4 Presentations

• 
  03:30 PM - 03:55 PM

  Towards Resilience: Primal Large-Scale Re-optimization

  • El Mehdi Er Raqabi, presenter, Gerad, Polytechnique Montrél
  • Yong Wu, Griffith University
  • Issmail El Hallaoui, GERAD, Polytechnique Montréal
  • Francois Soumis, GERAD et Polytechnique

  Perturbations are universal in supply chains, and their appearance has become more frequent in the past few years due to global events. These perturbations affect industries and could significantly impact production, quality, cost/profitability, and consumer satisfaction. In large-scale contexts, companies rely on mathematical optimization. In such a case, re-optimization can support companies in achieving resilience by enabling them to simulate several what-if scenarios and adapt to changing circumstances and challenges in real-time. In this paper, we design a generic and scalable resilience re-optimization framework. We model perturbations, recovery decisions, and the resulting re-optimization problem, which maximizes resilience. We leverage the primal information through fixing, warm-start, valid inequalities, and machine learning. We conduct extensive computational experiments on a real-world, large-scale problem in Africa. The findings highlight that local optimization is enough to recover after perturbations and demonstrate the power of our proposed framework and solution methodology.

• 
  03:55 PM - 04:20 PM

  Combining Benders Decomposition and Column Generation for the Petrol Station Replenishment Problem with Inventory Management

  • Abderrahman Bani, presenter, GERAD
  • Issmail El Hallaoui, GERAD, Polytechnique Montréal
  • Ayoub Insa Corréa, Thiès University, Senegal

  The truck loading and the inventory routing problems are the two most important decisions made by companies replenishing petrol stations. When these two problems are solved sequentially, either the solution is suboptimal or infeasible. This work investigates a petrol station replenishment problem (PSRP) that integrates the truck loading problem (TLP) and the inventory routing problem (IRP). We introduce a compact mixed-integer linear programming formulation for the problem. Given its complexity, even for small instances, the compact formulation cannot be solved by general-purpose solvers. Thus, we develop an exact solution approach that combines Benders decomposition and column generation. Inspired by the traditional three-phase Benders decomposition, our approach consists of two phases. In the first phase, we solve relaxed (integrality) Benders subproblems until the inventory levels stabilize (to be explained). In the second phase, we optimally solve Benders subproblems using a Branch-and-Price framework. We enhance our approach with various acceleration strategies, including valid inequalities, warm-start, and parallelism. Extensive computational results using real-world instances from one of the leading companies in West Africa highlight the strength of our approach. We reach optimal solutions in these instances and note that acceleration strategies significantly boost the performance of our two-phase method. We generate several managerial insights that highlight the benefits achieved through integrated optimization.

• 
  04:20 PM - 04:45 PM

  Enhancing Access to Fertilizers in Developing Countries: A Case Study of Ethiopia.

  • Omar Boussouf, presenter, Polytechnique Montréal / GERAD
  • Issmail El Hallaoui, GERAD, Polytechnique Montréal
  • Amina Lamghari, Université du Québec à Trois-Rivières

  In developing countries, the challenge of limited access to fertilizers poses a significant barrier to sustainable agricultural development and food security. Recognizing the vital role that fertilizers play in enhancing agricultural productivity, this paper introduces a two-stage stochastic mixed-integer linear programming model designed to optimize the distribution network of fertilizers from a new production facility to Farmer Cooperative Unions (FCUs) in Ethiopia. Through strategic determination of warehouse locations and sizes, alongside the management of fertilizer flows, the model addresses both purchasing and leasing options for storage facilities. By focusing on seven key locations for warehouse establishment, the study ensures operational stability across various demand scenarios, offering leasing as a flexible solution for demand fluctuations. This strategic approach not only aims to improve agricultural practices by ensuring a consistent fertilizer supply but also highlights potential cost efficiencies in transport and storage, demonstrating the advantages of local fertilizer production over imports for sustainable agricultural development in Ethiopia.

• 
  04:45 PM - 05:10 PM

  Generalized integral simplex

  • Alpha Saliou Barry, presenter, Gerad

  The set partitioning problem can be generalized. One generalization is to consider that certain tasks
  must be covered several times. So it's no longer a partition that's sought, but a set of parts that verify
  the right number of coverages.
  Unlike the set partitioning problem, the graph of integer solutions is no longer connected when the
  possible arcs are simplex pivots. Howerver, in order to restore the connectedness of the graph, it is
  possible to add artificial variables locally, which allow new pivots to be made while preserving the
  integrity of the solution.
  We give priority to pivots that keep the solution integer. When this is no longer possible, we solve a
  linear program to obtain a non-degenerate sequence of simplex pivots to perform in order to
  improve the solution. When this improved solution is still not integer, in some cases the pivot
  sequence allows to add an artificial column associated with an integer artificial point. The linear
  program is solved again from this point to find the remaining pivots to be performed in order to
  obtain a better integer solution. If integrity is still not reached, a branching is performed.
  We present results for large pairing problems (around 2,000 constraints and 300,000 variables) and
  show that the method is around 2 to 5 times faster than traditional methods (CPLEX) and that in
  many cases, the addition of the artificial variable effectively allows moves on integer points not
  directly accessible by pivot.