Many optimization problems solved repeatedly in practice, such as in power systems or logistics, share a fixed structure but with different parameter values. Re-optimizing each instance from scratch can be computationally prohibitive, while adopting a single solution for all realizations is overly conservative. The K-adaptability paradigm offers a flexible compromise by precomputing a small set … Read more
Classical budget uncertainty is widely used in robust optimization. It bounds the aggregate absolute deviation of uncertain parameters from nominal values and yields tractable robust counterparts. In many applications, however, information concerns aggregate signed deviations. We therefore study signed budget uncertainty, in which bounds are imposed on signed aggregates rather than absolute deviations. For robust … Read more
We revisit the framework of generalized Benders decomposition over a compact but non-finite master domain. We show by counterexample that strong general dual functions alone may fail to guarantee convergence. We then define a condition of uniform local strongness and prove that strong general dual functions satisfying this condition guarantee finite \(\epsilon\)-termination. Finally, we show … Read more
Facility location decisions are typically made before demand is fully known, yet most applied studies solve a single deterministic model using expected or nominal demand. This paper formulates and solves a capacitated facility location problem using a real academic benchmark instance, then extends it to a two-stage stochastic program in which facility-opening decisions are made … Read more
We consider the probabilistic traveling salesman problem (PTSP) in which customer presences are Bernoulli random variables, and the objective is to determine an a priori tour minimizing the expected traveling cost of the a posteriori tour obtained by skipping absent customers after customer presence is revealed. The existing literature has established that, given an a … Read more
For integer activities, conditioning on the support makes a fixed-charge objective affine. If every support-conditioned cell is integral, an optimal solution is a vertex of its cell for arbitrary fixed charges and marginal rates. A totally unimodular constraint matrix with integral data guarantees this condition. This surviving property is weaker than the classical conclusions. A … Read more
We study the steady-state expansion problem for potential-based flow networks. Constructing a cost-minimal network that admits a flow satisfying the underlying physical laws is a central problem in the design of gas, hydrogen, water, and electricity infrastructures. The physical behavior of such networks is governed by nonlinear relations between arc flows and the potential differences … Read more
Georeferenced synthetic populations are essential inputs for agent-based simulations in epidemiology, transportation, and urban planning, yet existing methods for spatial allocation of households to residences lack formal optimality guarantees. We present a two-stage mathematical framework for generating such populations from publicly available census data. The first stage combines Iterative Proportional Fitting (IPF) with a mixed-integer … Read more
This paper proposes a four-stage decision-support framework for structuring and reducing large multi-objective solution sets into compact and interpretable collections of representative alternatives. The methodology combines: (Phase 1) systematic solution generation through extended goal programming and structured preference exploration; (Phase 2) robustness-aware enrichment and profiling under weight sensitivity analysis; (Phase 3) filtering and dominance-based reduction … Read more