A decomposition approach to a stochastic model for supply-and-return network design

This paper presents a generic stochastic model for the design of networks comprising both supply and return channels, organized in a closed loop system. Such situations are typical for manufacturing/re-manufacturing type of systems in reverse logistics. The model accounts for a number of alternative scenarios, which may be constructed based on critical levels of design parameters such as demand or returns. We propose a decomposition approach for this model based on the branch and cut procedure known as the integer L-shaped method. Computational results show a consistent performance efficiency of the method for the addressed location problem. The stochastic solutions obtained in a numerical setting generate a significant improvement in terms of average performance over the individual scenario solutions. A solution methodology as presented here can contribute to overcoming notorious challenges of stochastic network design models, such as increased problem sizes and computational difficulty.Decomposition;Location;Remanufacturing;Integer L-shaped;Uncertainty

A scenario aggregation based approach for determining a robust airline fleet composition

Strategic airline fleet planning is one of the major issues addressed through newly initiated decision support systems, designed to assist airlines and aircraft manufacturers in assessing the benefits of the emerging concept of dynamic capacity allocation. We present background research connected with such a system, which aims to explicitly account for the stochastic nature of passenger demand in supporting decisions related to the fleet composition problem. We address this problem through a scenario aggregation based approach and present results on representative case studies based on realistic data. Our investigations establish clear benefits of a stochastic approach as compared with deterministic formulations, as well as its implementation feasibility using state-of-the-artoptimization software.Dynamic capacity allocation;Airline fleet composition;Stochastic programming;Scenario aggregation;Fleet assignment

A decomposition approach to a stochastic model for supply-and-return network design

This paper presents a generic stochastic model for the design of networks comprising both supply and return channels, organized in a closed loop system. Such situations are typical for manufacturing/re-manufacturing type of systems in reverse logistics. The model accounts for a number of alternative scenarios, which may be constructed based on critical levels of design parameters such as demand or returns. We propose a decomposition approach for this model based on the branch and cut procedure known as the integer L-shaped method. Computational results show a consistent performance efficiency of the method for the addressed location problem. The stochastic solutions obtained in a numerical setting generate a significant improvement in terms of average performance over the individual scenario solutions. A solution methodology as presented here can contribute to overcoming notorious challenges of stochastic network design models, such as increased problem sizes and computational difficulty

Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis

We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated.Such programs can be used for modeling average or steady-state behavior of complex stochastic systems.Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models.Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints.The convergence analysis of sample-path methods rely heavily on stability conditions.We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence.Alongside we provide a complementary sensitivity result for the corresponding deterministic problems.In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.stochastic processes;mathematics;stability;simulation;regulations;general equilibrium

Simulation-based solution of stochastic mathematical programs with complementarity constraints: sample-path analyis

We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling "average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions

A scenario aggregation based approach for determining a robust airline fleet composition

Strategic airline fleet planning is one of the major issues addressed through newly initiated decision support systems, designed to assist airlines and aircraft manufacturers in assessing the benefits of the emerging concept of dynamic capacity allocation. We present background research connected with such a system, which aims to explicitly account for the stochastic nature of passenger demand in supporting decisions related to the fleet composition problem. We address this problem through a scenario aggregation based approach and present results on representative case studies based on realistic data. Our investigations establish clear benefits of a stochastic approach as compared with deterministic formulations, as well as its implementation feasibility using state-of-the-art optimization software

Stochastic approaches for product recovery network design: a case study

Increased uncertainty is one of the characteristics of product recovery networks. In particular the strategic design of their logistic infrastructure has to take uncertain information into account. In this paper we present stochastic programming based approaches by which a deterministic location model for product recovery network design may be extended to explicitly account for the uncertainties. Such a stochastic model seeks a solution which is appropriately balanced between some alternative scenarios identified by field experts. We apply the stochastic models to a representative real case study on recycling sand from demolition waste in The Netherlands. The interpretation of the results is meant to give more insight into decision-making for reverse logistics

Simulation-based solution of stochastic mathematical programs with complementarity constraints: sample-path analyis

We consider a class of stochastic mathematical programs withcomplementarity constraints, in which both the objective and theconstraints involve limit functions or expectations that need to beestimated or approximated. Such programs can be used for modeling"average" or steady-state behavior of complex stochasticsystems. Recently, simulation-based methods have been successfullyused for solving challenging stochastic optimization problems andequilibrium models. Here we broaden the applicability of so-calledthe sample-path method to include the solution of certain stochasticmathematical programs with equilibrium constraints. The convergenceanalysis of sample-path methods rely heavily on stabilityconditions. We first review necessary sensitivity results, thendescribe the method, and provide sufficient conditions for itsalmost-sure convergence. Alongside we provide a complementarysensitivity result for the corresponding deterministic problems. Inaddition, we also provide a unifying discussion on alternative set ofsufficient conditions, derive a complementary result regarding theanalysis of stochastic variational inequalities, and prove theequivalence of two different regularity conditions.simulation;mathematical programs with equilibrium constraints;stability;regularity conditions;sample-path methods;stochastic mathematical programs with complementarity constraints