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 ...

We construct an integrated multi-period inventory-production-distribution replenishment plan for three-stage supply chains. The supply chain maintains close-relationships with a small group of suppliers, and the nature of the products (bulk, chemical, etc.) makes it more economical to rely upon a direct shipment, full-truck load distribution policy between supply chain nodes. In this paper, we ...

This paper considers a modification of the branch-and-cut algorithm for Mixed Integer Linear Programming where branching is performed on general disjunctions rather than on variables. We select promising branching disjunctions based on a heuristic measure of disjunction quality. This measure exploits the relation between branching disjunctions and intersection cuts. In this work, we focus on di...

This paper develops a linear programming based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algorithms for mixed integer nonlinear programs in ...

This paper proposes a tractable model for the design of a rapid transit system. Travel cost is minimized and traffic capture is maximized. The problem is modeled on an undirected graph and cast as an integer linear program. The idea is to build segments within broad corridors to connect some vertex sets. These segments can then be assembled into lines, at a later stage. The model is solved by b...

We consider a distribution problem in which a product has to be shipped from a supplier to several retailers over a given time horizon. Each retailer defines a maximum inventory level. The supplier monitors the inventory of each retailer and determines its replenishment policy, guaranteeing that no stockout occurs at the retailer (Vendor Managed Inventory policy). Every time a retailer is visit...

this paper aims to investigate the integrated production/distribution and inventory planning for perishable products with fixed life time in the constant condition of storage throughout a two-echelon supply chain by integrating producers and distributors. this problem arises from real environment in which multi-plant with multi-function lines produce multi-perishable products with fixed life ti...

Given an undirected graph and a positive integer k, the maximum k-colorable subgraph problem consists of selecting a k-colorable induced subgraph of maximum cardinality. The natural integer programming formulation for this problem exhibits two kinds of symmetry: arbitrarily permuting the color classes and/or applying a nontrivial graph automorphism gives equivalent solutions. It is well known t...

We investigate several complexity issues related to branch and cut algorithms for integer programming based on lifted cover inequalities LCIs We show that given a fractional point determining a violated LCI over all minimal covers is NP hard The main result is that there exists a class of knapsack instances for which any branch and cut algorithm based on LCIs has to evaluate an exponential numb...