We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. can be added a Benders reformulation, and are derived from solving single scenario programming subproblems identical those used in the nonanticipative dual of program. While have potential significantly strengthen relaxation, computationally demanding. techniques with goal obtaining that pr...

Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea problems with integer decisions is difficult because of the need for rules that lead integral decisions. In work, we introduce Lagrangian dual (LDDRs) multistage mixed-integer programming (MSMIP) which overcome difficulty in a MSMIP. We propose two new bounding techni...

Many supply chain problems involve optimization of various conflicting objectives. This paper formulates a green supply chain network throughout a two-stage mixed integer linear problem with uncertain demand and stochastic environmental respects level. The first objective function of the proposed model considers minimization of supply chain costs while the second objective function minimizes CO...

Design of a logistics network in proper way provides a proper platform for efficient and effective supply chain management. This paper studies a multi-period, multi echelon and multi-product integrated forward-reverse logistics network under uncertainty. First, an efficient complex mixed-integer linear programming (MILP) model by considering some real-world assumptions is developed for the inte...

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic ...

We consider the integer L-shaped method for two-stage stochastic integer programs. To improve the performance of the algorithm, we present and combine two strategies. First, to avoid timeconsuming exact evaluations of the second-stage cost function, we propose a simple modification that alternates between linear and mixed-integer subproblems. Then, to better approximate the shape of the second-...

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DECOMPOSITION ALGORITHMS FOR TWO-STAGE STOCHASTIC INTEGER PROGRAMMING By John H. Penuel, Jr. August 2009 Chair: J. Cole Smith Major: Industrial and Systems Engineering Stochastic programming seeks to optimize decision making in uncertain...

We survey structural properties of and algorithms for stochastic integer programming models, mainly considering linear two-stage models with mixedinteger recourse (and their multi-stage extensions).

In this chapter, we will study algorithms for both two-stage as well as multi-stage stochastic mixed-integer programs. We present stagewise (resourcedirective) decomposition methods for two-stage models, and scenario (pricedirective) decomposition methods for multi-stage models. The manner in which these models are decomposed relies not only on the specific data elements that are random, but al...