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.

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.

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Item Type: Ghanaian Topic  |  Size: 85 pages  |  Chapters: 1-5
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