SCRO / Journées de l'optimisation

HEC Montréal, 29-31 mai 2023


HEC Montréal, 29 — 31 mai 2023

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SPII Stochastic Programming II

29 mai 2023 15h30 – 17h10

Salle: Xerox Canada (jaune)

Présidée par Caio Tomazella

4 présentations

  • 15h30 - 15h55

    Modelling spot and option-on-futures prices of the EU carbon allowance

    • Yiyang Chen, prés., Western University
    • Mamon Rogemar , Western University

    This study begins with the investigation of the behaviour of the spot price of carbon emission allowance in the European Union Emissions Trading Scheme (EU ETS). The volatility clustering phenomenon is observed in the daily returns of the spot price. Motivated by this phenomenon, we embed a regime-switching mechanism into four stochastic models. The parameters of the proposed regime-switching-driven models are governed by a hidden Markov chain, which enables the time-dependent parametrisation and captures the volatility-clustering property. The non-switching stochastic models are used as baseline to benchmark the models with regime switching in the context of in-sample fitting and out-of-sample forecasting performance. Then, this research turns focus on the pricing of European-style futures call options under the proposed modelling setups. The models are assessed by comparing the pricing errors with the aid of the EUA futures call option data compiled by the Bloomberg Professional Services. Based on the results of the spot-price modelling and the in-sample and out-of-sample analyses involved in option pricing, the proposed regime-switching geometric Brownian motion is deemed as the best-fitting model amongst the alternatives included in our study.

  • 15h55 - 16h20

    Two-Stage Distributionally Robust Optimization for Service Region Design in Crowdsourced Delivery

    • Aliaa Alnaggar, prés., Toronto Metropolitan University
    • Gohram Baloch, Simon Fraser University

    We consider a service region planning problem faced by a crowdsourced delivery platform where drivers are commuters who are willing to deviate from their original routes to a make a delivery in exchange for a compensation. The availability of drivers and service demand are uncertain, and it is difficult to estimate their probability distributions due to the absence of service history. To mitigate the effects of data ambiguity, we propose a two-stage distributionally robust optimization (DRO) model. The first stage selects which nodes to offer service in, while the second stage matches drivers and orders after uncertainty is realized. We derive an exact reformulation of the DRO model and develop a monolithic approximation based on a convex relaxation of the subproblem. We further strengthen the proposed approximation by a set of valid inequalities inspired by the linearization reformulation technique. The benefit of the proposed approach for service region design in crowdsourced delivery is demonstrated through numerical experiments.

  • 16h20 - 16h45

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

    • David Pinzon Ulloa, prés., CIRRELT
    • Emma Frejinger, DIRO and CIRRELT

    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 depends 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 highly depends on shippers' price sensitivity. Underestimating it can lead to an overestimation of expected profits.

  • 16h45 - 17h10

    The Stochastic Procurement and Production Lot-Sizing Problem

    • Paziani Tomazella Caio, prés., HEC Montreal
    • Jans Raf, HEC Montréal
    • Oliveira Santos Maristela, University of São Paulo
    • Alem Douglas, University of Edinburgh

    We address the problem of integrating production and raw material procurement with demand uncertainty via the scenario-based two-stage stochastic programming approach. Three variants of the problem are presented: one static model, in which all decisions are made before demand realization; and two static-dynamic models, in which production decisions are flexible to be made after demand realization. In all cases, procurement decisions must be made in advance since they involve third-party suppliers, therefore, before the demand is known. We present mixed-integer programming models for each of the stochastic approaches and propose heuristic methods used to obtain good-quality solutions for some difficult cases. Our computational experiments show the value of using a stochastic model over solving the deterministic problem with the expected demand, and we also analyze the difference between the three proposed models in terms of cost savings, backlogged demand and inventory.