Integer goal programming for multistage lot sizing: Experimentation and implementation

This article considers the issues involved in implementing a large-scale multistage lot sizing model in a pharmaceutical manufacturing environment, and reports on a series of sensitivity experiments that subsequently examined the critical impacts of system capacity and inventory policy on the specification of a multistage schedule. The model was initially developed as a aggregate scheduling aid for a class of tablet pharmaceuticals. The manufacture of tablet products is a serial-type process characterized by batch flow. The model placed multiple resource capacity restrictions on various stages of the multistage system to ensure the feasibility of the resultant schedules. Difficulties in estimating penalty costs for shortages were circumvented by employing a multi-objective formulation of the lot-sizing problem. Various obstacles encountered during the implementation process are discussed. Model implementation encompassed the development of an approximation algorithm for efficiently solving the large-scale problem. The performance of the algorithm was evaluated by examining the closeness to optimality of the solutions obtained using the procedure. Performance statistics are presented for the sensitivity experiments discussed herein. Another essential aspect of implementation involved the timely revision of model input parameters. This facet of implementation proved to be at least as important to management as the efficient provision of a ‘good’ solution. Model experimentation centered on variations in the capacities of bottleneck resources and changes in target inventory parameters whose values are predetermined by company policy. The first set of experiments was designed to demonstrate the importance of system capacity to the lot-sizing process and to illustrate that the location of a system bottleneck can vary over time as a function of both internal and external factors. The results indicated that lot-sizing procedures that fail to incorporate capacity information or that focus on a single bottleneck production stage in order to schedule production are severely limited with respect to practical and/or long-term applicability. The final set of inventory-related experiments indicated that the specification of target ending inventory levels was a crucial factor in the lot-sizing process. The determination of appropriate target levels must reflect the inherent trade-off between the objective of minimizing shortages and the desire to avoid excessive inventory accumulations. The generation of usable model information was found to be contingent upon the realistic definition of target level parameters.