arXiv subjects

Gilles Savard

Publications and source records attributed to Gilles Savard.

4 recordsLinked to original sources

arXiv2022

Periodic Freight Demand Estimation for Large-scale Tactical Planning

Freight carriers rely on tactical planning to design their service network to satisfy demand in a cost-effective way. For computational tractability, deterministic and cyclic Service Network Design (SND) formulations are used to solve large-scale problems. A central input is the periodic demand, that is, the demand expected to repeat in every period in the planning horizon. In practice, demand is predicted by a time series forecasting model and the periodic demand is the average of those forecasts. This is, however, only one of many possible mappings. The problem consisting in selecting this mapping has hitherto been overlooked in the literature. We propose to use the structure of the downstream decision-making problem to select a good mapping. For this purpose, we introduce a multilevel mathematical programming formulation that explicitly links the time series forecasts to the SND problem of interest. The solution is a periodic demand estimate that minimizes costs over the tactical planning horizon. We report results in an extensive empirical study of a large-scale application from the Canadian National Railway Company. They clearly show the importance of the periodic demand estimation problem. Indeed, the planning costs exhibit an important variation over different periodic demand estimates and using an estimate different from the mean forecast can lead to substantial cost reductions. Moreover, the costs associated with the periodic demand estimates based on forecasts were comparable to, or even better than those obtained using the mean of actual demand.

cs.LG↗

arXiv2021

A Two-step Heuristic for the Periodic Demand Estimation Problem

Freight carriers rely on tactical plans to satisfy demand in a cost-effective way. For computational tractability in real large-scale settings, such plans are typically computed by solving deterministic and cyclic formulations. An important input is the periodic demand, i.e., the demand that is expected to repeat in each period of the planning horizon. Motivated by the discrepancy between time series forecasts of demand in each period and the periodic demand, Laage et al. (2021) recently introduced the Periodic Demand Estimation (PDE) problem and showed that it has a high value. However, they made strong assumptions on the solution space so that the problem could be solved by enumeration. In this paper we significantly extend their work. We propose a new PDE formulation that relaxes the strong assumptions on the solution space. We solve large instances of this formulation with a two-step heuristic. The first step reduces the dimension of the feasible space by performing clustering of commodities based on instance-specific information about demand and supply interactions. The formulation along with the first step allow to solve the problem in a second step by either metaheuristics or the state-of-the-art black-box optimization solver NOMAD. In an extensive empirical study using real data from the Canadian National Railway Company, we show that our methodology produces high quality solutions and outperforms existing ones.

math.OC↗

arXiv2019

Product-Closing Approximation for Ranking-based Choice Network Revenue Management

Most recent research in network revenue management incorporates choice behavior that models the customers' buying logic. These models are consequently more complex to solve, but they return a more robust policy that usually generates better expected revenue than an independent-demand model. Choice network revenue management has an exact dynamic programming formulation that rapidly becomes intractable. Approximations have been developed, and many of them are based on the multinomial logit demand model. However, this parametric model has the property known as the independence of irrelevant alternatives and is often replaced in practice by a nonparametric model. We propose a new approximation called the product closing program that is specifically designed for a ranking-based choice model representing a nonparametric demand. Numerical experiments show that our approach quickly returns expected revenues that are slightly better than those of other approximations, especially for large instances. Our approximation can also supply a good initial solution for other approaches.

math.OC↗

arXiv2016

Achieving an optimal trade-off between revenue and energy peak within a smart grid environment

We consider an energy provider whose goal is to simultaneously set revenue-maximizing prices and meet a peak load constraint. In our bilevel setting, the provider acts as a leader (upper level) that takes into account a smart grid (lower level) that minimizes the sum of users' disutilities. The latter bases its decisions on the hourly prices set by the leader, as well as the schedule preferences set by the users for each task. Considering both the monopolistic and competitive situations, we illustrate numerically the validity of the approach, which achieves an 'optimal' trade-off between three objectives: revenue, user cost, and peak demand.

math.OC↗