The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives. In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this...

The budget network design problem and fixed-charge network design problem imply different economic pursuits on travel cost and construction cost and structure these two cost components in different ways. A more general version of these two classic formulations is the biobjective network design problem. This article discusses an exact solution strategy for the biobjective discrete network design...

The article presents a study on a biobjective generalization of the inventory routing problem, an important optimization problem found in logistical networks in which aspects of inventory management and vehicle routing intersect. A compact solution representation and a heuristic optimization approach are presented, and experimental investigations involving novel benchmark instances are carried ...

This paper proposes a biobjective continuous transportation network design problem concerning road congestion charging with the consideration of speed limit. The efficiency traffic and reduction pollution in environment are improved by designing reasonable capacity enhancement limit strategy. A bilevel programming model is developed to formulate proposed problem. first target upper optimization...

This article introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective combinatorial optimization problem with respect to uniformity, coverage and the -indicator. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobje...

Transportation problem is a linear programming which considers minimum cost for shipping a product from some origins to other destinations such as from factories to warehouse, or from a warehouse to supermarkets. To solve this problem simplex algorithmis utilized. In real projects costs and the value of supply and demands are fuzzy numbers and it is expected that optimal solutions for determini...

This article introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the -indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as parti...

In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind problems arises whenever associated decision-makers have their respective many solutions. For purpose, we develop branch-and-cut algorithm based on programming, for finding solutions in terms both and ...