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glomery cuts were introduced by ralph gomery in his 1958 paper and this was a major theoretical breakthrough at that time and for the next couple of decades these methods were largely considered to be a theoretical value but this gradually changed and by the end of 90s it wouldnt be exaggeration to say that the kite and plane methods became the single most important factor contributing to the success of modern commercial solvers for mixed integer programs i will illustrate the ideas of glomery cuts using this simple two-dimensional example in this example we have the following formulation maximize x1 plus x2 so you have the isoprofit line shown here on the plot and the constraints would be 4x1 plus 7x2 is less than or equal to 28 and 2x1 minus 2x2 is less than or equal to 3. both variables are non-negative and are required to be integer so we can see that this formulation is clearly not perfect and in an ideal formulation this is what we want to have so you would like to have the lp