Correlations in Stochastic Programming: A Case From Stochastic Service Network Design

Abstract

Deterministic models, even if used repeatedly, will not capture the essence of planning in an uncertain world. Flexibility and robustness can only be properly valued in models that use stochastics explicitly, such as stochastic optimization models. However, it may also be very important to capture how the random phenomena are related to one another. In this article we show how the solution to a stochastic service network design model depends heavily on the correlation structure among the random demands. The major goal of this paper is to discuss why this happens, and to provide insights into the effects of correlations on solution structures. We illustrate by an example.

Planning for charters: A stochastic maritime fleet composition and deployment problem

“…Whichever scenario generation method is used, an important but often overlooked question is how the properties of the uncertain phenomena affect the stochastic program, see discussions in, e.g., Kallberg and Ziemba [10], Chopra and Ziemba [3], Kaut et al [11], Lium et al [14], Pantuso et al [21].…”

Single source single-commodity stochastic network design

“…The possible source nodes are listed in the second column of Table 1. We know from the work of Lium et al (2007) that correlations are important in shaping the structure of the network. Hence, we further create three cases from each problem instance: one with uncorrelated demands, one with positively correlated demands and one with mixed correlated demands.…”

A metaheuristic for stochastic service network design

“…The best we then can do is to find a solution or a plan that minimizes the cost of offering services and the expected cost of possible ad-hoc changes required for executing the plan. We propose a model inspired by the time-dependent stochastic service network design formulation by Lium et al (2007Lium et al ( , 2009. Their model assumes the use of a homogeneous fleet of vehicles to move commodities.…”

“…Studies by Lium et al (2007Lium et al ( , 2009 indicate, however, that cost reductions can be achieved when building plans based on the explicit consideration of stochastic demand compared to plans based on the assumption of deterministic demand. Due to combinatorial challenges, only small instances could be solved by the authors.…”

“…This paper is based on their formulations and looks into how to obtain good solutions for large instances of the time-dependent service network design problem with stochastic demand. We also extend the formulation proposed by Lium et al (2007Lium et al ( , 2009 to incorporate the cost of handling freight at intermediate terminals as well as the cost associated to movement/storage of the commodities (for example inventory cost of storing freight at intermediate terminals). In previous research, Ghamlouche et al (2003Ghamlouche et al ( , 2004 used linear programming to optimize the commodity flow associated to a given service design.…”