We present an algorithmic approach for solving two-stage stochastic mixed 0-1 problems. The first stage constraints of the Deterministic Equivalent Model have 0–1 variables and continuous variables. The approach uses the Twin Node Family (TNF) concept within the algorithmic framework so-called Branch-and-Fix Coordination for satisfying the nonanticipativity constraints, jointly with a Benders D...

We present two exact algorithms based on Benders decomposition for solving the multicommodity uncapacitated fixed-charge network design problem. The first implements Benders decomposition within a branch-and-cut framework. We present implementation techniques crucial for the algorithm's efficiency such as cut selection criteria and core point definition and highlight their impact on the solutio...

In this paper, two Benders decomposition algorithms and a novel two-stage integer programming-based heuristic are presented to optimize the beam angle and fluence map in Intensity Modulated Radiation Therapy (IMRT) planning. Benders decomposition is first implemented in the traditional manner by iteratively solving the restricted master problem and then identifying and adding the violated Bende...

An airline’s operational disruptions can lead to flight delays that in turn impact passengers, not only through the delays themselves but also through possible missed connections. Since the length of a delay is often not known in advance, we consider preemptive rerouting of airline passengers before the length of the delay is realized. Our goal is to reaccommodate passengers proactively as soon...

We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logicbased Benders decomposition approach is proposed to minimize the makespan. The decomposition approach is a hybrid model that makes use of a mixed integer programming master problem and a travelling salesman problem subproblem. The master problem is a relaxation of the problem and i...

We study an unrelated parallel machines scheduling problem with sequence and machine dependent setup times. A logicbased Benders decomposition approach is proposed to minimize the makespan. The decomposition approach is a hybrid model that makes use of a mixed integer programming master problem and a travelling salesman problem subproblem. The master problem is a relaxation of the problem and i...

In this paper we introduce a new formulation of the logistics network design problem encountered in deterministic, single-country, single-period contexts. Our formulation is flexible and integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, product range assignment and product flows. We next describe two approaches for solving the pr...

in order to implement the cellular manufacturing system in practice, some essential factors should be taken into account. in this paper, a new mathematical model for cellular manufacturing system considering different production factors including alternative process routings and machine reliability with stochastic arrival and service times in a dynamic environment is proposed. also because of t...

Benders' decomposition is a well-known technique for solving large linear programs with a special structure. In particular it is a popular technique for solving multi-stage stochastic linear programming problems. Early termination in the subproblems generated during Benders' decomposition (assuming dual feasibility) produces valid cuts which are inexact in the sense that they are not as constra...