Presolving a linear program is important for fast solution and can sometimes detect infeasibility before the reduced model is solved. But presolving typically interferes with finding an Irreducible Infeasible Subset (IIS) of row constraints and variable bounds, the main way to analyze infeasibility. Early attempts to backtrack the set of logical model reductions when the presolver detects infeasibility, with the goal of finding an IIS, were abandoned as impractical. However, the OptVerse solver has now implemented a very fast backtrack capability that greatly speeds IIS isolation whether or not the presolver detects infeasibility. In both cases, the backtracker isolates a small subset of the model that is then subjected to typical IIS isolation procedures. The speed advantage is demonstrated experimentally vs. other major LP solvers.

Due to the computational complexity of solving large Mixed Integer Programming (MIP) problems, many industry specific problems – requiring complex formulations and having many variables and constraints – are routinely left unsolved or solved sub-optimally, resulting in lost profits and productivity. Parallelization combined with techniques for managing the “Branch and Bound” (BB) tree search and “branching variable selection” (BVS) are often required to reduce the time it takes to solve such problems.
We seek to improve upon solutions that leverage parallel computing to solve large MIPs relevant to industrial use cases by introducing two key features: distributed data structures with implicit concurrency semantics and Machine learning-powered branching variable selection. We explore the integration of conflict-free replicated data types (CRDTs) into a parallel implementation of the Branch and Bound algorithm. Previous work has shown that an intelligent BVS technique can improve search efficiency, and the addition of CRDTs can simplify data management in a parallel compute environment; improving sub-problem load-balancing and ensuring consistent replication of global information across distributed resources involved in solving a MIP.
In this presentation, we demonstrate the feasibility of our approach on MIPLIB problem instances and we report preliminary results from a proof-of-concept implementation of our framework that uses the open-source HiGHS solver.

This paper considers a joint transshipment, markdown, and clearance sales decisions of multiple products for a fast-fashion retailer that owns and operates a large network of retail stores. This problem is motivated by the logistics operations of the largest apparel retailer in Turkey, namely LC Waikiki Particularly, the emphasis is on the following questions: How should the products be re-distributed among retail stores after a few weeks of demand observation? What should be the price level for each product? And, finally, which products should be marked for clearance sales? To answer these questions, a mathematical model is proposed considering the business rules and the practices of the retailer encounters. We develop a Bender-Decomposition-based heuristic to find upper bounds and a simulated annealing-based metaheuristic to find incumbent solutions, both of which have proven to be quite effective. A Covering-Cut-Bundle approach is used to accelerate the convergence of the Bender-Decomposition algorithm. We have also conducted a set of experiments to uncover the impact of business rules on the retailer's operations and the effectiveness of joint markdown and transshipment decisions.

ExPretio emerges from two decades of academic research in pricing and revenue optimization, integrating expertise from revenue management practitioners and operations research / data science specialists. Focused on helping rail passenger carriers better manager their capacity and pricing to maximize revenue, our challenge lay in understanding the intricate relationships between price, business rules, and passenger buying behaviors. Our AI-powered solution employs an interconnection of mathematical programming, machine learning, and simulation. Every day, we solve more than 125,000 mathematical programs, generating 60 million forecasts for over 20 global clients. This enables precise resource allocation, empowering rail companies to achieve revenue goals while considering broader business objectives. In our presentation, we will discuss our AI framework, the diverse challenges it addresses, and how we continue to collaborate with universities to improve our chain.