**ABSTRACT**

The transportation problem is a special class of the linear
programming problem. It deals with the situation in which a commodity is
transported from Sources to Destinations. The transshipment problem is an
extension of the transportation problem where intermediate nodes which are also
referred to as transshipment nodes are added to account for locations such as
warehouses. My main objective is to model Coca Cola transportation as a
transshipment problem and also minimize the cost in transporting them. We will
formulate the Transshipment problem as a Transportation problem and use the
Transportation algorithm to solve it. The QM for windows Software will be used
to analyze the data. It was concluded that if Coca Cola Bottling Company adapts
this method, transportation cost will be minimized.

**CHAPTER 1**

**INTRODUCTION**

**1.1 BACKGROUND OF THE STUDY**

One of the key problem most
organizational manager‘s faces is how to allocate scarce

resources among various activities
or projects. Linear programming [LP], which is one of most widely used
operations research tools and has been a decision making aid in almost all
manufacturing industries as well as service organizations, is a method of
allocating resources in an optimal way. Linear programming deals with
mathematical programming that serve as a planning process to allocates resources
which includes labor, materials, machines and capital in the best possible
(optimal) way so that costs are minimized or profits are maximized (Reeb and
Leavengood, 2002).

According to Hillier and Lieberman
(1995), in linear programming, resources are known as decision variables and
the criterion for selecting the best values of the decision variables to
maximize profits or minimize costs is known as the objective function. They
however hope that, limitations on resource availability form what is known as a
constraint set whiles the word linear indicates that the criterion for
selecting the best values of the decision variables can be described by a
linear function of variables.

A linear programming problem can
also be expressed in terms of straight lines, analogous geometrical figures and
planes. In addition to the linear requirements, non-negativity restrictions
state that variables cannot assume negative values. That is, it is not possible
to have negative resources. It would be mathematically impossible to solve linear
programming problem using more resources than are available without that
condition. (Reeb and Leavengood, 2002)

Physical distribution of resources
is one important application of linear programming from one place to another to
meet a specific set of supplies. Transportation problem [TP] mathematically is
very easy to express in terms of an LP model, simplex method can be used to
solve such model. In view of this, the study seeks to focus on the transshipment
problem of non-alcoholic beverage industry by applying linear programming to
minimize transshipment cost.

The contribution of transportation
in industries in the global world cannot be overemphasized. Transportation is
said to contribute to customer satisfaction in most industry, more especially
the brewery industry by providing additional customer value when products
arrives on time, in the quantities required and undamaged. This serves as the
basis of enhancing market share, customer satisfaction and profitability.
According to Grant and Damel, (2006), the transportation sector of most
industrialized economics is so pervasive that often there is a failure to
comprehend the magnitude of its impact on our way of life.

Furthermore, Agyeman (2011),
emphasized that transportation is one of the largest logistics costs which
accounts for important portion of the selling price of most products. Hence,
the efficient management of transportation becomes more vital to a firm as both
inbound and outbound transportation costs increases.

Nevertheless,
Gibbons and Machin (2006) explained that transportation management and
operation has significant bearing on a firm's operations. Road, rail and air
transport networks for instance bring migrant workers into the cities, convey
commuters to and from work, and move the finished products of production to
their place of consumption.

Transportation problem refers to a
class of linear programming problems that involves selection of most economical
shipping routes for transfer of a uniform commodity from a number of sources to
a number of destinations. However, unbalanced transportation problem deals with
the total availability which is not equal to total demand, hence some of the
source or destination constraints are satisfied as inequalities.

Transportation problem concerns the
amount to be sent from each origin, the amount to be received at each
destination, and the cost per unit shipped from any origin to any given
destination is specified. The transshipment problem is an extension of the
transportation problem in which the commodity can be transported to a
particular destination through one or more intermediate or transshipment nodes
where each of these nodes in turn supply to other destinations. Therefore, for
transshipment, each point acts as shipper only or as a receiver only. Hence,
shipments may go through any sequence of points rather than being restricted to
direct connections from one origin to one of the destinations.

The unit cost considered from a
point considered as a shipper to the same point considered as a receiver is set
equal to zero. It is also assumed that a large amount of material to be shipped
is available at each point and act as stockpile, which can be drawn or
replenished. The main aim of transshipment problem is to ascertain the number
of units to be
shipped over each node so that all the demand requirements are met with the
minimum transportation cost. However, transshipment problem can be converted
easily into an equivalent transportation problem. This makes it possible to
apply the algorithm for solving transportation problem.

Transportation problem have been
studied extensively by many scholars in the past years. According to Brigden
(1974), transportation problem (TP) deals with mixed constraints. Brigden
(1974) solved this problem by considering a related standard transportation
problem having two additional supply points and two additional destinations.
Also, Klingman and Russel (1975) applied a specialized method for solving
transportation problem with several additional linear constraints. Furthermore,
Adlakha (2006) also designed a heuristic for solving transportation problem
with mixed constraints.

Firms in Ghana are currently facing
a number of difficulties in managing transportation due to recent fuel hikes in
the country and the current economic crises. This has affected the operational
cost, efficiency and reduces the profit margin of firms who are not able to
manage its transport well. However, many firms are still striving to strengthen
its internal process in order to minimize cost and gain competitive advantage.
Transshipment and transportation are adopted for planning bulk distribution in
most of the industries. Normally, in the absence of the transshipment, the
transportation cost goes higher. In the transshipment problem all the sources
and destinations can function in any direction. Therefore, transshipment is
regarded as very important instrument to reduce the transportation cost.

*For more Mathematics*

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**Item Type:**

**Ghanaian Postgraduate Material**

**| Attribute:**

**85 pages**

**| Chapters:**

**1-5**

**Format:**

**MS Word**

**| Price:**

**GH**

**₵**

**50**

**| Delivery:**

**Within 30Mins.**

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