%0 Report %T Multi-Item Single Machine Scheduling Optimization. The Case with Piecewise Deterministic Demands %+ Mathematical Programming (PROMATH) %A Mancinelli, Elina %A González, Roberto L.V. %Z Projet PROMATH %N RR-3144 %I INRIA %8 1997 %D 1997 %K SCHEDULING PROBLEMS %K PIECEWISE DETERMINISTIC DEMANDS %K QUASI-VARIATIONAL INEQUALITIES %K HAMILTON-JACOBI-BELLMAN EQUATION %K NUMERICAL SOLUTION %Z Computer Science [cs]/Other [cs.OH]Reports %X In this work we study the optimization of a production system comprising a multi-item single machine with piecewise deterministic demands. Demands can only take a finite number of values and the demand changes are described by Poisson processes. We present the theoretical characterization of the solution and a numerical procedure to solve it. We establish the rate of convergence of the discrete solution toward the original continuous solution. %G English %2 https://inria.hal.science/inria-00073545/document %2 https://inria.hal.science/inria-00073545/file/RR-3144.pdf %L inria-00073545 %U https://inria.hal.science/inria-00073545 %~ INRIA %~ INRIA-ROCQ %~ INRIA-RRRT %~ INRIA_TEST %~ TESTALAIN1 %~ INRIA2 %~ LARA