transportation problem is expressed as a linear

transportation model as follows:

Minimize

 



m

i

n

j

ij ij z c x

1 1

Subject to

1,2,....., ( )

,

1

x a i m Supply i

n

j

 ij

 



1,2,....., ( ) ,

1

x bj

j n Demand

m

i

 ij

 



x foralli and j

ij  0

Where,

xij



the amount of goods moved from origin

i

to destination

j

ij c 

the cost of moving a unit amount goods from origin

i

to destination

j

i a 

the supply available at each origin

i

j b 

the demand available at each destination

j

m 

total number of origins (Sources)

n 

total number of destinations (Sinks)

This problem can be solved by classical transportation methods [17].

The transportation problem makes an important role in real life as for example minimization

of total cost, consumption of certain scarce resources such as energy, total deterioration of

goods during transportation, vehicle scheduling in public transit etc. From the investigation,

Page 3 of 11

European Journal of Business &

Social Sciences

Available at https://ejbss.org/

ISSN: 2235-767X

Volume 07 Issue 03

March 2019

Available online: https://ejbss.org/ P a g e | 886

the entire existing objectives in single objective transportation models are represented by

quantitative information. This may cause the negligence of some crucial points which cannot

be described by quantitative data [12], [13]. Real life decision making takes into account

multiple, often conflicting, criteria. For example in shortest path problem, where cyclists aims

to reach their destination in minimal time but along a safe route[9].

Factors that may influence route choice are road traffic, road condition and presence of

dedicated cycling facilities. Therefore, it is reasonable to formulate cyclist route choice as a

bi-objective problem with travel time as one objective, whereas all other route choice factors

are combined into a second objective that we call attractiveness. That means in reality,

considering only one objective of TP is not sufficient because it may not lead to the practical

optimal solution. Thus the Decision Maker (DM) is rather to pay attention on several

objectives on same time or in other words we can describe this as the limitation of single

objective TP. This limitation can be sought out by generating multi-objective TP.

MULTI-OBJECTIVE TRANSPORTATION PROBLEM (MOTP):

The multi-objective transportation model is set to solve the transportation problem

simultaneously associated with several objectives. Normally, existing multi-objective

transportation models use a minimization of the total cost objective as one of their objectives.

The other objectives may concern about delivery time, quantity of goods delivered,

underused capacity, reliability of delivery, energy consumption, safety of delivery, etc. The

multi-objective transportation problem with k objectives can be represented as [8]

min

 



m

i

n

j

ij f x c ij x

1 1

1

1

( )

min

 



m

i

n

j

ij ij

k

k

f x c x

1 1

( )

Subject to

1,2,....., .

,

1

x a i m for alli

i

n

j

 ij  

