The choice of the cutting plane in each iteration of the related ILP algorithm is very important in terms of convergence speediness and then it is increasingly important for economic applications. Gomory [2] proved that the optimal cutting plane is the one that maximizes the number of feasible integer points the cut touches. A theorem introduced by Pick [3] allows calculating the area of each polygon whose vertices belong to a bi-dimensional lattice, as a function of the number of its internal and boundary lattice points. In 1957, Reeve proposed a generalization of Pick’s theorem to the three-dimensional case [5]. Starting from results obtained by Caristi and Stoka [1], in this paper, we consider a cutting plane problem for an irregular lattice  with a lattice with the fundamental cell C₀ represented in Figure 1.

cutting planes, lattice points, random sets, linear integer programming.