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
In this note, we study the size of the support of solutions to linear Diophantine equations $Ax=b, ~x\in\Z^n$ where $A\in\Z^{m\times n}, b\in\Z^n$. We give an asymptotically tight upper bound on the smallest support size, parameterized by $\|A\|_\infty$ and $m$, and taken as a worst case over all $b$ such that the above system has a … Read more
We describe a method to generate cutting planes for quadratically constrained optimization problems. The method uses information from the simplex tableau of a linear relaxation of the problem in combination with McCormick estimators. The method is guaranteed to cut off a basic feasible solution of the linear relaxation that violates the quadratic constraints in the … 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
This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length \(L\) of the integer program) for the size of a general branch-and-bound tree for a particular class of (compact) integer programs, namely \(2^{\Omega(L^{1/12 -\epsilon})}\) for … Read more
CitationOjha, R., Chen, W., Zhang, H., Khir, R., Erera, A. & Van Hentenryck, P. (2023). Optimization-based Learning for Dynamic Load Planning in Trucking Service Networks.ArticleDownload View PDF
Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from weak linear programming (LP) relaxations. Many existing MIP approaches employ big-M constraints to ensure observations are … Read more
Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more
Numerous industrial fields, like supply chain management, face mixed-integer optimization problems on a regular basis. Such problems typically show a sparse structure and vary in size, as well as complexity. However, in order to satisfy customer demands, it is crucial to find good solutions to all such problems quickly. Current research often focuses on the … Read more