Time-dependent demand in requirements planning: An exploratory assessment of the effects of serially correlated demand sequences on lot-sizing performance

The problem of determining the appropriate stock replenishment quantity within a time-phased requirements planning environment has received considerable research attention in recent years. Relative performance characteristics of lot-sizing policies have been assessed as a function of the cost structure, the demand pattern, the product structure, forecast error, the length of the planning horizon, and the interaction between replenishment quantities and sequencing decisions. In particular, the relationship between lot sizing behavior and variability in the requirements profile has been intensely investigated. However, despite these efforts, the empirical evidence linking lot-sizing performance with demand variability remains inconclusive. This article suggests that, in part, some of the ambiguity in the literature may be an artifact of a failure to adequately control for other important dimensions of simulated demand sequences. The features that have been thought to describe ‘lumpy’ requirements profiles are discussed and the characteristic of periodicity or time-dependency in the demand entries is identified as a variable that has been insufficiently controlled in prior work. A reanalysis of the demand sequences originally published by Kaimann, and subsequently used in a number of comparative lot-sizing studies, reveals that the patterns differ not only in variability as measured by the coefficient of variation, but also in terms of correlation structure as described by the autocorrelation function. Alternative methods for simulating demand sequences are reviewed and a correlation transfer technique, which has the capability to simultaneously control both the degree of variability and correlation, is suggested as an improved method for the generation of synthetic sequences of ‘lumpy’ demand. Using this technique, five of Kaimann’s original sequences are rearranged, resulting in three sets of sequences differing only in the strength of serial correlation. Four lot-sizing procedures are applied to each of these sets to discern if the correlation structure has any appreciable effect on lot-sizing performance. Results indicate that, on average, higher total inventory costs are experienced when the demand environment is characterized by randomness. Economic order quantity and part-period balancing achieve lowest average costs when confronted with highly autocorrelated demand of patterns of few runs; conversely, minimum cost per period and Wagner-Whitin perform best under conditions of many runs. Both economic order quantity and part-period balancing perform most favorably in comparison to Wagner-Whitin when runs are few. In addition, there appears to be a potential interaction between the level of demand variability and the degree of serial correlation. This finding is somewhat disconcerting since high variability demand sequences used in some prior research were also characterized by relatively high levels of autocorrelation; hence it becomes most difficult to identify and decompose the unique influences of each demand pattern dimension on lot-sizing behavior. Because of this phenomenon, it is suggested that future studies direct greater attention to the demand simulating methodology than has heretofore been accorded.