Uncertain Chinese Postman Problem with Budget Constraint: A Robust Optimization Approach

Abstract

Abstract The Chinese postman problem (CPP) is a well-known combinatorial optimization problem, that is used in various real-world applications. Modeling such real-world applications frequently necessitates taking into account some uncertain variables. Robust optimization is one of the prominent approach to solves optimization problems when there is uncertainty in the parameters of the optimization problem. In this paper, we study uncertain multi-objective Chinese postman problem with budget constraint by maximizing profit and minimizing time under the light of robust optimization theory. We formulate the deterministic form of uncertain multi-objective CPP for three different types of uncertainty sets like ellipsoidal, polyhedral and budgeted uncertainty sets. The models are then solved using two well-known multi-objective solution strategies: the global criteria approach and the fuzzy programming method. Finally, numerical experiment are made through the models. MSC Classification: 90C17 , 90C05 , 90C90</jats:p