Error bound for the dynamic lot size model allowing speculative motive

Abstract

This paper studies the dynamic lot size model with speculative motive for holding inventory being allowed, where speculative motive means that producing a unit in a period and holding it to a future period may be cheaper than producing it at the later time. In a rolling horizon environment, one usually makes decisions for the first few periods based on the forecast data for some fixed time horizon. This fixed time horizon may not be long enough, in the sense that information beyond that time horizon may affect decisions in the first few periods. Hence it is desirable to find a worst-case bound on the error induced by imposing a finite time horizon on the model. This paper shows how to adapt recently developed O(TlogT) algorithms for the model to find an attainable bound. Furthermore, a planning horizon theorem that is more general than that in the literature is also provided.