# Location Analysis in Logistics Management

Plant and distribution center location is a common problem faced by logistics managers. Increased production economics of scale and reduced transportation cost have focused attention on distribution centers. In recent years, location analysis has been further extended to include logistics channel design as a result of global sourcing and marketing decisions. Global operations increase logistics channel decision complexity, design alternatives and related logistics cost.

Location Decisions

Location decision stage of location analysis in logistics management,  focus on selecting the number and location of distribution centers. Typical management questions:-

1. How many distribution centers should the firm use and where should they be located?
2. What customers or market areas should be serviced from each distribution center?
3. Which product lines should be produced or stopped at each plant or distribution center?
4. What logistics channels should be used to source material and serve international markets?
5. What combination of public and private distribution facilities should be used?

Location Analysis Techniques

Location analysis problems are very complex and data intense. Complexities are created because of the number of locations multiplied by the alternative location sites multiplied by the stocking strategies for each location. Data intensity is created because the analysis requires detailed demand and transportation information. The techniques used are:

1. Analytic techniques
2. Optimization or linear programming techniques
3. Simulation techniques

Analytic techniques: generally describe methods that identify the center of gravity of logistics geography. A center of gravity method is appropriate for locating a single distribution plant or center. A number of methods both mathematical and non mathematical can be applied to a problem of a single location. The cost and complexity of the technique is to be matched to the difficulty of the problem.

In the following example technique employed is evolved from analytic geometry.

The model is based on Cartesian co-ordinates, where the horizontal axis is labeled as the x-axis, and the vertical axis is labeled as the y-axis.   Any given point in the quadrant can be identified with reference to x and y coordinates. Taken together, these co-ordinates define unique points. The x and y co-ordinate system can be used to calculate the distance between any two points on the plane using the Pythagoras theorem.

By use of this basic system of orientation, it is possible to replicate the geographic market area in which the distribution center is to be located.

This method to solve the location problem determines the ideal co-ordinate position of the distribution warehouse on the basis of distance, weight or a combination of both. The computation is a weighted average of the distance, weight or combined factors, with the warehouse location as the dependent variable. The algebraic solution may use either the weighted average x and y co-ordinate or the median location. The median location uses the coordinate location with half the demand on each side. The formula of this calculation depend on the independent variables expressed in the location measure. The problem is in a manner such that identical service standards exist for all potential distribution warehouse locations. The objectives are to minimize transportation cost.

Transportation cost are a function of time, weight and distance. Historically, in mathematical techniques it is not possible to consider all the factors together. The 4 solution methods that consider combination of factors are:

1. Ton — Center solution: the location point represents the center of gravity or movement in market area. The assumption is that the center of movement represents the least cost location. In Ton — center solution only weight is given consideration. All demand locations are plotted on the co-ordinate plane and identified by subscripts. To express tonnage requirements to each demand center, annual tonnage is reduced to standard units. Once each demand location is defined and the total units load to each demand center are known, the best warehouse location can be determined. The location solution is found by adding the products of location and delivery frequency to each demand center from the x- co-ordinate and dividing the total number of units. The process is requested from the y co-ordinate. The result is a location in terms of x and y for the distribution warehouse. The final location solution indicates the point that provides the balance of weight between destinations over a specific period.
2. Mile — Center solution: this determines the geographical point that minimizes the combined distance to all demand centers. The assumption underlying the solution is that delivery costs are solely a function of distance. Therefore, if distance is minimized a least cost location is determined. The basic deficiency of this omission of weight and time considerations. The mile center solution cannot be determined by solving for the weighted average co-ordinate location along each dimension. It requires a iterative process to detmine an increasingly improved warehouse location. This optimum location is determined by utilizing the general formula for the length of a straight line between two points.
3. Ton —Mile — Center Solution: it combines the variables of weight and distance in selecting warehouse locations. This solution considers the frequency of delivery to each destination in when selecting a warehouse location. This solution also requires an iterative process since the distance between demand point and warehouse is included.
4. Time — Ton — Mile — Center Solution: it includes all factors influenced by cost. Costs are a function of time weight and distance. The warehouse site derived as a product of this solution is a least cost location. The procedure for selecting the solution is iterative because time and distance factors are differentiated from a given ware house location.

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