In this paper, we study a two-level lot-sizing problem with supplier selection (LSS). This NP-hard problem arises in different production planning and supply chain management applications. We first present a dynamic programming algorithm for LSS that is polynomial when the number of plants is fixed. We use this algorithm to describe the convex hull of solutions to the problem in an extended spa...

The classical Hurwitz theorem says that if n first “harmonics” (2n+1 Fourier coefficients) of a continuous function f(x) on the unit circle are zero, then f(x) changes sign at least 2n + 1 times. We show that similar facts and its converse hold for any function that are orthogonal to a Chebyshev system. These theorems can be extended for convex curves in d-dimensional Euclidean space. Namely, i...

We investigate the utility of the convex hull ofmany Lagrangian tracers to analyze transport properties of turbulent flowswith different anisotropy. In direct numerical simulations of statistically homogeneous and stationaryNavier–Stokes turbulence, neutral fluid Boussinesq convection, and MHDBoussinesq convection a comparisonwith Lagrangian pair dispersion shows that convex hull statistics cap...

in the present work, the effects of operating conditions including ph, transmembrane pressure, oil concentration, and temperature on fouling resistance and the rejection of turbidity for a polymeric membrane in an ultrafiltration system of wastewater treatment were studied. a new modeling technique called evolutionary polynomial regression (epr) was investigated. epr is a method based on regres...

This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex hull of a plane quartic to be exactly semidefinite representable with at most 12 lifting variables. If the quartic is rationally parametrizable, an exact se...