Quantity discount is a frequently adopted scheme that has not been explicitly investigated in logistics service procurement auctions. This paper focuses on revised winner determination problem under quantity discounts and demand uncertainty for fourth-party (4PL) provider combinatorial reverse auction. To characterize our research problem, two-stage stochastic nonlinear programming model constr...

The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certai...

Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide approximate function data and subgradients. In ...

This paper presents an exact algorithm for the Lock Scheduling Problem (LSP) based on a Combinatorial Benders decomposition. LSP consists of three strongly interconnected sub problems: scheduling the lockages, assigning ships to chambers, and positioning the ships inside the chambers. These three sub problems are interpreted resp. as a scheduling, an assignment, and a packing problem. By combin...

We present an approximate method for solving nonlinear control problems over long time horizons, in which the full model is preserved initial part of horizon, while remainder horizon modeled using a linear relaxation. As this problem may still be too large to solve directly, we Benders decomposition-based solution algorithm that iterates between and parts horizon. This extends dual dynamic prog...

We examine a decomposition approach to find good quality feasible solutions. In particular, we study a method to reduce the search-space by decomposing a problem into two partitions, where the second partition (i.e., the subproblem) contains the fixed solution of the first (i.e., the master). This type of approach is usually motivated by the presence of two sub-problems that are each more easil...

Abstract This paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the is that it does not assume fixed recourse and as consequence values dimensions matrix can be uncertain. The proposed contains multi-cut (partial) Benders decomposition deterministic equivalent model special cases used to trade-off computational sp...

This paper presents a parameter-free integer-programming based algorithm for the global resolution of a linear program with linear complementarity constraints (LPEC). The cornerstone of the algorithm is a minimax integer program formulation that characterizes and provides certificates for the three outcomes—infeasibility, unboundedness, or solvability—of an LPEC. An extreme point/ray generation...

Logic-based Benders decomposition (BD) extends classic BD by allowing more complex subproblems with integral variables. Metaheuristics like variable neighborhood search are becoming useful here for faster solving the subproblems’ inference duals in order to separate approximate Benders cuts. After performing such a purely heuristic BD approach, we continue by exactly verifying and possibly corr...

We consider decomposition approaches for the solution of multistage stochastic programs that appear in financial applications. In particular, we discuss the performance of two algorithms that we test on the mean-variance portfolio optimization problem. The first algorithm is based on a regularized version of Benders decomposition, and we discuss its extension to the quadratic case. The second a...