Dynamic multistage stochastic linear programming has many practical applications for problems whose current decisions have to be made under future uncertainty. There are a variety of methods for solving these problems, including nested Benders decomposition. In this method, recently shown to be superior to the alternatives for large problems, the problem is decomposed into a set of smaller line...

An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a nite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time.

The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice, the weights on the connections are either uncertain or hard to estimate so recently robust optimization approaches have been considered for CNP. In this article, we address very general uncertainty sets, only requiring a linear optimiza...

Benders is one of the most famous decomposition tools for Mathematical Programming, and it is the method of choice e.g., in Mixed-Integer Stochastic Programming. Its hallmark is the capability of decomposing certain types of models into smaller subproblems, each of which can be solved individually to produce local information (notably, cutting planes) to be exploited by a centralized “master” p...

The hub location–allocation problem under uncertainty is a real-world task arising in the areas such as public and freight transportation and telecommunication systems. In many applications, the demand is considered as inexact because of the forecasting inaccuracies or human’s unpredictability. This study addresses the robust uncapacitated multiple allocation hub location problem with a set of ...

Abstract: In order to improve the efficiency for solving MINLP problems, we present in this paper three computational strategies. These include multiple-generation cuts, hybrid methods and partial surrogate cuts for the Outer Approximation and Generalized Benders Decomposition. The properties and convergence of the strategies are analyzed. Five new MINLP algorithms are described based on the pr...

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This paper investigates the integration of the employee timetabling and production scheduling problems. At the first level, we manage a classical employee timetabling problem. At the second level, we aim at supplying a feasible production schedule for a set of interruptible tasks with qualification requirements and time-windows. Instead of hierarchically solving these two problems as in the cur...

We study a class of chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. In addition, we propose a new model, where “recovery” decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second-stage problem. We develop decomposition algorithms with specialized optimality and feasibility...

Constraint Integer Programming (CIP) is a generalization of mixed-integer programming (MIP) in the direction of constraint programming (CP) allowing the inference techniques that have traditionally been the core of CP to be integrated with the problem solving techniques that form the core of complete MIP solvers. In this paper, we investigate the application of CIP to scheduling problems that r...