## A Discounted-cost Continuous-time Flexible Manufacturing and Operator Scheduling Model Solved by Deconvexification Over TimeStanford University. Dept. of Operations Research. Systems Optimization Laboratory, B. Curtis Eaves, Uriel G. Rothblum DIMACS, Center for Discrete Mathematics and Theoretical Computer Science, 1990 - Flexible manufacturing systems - 52 pages Abstract: "A discounted-cost, continuous-time, infinite-horizon version of a flexible manufacturing and operator scheduling model is solved. The solution procedure is to convexify the discrete operator- assignment constraints to obtain a linear program, and then to regain the discreteness and obtain an approximate manufacturing schedule by deconvexification of the solution of the linear program over time. The strong features of the model are the accommodation of linear inequality relations among the manufacturing activities and the discrete manufacturing scheduling, whereas the weak features are intra-period relaxation of inventory availability constraints, and the absence of inventory costs, setup times, and setup charges." |

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A-stationary policy AT(pA Buy-Sell Example computed constraints of RDP convex hull Corollary 4.6 Cx(t define denote the objective discounted inventory constraints discounted inventory levels DP3A DP3B Dy(x)dx dynamic program RRDP e-PTDy(x)dx Example for RDP feasible solution FMOS function given hence implies in-process infimizes the objective infimum interest rate inventory availability constraints inventory costs L'Hopital's Rule Lemma linear program LP LP(p Manufacturing and Operator nonnegative Operator Scheduling Model operator-assignment optimal for RRDP optimal objective value optimal policy optimal solution p(Ax period lengths place over policies policy 7t policy for RRDP policy n policy satisfying problem Proof R+ DPI RDPU relaxation of RDP RFMOS right inequalities RRDP and RDP RRDP(p s e Z+ satisfying the constraints search takes place Section select a policy select an optimal solution of LP stationary t e R+ Theorem vectors Vlp(p VRDP Vrrdp Vxy(p