Business and Industries are practically faced with both economic optimizationssuch as cost minimization of non-economic items that are vital to the existence of their firms. Transportation problems are primarily concerned with the optimal (best possible) way in which a product produced at different factories (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. The technique used for solving transportation problem shall be examined and interest will be in improving execution rate at minimum efforts. The techniques include.
- North West Corner Rule
- Matrix Minimum (Least cost) Methods
- Vogel Approximation Method.
But Least cost Method will be used explicitly in the course of this project. The final results will yield the objective function of the transportation model and how the products are been shipped to different warehousing or customers at a minimum possible cost in summary transportation problems are relevant I providing decision business makers with the information they need in order to properly balance cost and supply
Business and Industries are practically faced with both economic optimization such as cost minimization of non-economic items that are vital to the existence of their firms. Transportation problems are primarily concerned with the optimal (best possible) way in which a product produced at different factories (called supply origins) can be transported to a number of Bus stations 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/people from the point of manufacturer to the final consumers/destination 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 profit on sales.
The transportation problem is a special class of linear programming problem, which deals with transportation commodities from source to destinations. The objective of the transportation problem is to determine the transportation schedule that minimizes the total transportation cost while satisfying supply and demand limits The transportation problem has an application in industry, communication network, planning, scheduling transportation and allotment etc.
Transportation problem deals with the problem of how to plan production and transportation in such an industry given several factories at different locations and larger number of customers of their products. The transportation problem received this name because many of its applications involve determining how to optimally transport goods.
Transportation problem is a logistical problem for organizations especially for manufacturing and transport companies.
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 Bus stations, often known as destinations. Each source is able to supply a fixed number of units of products, usually called the capacity or availability, and each destination has a fixed demand, usually known as requirement.
The classical transportation problem is referred to as special case of Linear Programming (LP) problem and its model is applied to determine an optimal solution of available amount of satisfied 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.
1.2 BACKGROUND OF THE STUDY
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 passengers are transported from a set of sources (e.g., Bus stations) to a set of routes (e.g., final destination) to meet the specific requirements.
There is a type of linear programming problem that may be solved using a simplified 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.
The two common objectives of transportation problems are either
(i). minimize the cost of transportation m units to n destinations or
(i)i. maximize the profit of transportation m units to n destinations
The model is useful for making strategic decisions involved in selecting optimum transportation routes so as to allocate the transportation of various passengers to several routes scattered across the country. The transportation model can also be used in making location decisions. The model helps in locating a new facility, a manufacturing plant or an office when two or more number of locations is under consideration. The total transportation cost, distribution cost or transportation cost and production costs are to be minimized by applying the model.
Monge (1781) formulated it and solved it by geometrical means.
The transportation problem itself was first formulated by Hitchcock (1941), and was independently treated by Koopmans and Kantorovich.
Hitchaxic (1941) developed the basic transportation problem; however it could be solved for 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 LP-formulation TP and applied the simplex method to solve it. Since then the transportation problem has become the classical common subject in almost every textbook on operation research and mathematical programming.
The transportation problem can be described using linear programming mathematical model and usually it appears in a transportation tableau. Linear programming has been used successfully in solution of problems concerned with the assignment of personnel, distribution and transportation, engineering, banking, education, petroleum, etc.
1.3 BACKGROUND OF COMPANY
1.3.1 COMPANY PROFILE
Deacon Edwin Ajaere of the blessed memory and his lovely wife Mrs. Stella Ajaere had a vision for a successful business. Like all great businesses, God Is Good Motors was built upon a simple idea: provide great customer service all the time. They found inspiration from one of their favorite quotes from the Scriptures, “Though thy beginning was small, yet thy latter end should greatly increase.” Job 8:7.
They were involved in intra-city transportation using refurbished cars. So, in the early 1990s, they bought their first 14-seater Nissan Urvan bus and began to run their business with this simple plan using the same name ‘God Is Good Motors’. Their first route was Benin to Lagos.
In 1997, the company was formally incorporated and commenced operations as God Is Good Motors Nigeria Limited. They attracted talented team members and gave them the freedom to do their jobs, and they always listened to our customers, tirelessly working to surpass their expectations.
Today, God Is Good as they are fondly called owns about 900 buses servicing the South-South region of Nigeria. New routes have been added to accommodate the unprecedented increase in the number of our fleet. It was Deacon Edwin Ajaere’s leadership and commitment that fueled our growth and set us apart from our competitors.
In March 2009, the great founder of God is Good Group passed away and the management of the family business continued with his wife and children.
ChidiAjaere took over the leadership of the business and was named Chairman and Chief Executive Officer of the renowned group. And the family is continuing to further expand God Is Good Motors into a business conglomerate. God Is Good Motors became synonymous with outstanding service and a leader in the road transportation industry in Nigeria. With the family members now in leadership roles, Deacon Edwin Ajaere’s vision has been passed on.
They continue to expand our signature service into the global market and remain true to the very principles theirr founder promoted years ago.
1.4 PROBLEM STATEMENT
The Project seeks to address the problem of determining the optimal transportation schedule that will minimize the total cost of transporting passengers from the various God is Good Bus stations at Benin and Asaba to various routes geographically scattered in Nigeria
The study intends:
- To model the transportation system of God is Good Motors as a transportation problem
- To minimize the transportation cost.
The least costmethod and modified distribution method will be used for finding an optimal solution of transportation problem with equality constraint. The information required for this project will be gathered from the internet, the libraries, mathematical books and Journal. Data would be collected from God is Good Motors for transporting passengers to their various destination. This problem could be solved by transportation model with intermediate destinations between the source and the destinations e.g. passengers are transported from Bus stations to various routes. Given pure supply nodes with demand, pure demand nodes with demandand transportation nodes. Suppose the unit transportation cost from supply node to transtransportation node k is node j is and the unit transportation cost for transportation node k to demand , and problem of God is Good Motors is to be modeled as the linear programming model of transportation type, and represent the Linear Programming or the transportation problem as tableau and solve it with the least cost method explicitly.
1.7 Limitation of study
This research work is limited to providing a more reliable transportation model that will be used by logistic manager in God is Good Motors to minimize the cost of transporting passengers from the Bus stations to Various route (final destination).
1.8 Organization of the thesis
Chapter one introduces the thesis in general, the review of transportation problem ,the background of company(God is Good motors),the problem statement, objectives , methodology, limitation of study and the organization of the thesis.
Chapter two is concerned with the definition and detailed literature review of the transportation problem/model.
Chapter three discusses detailed methodology.
This includes the formulation of the transportation problem, the transportation tableau, the solutions for the transportation problem and methods for solving transportation problems to optimality.
Chapter four provides an overview of the computational platforms for implementation and solution of the modal and introduce the real-life data sets used in the solution process.
Finally chapter five summarize the conclusions with respect to overall aims of the project and proposed recommendation for future research/study. It reports the computational results and provides a comprehensive analysis of the outcome and performance of the proposed solution approaches.