We study the vehicle routing problem with stochastic demands (VRPSD), an important variant of the classical capacitated vehicle routing problem in which customer demands are modeled as random variables. We develop the first algorithm for the VRPSD in the case where the demands are given by an empirical probability distribution of scenarios — a data-driven … Read more
We introduce a novel technique to generate Benders’ cuts from a conic relaxation (“corner”) derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining inequalities for the epigraph associated to this corner, we develop a computationally-efficient algorithm based on a compact reverse polar formulation … Read more
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In this paper, we investigate the partial inverse knapsack problem, a bilevel optimization problem in which the follower solves a classical 0/1-knapsack problem with item profit values comprised of a fixed part and a modification determined by the leader. Specifically, the leader problem seeks a minimal change to given item profits such that there is … Read more
This study addresses the problem of minimizing the weighted completion time variance (WCTV) in single-machine scheduling. Unlike the unweighted version, which has been extensively studied, the weighted variant introduces unique challenges due to the absence of theoretical properties that could guide the design of efficient algorithms. We propose a mathematical programming framework based on a … Read more
Bilevel optimization problems arise in numerous real-world applications. While single-level reformulations are a common strategy for solving convex bilevel problems, such approaches usually fail when the follower’s problem includes integer variables. In this paper, we present the first single-level reformulation for mixed-integer linear bilevel optimization, which does not rely on the follower’s value function. Our … Read more
Optimization problems with norm-bounding constraints appear in various applications, from portfolio optimization to machine learning, feature selection, and beyond. A widely used variant of these problems relaxes the norm-bounding constraint through Lagrangian relaxation and moves it to the objective function as a form of penalty or regularization term. A challenging class of these models uses … Read more
The Chance-Constrained Parallel Machine Scheduling Problem (CC-PMSP) assigns jobs with uncertain processing times to machines, ensuring that each machine’s availability constraints are met with a certain probability. We present a decomposition approach where the master problem assigns jobs to machines, and the subproblems schedule the jobs on each machine while verifying the solution’s feasibility under … Read more
We address the Undirected Team Orienteering Arc Routing Problem (UTOARP). In this problem, demand is placed at some edges of a given undirected graph and served demand edges produce a profit. Feasible routes must start and end at a given depot and there is a time limit constraint on the maximum duration of each route. … Read more
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from solving an SAA is random, statistical estimates on the optimal value of the true problem can be obtained by solving … Read more