Sensitivity analysis and efficient algorithms for some economic lot-sizing and scheduling problems

Many of optimization problems can be decomposed into a number of easier subproblems of the same type. Then dynamic programming (DP) seems to be a natural way to obtain an optimal solution. A straightforward application of DP usually leads to algorithms whose running time heavily depends on the magnitude of the input data. It has been shown in the thesis that it is possible to improve the complexity status of straightforward DP algorithms for different optimization problems, arising in production planning and scheduling, by means
of a sensitivity analysis that allows to shrink the state space and to reduce thereby the amount of unnecessary computations. Using the suggested approach, we transform DP algorithms into polynomial ones and into so-called fully polynomial time approximation schemes.