A Class of Collocating Problem in Production and its Optimization Models

Abstract

The paper gives a general description of a typical combinatorial optimization problem-the collocation problem of production, and respectively establish the integer linear programming model based on the collocation ways and the integer linear programming model based on the optimal collocation amounts and the integer nonlinear programming model based on the local optimum. In the solving methods of the models, we have mainly analyzed the enumeration method and the method by using LINGO optimization software to solve the model. The instance shows that the models and solutions are all effective. The first model reflects the mechanism of the collocation problem better and gets the global optimal solution most likely, but more difficult to solve large-scale; the second model can quickly obtain the optimal the numbers of the finished products and all kinds of materials consumptions, but still need to enumerate the collocation ways step by step; the third model can gets the local optimal solution and the specific collocation ways through solving the model circularly. The optimization models and solution methods in this paper can be extended to the similar sub-problems of the combinatorial optimization problems, such as assembly problem, packing problem, the cutting problem, etc.