In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) is considered. DLSP relates to capacitated lotsizing as well as to job scheduling problems and is concerned with determining a feasible production schedule with minimal total costs in a single-stage manufacturing process. This involves the sequencing and sizing of production lots for a number of different items over a discrete and finite planning horizon. Feasibility of production schedules is subject to production quantities being within bounds set by capacity. A problem classification for DLSP is introduced and results on computational complexity are derived for a number of single and parallel machine problems. Furthermore, efficient algorithms are discussed for solving special single and parallel machine variants of DLSP.
This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These models specify a customer’s transaction and defection processes in a non-contractual setting. They are typically used to identify active customers in a com- pany’s customer base and to predict the number of purchases. Surprisingly, the literature shows that models with quite different assumptions tend to have a similar predictive performance. We show that BTYD models can also be used to predict the timing of the next purchase. Such predictions are managerially relevant as they enable managers to choose appropriate promotion strategies to improve revenues. Moreover, the predictive performance on the purchase timing can be more informative on the relative quality of BTYD models. For each of the established models, we discuss the prediction of the purchase timing. Next, we compare these models across three datasets on the predictive performance on the purchase timing as well as purchase frequency. We show that while the Pareto/NBD and its Hierarchical Bayes extension [HB] models perform the best in predicting transaction frequency, the PDO and HB models predict transaction timing more accurately. Furthermore, we find that differences in a model’s predictive performance across datasets can be explained by the correlation between behavioral parameters and the proportion of customers without repeat purchases.
