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 source to destinations.
The proposed transportation model of
manufacturing good to customers (key distributors) is considered in this
research. The data gathered were modelled as a linear programming model of
transportation type and represent the transport problem as a tableau and solve
it with computer software solves to generate an optional solution.
The main objective is to model the product of ABTS transportation as a
transportation problem and minimize the cost of transportation of plywood in
the ABTS Company. The quantitative method (QM) software will be used to analyze
the data.
CHAPTER 1
INTRODUCTION
1.1 Introduction
Forests are very important in the development of many African
countries as they play a key role in most aspects of the socio-economic lives
of the people.
Also, considering the signicant role forests play in
mitigating climate change, it is essential to conserve forests by reducing
deforestation and increasing forest cover. The United Nations' Millennium
Development Goals (Henceforth referred to as MDG) encourages developing
countries to meet certain targets aimed at helping them achieve a higher status
of development. Forestry plays an important part in Ghana's economy. In the
1980s, timber was the third-largest export commodity after cocoa and gold,
accounting for 5-7% of the total gross domestic product (GDP), and the forestry
sector employed some 70 000 people. Forests also provide 75% of Ghana's energy
requirements(Arsham,1992).
1.1.1 TIMBER USES
Some of the uses of timber are as follows: Air dispensers (eg
aquariums),Articial limbs, Bakers equipment, Balance, decks and terraces, Boat
and ship construction, Cladding, Beehives, Carving and sculpture, Cooperage,
Cabinet making, Fencing, Flooring, Furniture's, Glass manufacture log cabins,
Musical instruments, Pallets, Paper and paper products, Power poles, Saunas and
hot tubs, Scaolding, Shingles, Smocking produce(eg sh and meat), Railways
sleepers and Windows.
1.1.2 Timber benets (over other construction materials)
Timber is the only 100% renewable resource of construction
material
Renewable resource allows for the direct employment of
hundreds of thousands of people. Thus improving local economy.
Timber from managed plantations are Greenhouse Gas Reducing.
Ecologically safe and sound to handle and dispose
Natural Variations add esthetic interest.
1.1.3 Some Types of
Timbers Found in Ghana
Some of these timber are;
Odum(miliciaexcelsa), Awilemfosamina (albiziaferruginea),
teak (tactinagranais), wawa (tropolochitmseleroxylon), watapuo (cola
gigantean), potrodom (erythrophleumivorense), kokradua (pericopsiselata), kusia
(naucleadiderrichii), mansonai (African black walnut) , ofram
(terminaliasuperba) and ceiba.
1.2 Background to
the Research
1.2.1 Overview of
Forestation in Africa
Forest resources are essential to social and economic
activities in Africa;
as a result, they are important elements in both poverty
reduction and sustainable development strategies for many Sub-Saharan African
countries(Reeb and Leavengood,2000). There is therefore
the need to protect forests and implement policies and programs that ensure
that these forests are sustained for future generations. Also, considering the
rise in development activities such as the discovery of oil, increasing
activities in mining and the ever growing telecommunications industry on the
continent, it is necessary to evaluate or assess policies aimed at sustaining
forests so this essential resource is not lost in the future(? ).
One of the most important and successful applications of
quantitative analysis to solving business problem has been in the physical
distribution of products, commonly referred to as transportation problems(Goldfarb and Kai,1986).
Basically, the cost of shipping goods from one location to
another is to meet the needs of each arrival area and every shipping location operation
within its capacity. In this context, it refers to a planning process that
allocates resources-labour, materials, machines, capital in the best possible
(optional) way so that cost are minimized or prots are maximized. In Linear
programming (LP), these resources are known as decision variable. The criterion
for selecting the best values of the decision variable (eg to maximize prots or
minimize cost) is known as the objective function.
Limitations on resource availability form what is known as a constraint
set( ? ).
Transportation model is one of those techniques that can help
to nd an optimum solution and save the cost in transportation models or
problems primarily concerned with the optimal (best possible) way in which a
product factories or plants (called supply origins) can be transported to a
number of warehouses or customers (called demand destinations)( ? ). The
objective in a transportation problem is to fully satisfy the destination
requirements within the operating production capacity constraints at the
minimum possible cost. Whenever there is a physical movement of goods from the
point of manufacturer to the nal consumers through a variety of channels of
distribution (wholesalers, retailers, distributors etc), there is a need to minimize
the cost of transportation so as to increase prot on sales( ? ).
The transportation problem is a special class of linear
programming problem that commodities from source to destinations. The objective
of the transportation problem is to determine the shipping schedule that
minimizes the total shipping cost while satisfying supply and demand limits.
The model assumes that the shipping cost is proportional to the number of units
shipped on a given route. In general, the transportation model can be extended
to other areas of operation, including, among others, inventory control,
employment scheduling and personnel assignment.
The transportation problem received this name because many of
its applications involve in determining how to optimally transport goods. The
transportation problem deals with the distribution of goods from several
points, such as factories often known as sources, to a number of points of
demand, such as warehouses, often known as destinations. Each source is able to
supply a xed number of units of products, usually called the capacity or
availability and each destination has a xed demand, usually known as
requirement.
Because of its major application in solving problems which
involves several products sources and several destinations of products, this
type of problem is frequently called the transportation problem. The classical
transportation problem is referred to as a special case of Linear Programming
(LP) problem and its model is applied to determine an optional solution for
delivering available amount of satised demand in which the total transportation
cost is minimized. The transportation problem can be described using linear
programming mathematical model and usually it appears in a transportation
tableau.
One possibility to solve the optional problem would be
optimization method. The problem is however formulated so that objective
function and all constraints are linear and thus the problem can be solved. There is a type of
linear programming problem that may be solved using a simplied version of the
simplex technique called transportation method. The simplex method is an
iterative algebraic procedure for solving linear programming problems(Badr,2007).
Transportation theory is the name given to the study of
optional transportation and allocation of resources. The model is useful for
making strategic decisions involved in selecting optimum transportation routes
so as to allocate the production of various plants to several warehouses or
distribution centres. The transportation model can also be used in making
location decisions. The model helps in locating a new facility, manufacturing a
new facility, manufacturing plant or an oce when two or more of the locations
are under consideration.
The total transportation cost, distribution cost or shipping
cost and production costs are to be minimized by applying the model.
Transportation problem is a particular class of linear programming, which is
associated with day-to-day activities in our real life and mainly deals with
logistics. It helps in solving problems on distribution and transportation of
resources from one place to another. The goods are transported from a set of
sources (eg factory) to a set of destinations (eg. warehouse) to meet the
specic requirements.
There is a type of Linear programming problem that may be
solved using a simplied version of the simplex technique called transportation
method. Because of its major application in solving problems involving several
product sources and several destinations of products, this type of problem is
frequently called the transportation problem. It gets its name from its
application to problems involving transporting products from several sources to
several destinations. Although the formation can be used to represent more
general assignment and scheduling problems it is also a transportation and
distribution problems. The two common objectives of such problems are to;
Minimize the cost of shipping in
units to destinations
Maximize the prot of shipping in units to destinations
The transportation problem itself was rst formulated by
Hitchcock (1941), and was independently treated by Koopmans and Kantorovich. In
fact, Monge (1781) formulated it and solved it by geometrical means. Hitchaxic
(1941) developed the basic transportation problem; however it could be solved
for optimally as answers to complex business problem only in 1951. When George
B. Dantizig applied the concept of Linear programming in solving the
transportation model, Dantzing (1951) gave the standard Linear Programming (LP)
formulation, Transportation problem (TP) and applied the simplex method subject
in almost every textbook on operation research and mathematical programming.
Linear programming has been used successfully in solution of
problem concerned with the assignment of personnel, distribution and
transportation, engineering, banking education, petroleum etc. Furthermore, LP
algorithms are used in subroutines for solving more dicult optimization
problems. A widely considered quint essential LP algorithm is the simplex
Algorithm developed by Dantzig (1947) in response to a challenge to mechanise
the Air Force planning process. Linear Programming has been applied extensively
in various areas such as transportation, health care and public services etc.
The simplex algorithm was the forerunner of many computer programs that are
used to solve complex optimization problem (Baynto, 2006). The transportation
method has been employed to develop many dierent types of process. From machine
shop scheduling, Mohaglegh (2006) optimized operating room schedules in
hospitals (Goldfarb and Kai,1986).The transportation
problem is a special kind of the network optimization problem. The
transportation models play an important role in logistics and supply chains.
The objective is to schedule shipments from sources to destinations so that total transportation cost is
minimized. The problem seeks a production and distribution plan that minimizes
total transportation cost.
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