Reduced cost-based variable fixing in two-stage stochastic programming

The explicit consideration of uncertainty is essential in addressing most planning and operation issues encountered in the management of complex systems. Unfortunately, the resulting stochastic programming formulations, integer ones in particular, are generally hard to solve when applied to realistically-sized instances. A common approach is to consider the simpler deterministic version of the formulation, even if it is well known that the solution quality could be arbitrarily bad. In this paper, we aim to identify meaningful information, which can be extracted from the solution of the deterministic problem, in order to reduce the size of the stochastic one. Focusing on two-stage formulations, we show how and under which conditions the reduced costs associated to the variables in the deterministic formulation can be used as an indicator for excluding/retaining decision variables in the stochastic model. We introduce a new measure, the Loss of Reduced Costs-based Variable Fixing (LRCVF), computed as the difference between the optimal values of the stochastic problem and its reduced version obtained by fixing a certain number of variables. We relate the LRCVF with existing measures and show how to select the set of variables to fix. We then illustrate the interest of the proposed LRCVF and related heuristic procedure, in terms of computational time reduction and accuracy in finding the optimal solution, by applying them to a wide range of problems from the literature

Extreme-Point-based Heuristics for the Three-Dimensional Bin Packing problem

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the proble

Multicommodity, multimode freight transportation: A general modeling and algorithmic framework for the service network design problem

We examine the freight transportation problem which occurs when the same authority controls and plans both the supply of transportation services (modes, routes, frequencies for the services and classification, consolidation, transfer policies for terminals) and the routing of freight. We present a general modeling framework, based on a network optimization model, which may be used to assist and enhance the tactical and strategic planning process for such a system. The problem is solved by means of an algorithm, described in some detail, based on decomposition and column generation principles. We also present detailed results on the behaviour and performance of the algorithm, as observed during experimentation with a specific rail application.

A study of demand stochasticity in service network design

The objective of this paper is to investigate the importance of introducing stochastic elements into service network design formulations. To offer insights into this issue, we take a basic version of the problem in which periodic schedules are built for a number of vehicles and where only the demand may vary stochastically. We study how solutions based on uncertain demand differ from solutions based on deterministic demand and provide qualitative descriptions of the structural differences. Some of these structural differences provide a hedge against uncertainty by using consolidation. This way we get consolidation as output from the model rather than as an a priori required property. Service networks with such properties are robust, as seen by the customers, by providing operational flexibility

Single-commodity network design with random edge capacities

This paper examines the single-commodity network design problem with stochastic edge capacities. We characterize the structures of the optimal designs and compare with the deterministic counterparts. We do this primarily to understand what constitutes robust network designs, but hope that the results can be used also to develop better heuristics than those available today

Single source single-commodity stochastic network design

Stochastics affects the optimal design of a network. This paper examines the single-source single-commodity stochastic network design problem. We characterize the optimal designs under demand uncertainty and compare with the deterministic counterparts to outline the basic structural differences. We do this partly as a basis for developing better algorithms than are available today, partly to simply understand what constitutes robust network designs

Single-commodity stochastic network design with multiple sources and sinks

This paper examines the single-commodity network design problem with stochastic demand and multiple sources and sinks. We characterize the structures of the optimal designs and compare with the deterministic counterparts. We do this primarily to understand what constitutes good robust network designs. This can later be used to develop better heuristics than those available today

Real-Time Decision Problems: an Operations Research Perspective

This paper is concerned with real-time decision problems. These constitute a generic class of dynamic and stochastic problems. The objective is to provide responses of a required quality in a continuously evolving environment, within a prescribed time frame, using limited resources and information that is often incomplete or uncertain. Furthermore, the outcome of any particular decision may also be uncertain. This paper provides an overview of this class of problems, reviews the relevant Artificial Intelligence literature, proposes a dynamic programming framework, and assesses the potential usefulness of Operations Research approaches for their solution. Throughout the paper, a vehicle dispatching application illustrates the relevant concepts

A multilevel tabu search algorithm for the feature selection problem in biomedical data

NRC publication: Ye