This paper addresses sensitivity analysis for a deterministic multi-period production and inventory model. The model assumes a piecewise linear cost structure, but permits backlogging of unsatisfied demand. Our approach to sensitivity analysis here can be divided into two basic steps; (1) to find the optimal production policy through a forward dynamic programming algorithm similar to the backward version of Zangwill [1966] and (2) to apply the penalty network approach by the author [1986] in order to derive sensitivity ranges for various model parameters. Computational aspects are discussed and topics of further research are suggested.