Gravity Model

We will begin with the discussion of determining the best location for a single facility. We will present the gravity model and an iterative method for its solution. 

The gravity model considers several existing facilities (plants and demand regions), with known locations on a plane. Each facility has an associated weight. These weights may represent voliune or quantity handled at these 

Assume that there are N existing facilities. The weight of facility n(n = 1, 2,N) is and its coordinate location on a plane is x yj. If the new facility s location is x, y), then the distance for each facility is given by 

Note that the weights w for location n can be computed in two ways  

w = Q , where Q is the quantity handled (supply/demand) at location n, assuming the same freight rate (e.g., per ton-mile) at all locations. 

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Eaton, D.W. Hope, J. 2003. Structure of the crust and upper mantle of the Great Slave Lake shear zone, northwestern Canada, from teleseismic analysis and gravity modelling. Canadian Journal of Earth Sciences, 40, 1203-1218. 

Thomas, M. D. 1990. Deep structure of the Middle Proterozoic anorthositic intrusions in the eastern Canadian Shield insights from gravity modeling.-... 

Petit, C. Ebinger, C. 2000. Flexure and mechanical behaviour of cratonic lithosphere gravity models of the East African and Baikal rifts. Journal of Geophysical Research, 105, 19 151-19162. 

Gravity model is easy to solve and a good start for location decision evaluation. However, it does not fit supply chain context very well. 

Using these values, the new distances are calculated for iteration 2. The results for the first four iterations of the gravity model are shown in Table 5.14. 

Even though the gravity model is easy to imderstand and the iterative method is easy to implement on a spread sheet, there are limitations in the model s applicability. Listed in the following are few of its limitations ... 

It is not easy to extend the gravity model to multiple facilities. The main problem is that one has to decide not only the location of the multiple warehouses, but also the quantity shipped from each warehouse to the various... 

We then presented the basics of the "continuous location" models. We presented the "gravity model" for single facility location and the iterative algorithm for its solution. Extensions to the multiple facility location models were... 

Given this information, either gravity models or netwoik optimization models may be used to design the network. We organize the models according to the phase of the network design framework at which each model is likely to be useful. 

Gravity models assume that both the markets and the supply sources can be located as grid points on a plane. All distances are calculated as the geometric distance between two points on the plane. These models also assume that the transportation cost grows linearly with the quantity shipped. We discuss a gravity model for locating a single facility that receives raw material from supply sources and ships finished product to markets. The basic inputs to the model are as follows ... 

The manager thns identifies the coordinates (x, y) = (681, 882) as the location of the factory that minimizes total cost TC. From a map, these coordinates are close to the border between North Carolina and Virginia. The precise coordinates provided by the gravity model may not correspond to a feasible location, though. The manager should look for desirable sites close to... 

The gravity model can also be solved using the following iterative procedure. 

FIGURE 4 Gravity anomalies computed from the EGM-96 gravity model complete to degree and order 360. 

Electromagnetics Gamma-Ray Astronomy Global Gravity Modeling Gravitational Wave... 

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