arXiv subjects

Emma Frejinger

Publications and source records attributed to Emma Frejinger.

29 records · Page 2Linked to original sources

arXiv2023

A Logistics Provider's Profit Maximization Facility Location Problem with Random Utility Maximizing Followers

We introduce a strategic decision-making problem faced by logistics providers (LPs) seeking facility location decisions that lead to profitable operations. The profitability depends on the revenue generated through agreements with shippers, and the costs arising when satisfying those agreements. The latter depend in turn on service levels and on characteristics of the shippers' customers. However, at a strategic level, LP has imperfect information thereof. We propose a stochastic bilevel formulation where a given LP (leader) anticipates the decisions of shippers (followers) arising from a random utility maximization model. Using a sample average approximation and properties of the associated optimal solutions, we introduce a non-conventional single-level mixed integer linear programming formulation that can be solved by a general-purpose solver. We can quickly identify situations that lead to zero expected profit for the LP. Experimental results show that optimal expected profit is highly dependent on shippers' price sensitivity. Underestimating it can lead to an overestimation of expected profits.

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arXiv2022

Fast Continuous and Integer L-shaped Heuristics Through Supervised Learning

We propose a methodology at the nexus of operations research and machine learning (ML) leveraging generic approximators available from ML to accelerate the solution of mixed-integer linear two-stage stochastic programs. We aim at solving problems where the second stage is highly demanding. Our core idea is to gain large reductions in online solution time while incurring small reductions in first-stage solution accuracy by substituting the exact second-stage solutions with fast, yet accurate supervised ML predictions. This upfront investment in ML would be justified when similar problems are solved repeatedly over time, for example, in transport planning related to fleet management, routing and container yard management. Our numerical results focus on the problem class seminally addressed with the integer and continuous L-shaped cuts. Our extensive empirical analysis is grounded in standardized families of problems derived from stochastic server location (SSLP) and stochastic multi knapsack (SMKP) problems available in the literature. The proposed method can solve the hardest instances of SSLP in less than 9% of the time it takes the state-of-the-art exact method, and in the case of SMKP the same figure is 20%. Average optimality gaps are in most cases less than 0.1%.

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arXiv2022

Minimizing Entropy to Discover Good Solutions to Recurrent Mixed Integer Programs

Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has motivated the development of specialized methods that can exploit the information in historical datasets to guide the design of heuristics. Recent works have shown that machine learning (ML) can be integrated with an MIP solver to inject domain knowledge and efficiently close the optimality gap. This hybridization is usually done with deep learning (DL), which requires a large dataset and extensive hyperparameter tuning to perform well. This paper proposes an online heuristic that uses the notion of entropy to efficiently build a model with minimal training data and tuning. We test our method on the locomotive assignment problem (LAP), a recurring real-world problem that is challenging to solve at scale. Experimental results show a speed up of an order of magnitude compared to a general purpose solver (CPLEX) with a relative gap of less than 2%. We also observe that for some instances our method can discover better solutions than CPLEX within the time limit.

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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.

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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.

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arXiv2021

Assessing the Impact: Does an Improvement to a Revenue Management System Lead to an Improved Revenue?

Airlines and other industries have been making use of sophisticated Revenue Management Systems to maximize revenue for decades. While improving the different components of these systems has been the focus of numerous studies, estimating the impact of such improvements on the revenue has been overlooked in the literature despite its practical importance. Indeed, quantifying the benefit of a change in a system serves as support for investment decisions. This is a challenging problem as it corresponds to the difference between the generated value and the value that would have been generated keeping the system as before. The latter is not observable. Moreover, the expected impact can be small in relative value. In this paper, we cast the problem as counterfactual prediction of unobserved revenue. The impact on revenue is then the difference between the observed and the estimated revenue. The originality of this work lies in the innovative application of econometric methods proposed for macroeconomic applications to a new problem setting. Broadly applicable, the approach benefits from only requiring revenue data observed for origin-destination pairs in the network of the airline at each day, before and after a change in the system is applied. We report results using real large-scale data from Air Canada. We compare a deep neural network counterfactual predictions model with econometric models. They achieve respectively 1% and 1.1% of error on the counterfactual revenue predictions, and allow to accurately estimate small impacts (in the order of 2%).

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arXiv2021

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second stage problem, conditionally on the first stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training dataset consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

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arXiv2020

Modeling Route Choice with Real-Time Information: Comparing the Recursive and Non-Recursive Models

We study the routing policy choice problems in a stochastic time-dependent (STD) network. A routing policy is defined as a decision rule applied at the end of each link that maps the realized traffic condition to the decision on the link to take next. Two types of routing policy choice models are formulated with perfect online information (POI): recursive logit model and non-recursive logit model. In the non-recursive model, a choice set of routing policies between an origin-destination (OD) pair is generated, and a probabilistic choice is modeled at the origin, while the choice of the next link at each link is a deterministic execution of the chosen routing policy. In the recursive model, the probabilistic choice of the next link is modeled at each link, following the framework of dynamic discrete choice models. The two models are further compared in terms of computational efficiency in estimation and prediction, and flexibility in systematic utility specification and modeling correlation.

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arXiv2020

A tutorial on recursive models for analyzing and predicting path choice behavior

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice models. This article is a tutorial on a specific category of discrete choice models called recursive, and it makes three main contributions: First, for the purpose of assisting future research on route choice, we provide a comprehensive background on the problem, linking it to different fields including inverse optimization and inverse reinforcement learning. Second, we formally introduce the problem and the recursive modeling idea along with an overview of existing models, their properties and applications. Third, we extensively analyze illustrative examples from different angles so that a novice reader can gain intuition on the problem and the advantages provided by recursive models in comparison to path-based ones.

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arXiv2019

A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs

We propose a novel approach using supervised learning to obtain near-optimal primal solutions for two-stage stochastic integer programming (2SIP) problems with constraints in the first and second stages. The goal of the algorithm is to predict a "representative scenario" (RS) for the problem such that, deterministically solving the 2SIP with the random realization equal to the RS, gives a near-optimal solution to the original 2SIP. Predicting an RS, instead of directly predicting a solution ensures first-stage feasibility of the solution. If the problem is known to have complete recourse, second-stage feasibility is also guaranteed. For computational testing, we learn to find an RS for a two-stage stochastic facility location problem with integer variables and linear constraints in both stages and consistently provide near-optimal solutions. Our computing times are very competitive with those of general-purpose integer programming solvers to achieve a similar solution quality.

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arXiv2019

A language processing algorithm for predicting tactical solutions to an operational planning problem under uncertainty

This paper is devoted to the prediction of solutions to a stochastic discrete optimization problem. Through an application, we illustrate how we can use a state-of-the-art neural machine translation (NMT) algorithm to predict the solutions by defining appropriate vocabularies, syntaxes and constraints. We attend to applications where the predictions need to be computed in very short computing time -- in the order of milliseconds or less. The results show that with minimal adaptations to the model architecture and hyperparameter tuning, the NMT algorithm can produce accurate solutions within the computing time budget. While these predictions are slightly less accurate than approximate stochastic programming solutions (sample average approximation), they can be computed faster and with less variability.

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