Problem definition: We study the problem of designing large-scale resilient relay logistics hub networks. We propose a model of k-Shortest Path Network Design, which aims to improve a network’s efficiency and resilience through its topological configuration, by locating relay logistics hubs to connect each origin-destination pair with k paths of minimum lengths, weighted by their … Read more
Presolving has become an essential component of modern MIP solvers both in terms of computational performance and numerical robustness. In this paper we present PaPILO (https://github.com/scipopt/papilo), a new C++ header-only library that provides a large set of presolving routines for MIP and LP problems from the literature. The creation of \papilo was motivated by the … Read more
ODTLearn is an open-source Python package that provides methods for learning optimal decision trees for high-stakes predictive and prescriptive tasks based on the mixed-integer optimization (MIO) framework proposed in Aghaei et al. (2019) and several of its extensions. The current version of the package provides implementations for learning optimal classification trees, optimal fair classification trees, … Read more
Conflict analysis originally tried to exploit the knowledge that certain nodes in a relaxation-based branch-and-bound are infeasible. It has been extended to derive valid constraints also from feasible nodes. This paper adapts this approach to mixed-integer semidefinite programs. Using dual solutions, the primal constraints are aggregated and the resulting inequalities can be used at different … Read more
In this tutorial we consider single-leader-multi-follower games in which the models of the lower-level players have polyhedral feasible sets and convex objective functions. This situation allows for classic KKT reformulations of the separate lower-level problems, which lead to challenging single-level reformulations of MPCC type. The main contribution of this tutorial is to present a ready-to-use … Read more
In a series of essays, we introduce average incremental cost (AIC) pricing and present examples to help understand its advantages. In non-convex markets, AIC pricing is the rough equivalent to marginal cost pricing in convex markets. We present a qualitative comparison of current ISO pricing methods and the AIC approach. We argue that AIC better … Read more
Since the inception of ISOs, Locational Marginal Prices (LMPs) alone were not incentive compatible because an auction winner who offered its avoidable costs could lose money at the LMP. ISOs used make-whole payments to ensure market participants did not lose money. Make-whole payments were not public creating transparency issues. Over time, the ISOs employed methods … Read more
Efficient and effective scheduling is crucial for ensuring the productivity and competitiveness of production lines, contributing significantly to organizational sustainability. This study addresses the scheduling challenges faced by a UK-based steel reinforcement manufacturer. We propose a heuristic algorithm to tackle a multistage flexible flow shop scheduling problem, where each stage consists of parallel unrelated machines. … Read more
In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization. In this domain, the combination of ML and OR often relies on representing the ML model output using Mixed Integer Programming (MIP) formulations. Numerous studies … Read more
Due to their nested structure, bilevel problems are intrinsically hard to solve – even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. We provide an extension of the … Read more