Constraint programming have been identifying as promising technique for efficiently solving discrete optimization problem

Abstract

Constraint programming has roots in logic programming, where a model has both a declarative and a procedural interpretation. A model is declarative because its statements can be read as logical propositions that describe the problem, and it is procedural because the statements can be processed as instructions for how to find a solution. To make constraint programming material to practical problems one needs propagation algorithms that are both viable and proficient. The most incredible propagation algorithm for the alldifferent constraint, i.e. the one getting hyper-circular segment consistency, is to be sure extremely productive. The reason is that we can apply matching hypothesis from operations research. Likewise for the symmetric alldifferent constraint and the weighted alldifferent constraint powerful and effective propagation algorithms exist, again dependent on techniques from operations research. From this paper we show that some time alldifferent constraint is more easy way to solve the MIP. For this we will choose an auction strategy by which a company get more revenue.Despite this considerable progress, there remains great potential for further integration, with the concomitantimprovement in both modeling and solution method.