Service-level-driven procurement and production lot-sizing problem with demand fulfilment

This paper presents novel models for the Integrated Procurement and Lot-Sizing Problem with multiple customers and backlogging. Since allowing backlog in a traditional cost minimisation model involves dealing with intangible costs of not fulfilling the demand on time, we propose optimising service-levels while keeping the costs minimal using a budget constraint. The motivation of this study emanates from a manufacturing company that assembles commercial and industrial refrigeration equipment, using both purchased materials and in-house products. Instead of considering an aggregate demand, we consider the specific demand from various customers. This allows us to incorporate demand fulfilment decisions into the model in case of stock-outs by deciding which customers will have their orders backlogged. The fill-rate, or beta service-level, is considered both globally and for customers and products individually. Computational experiments show that the service-level-driven models improve service when compared to the traditional cost model and also end up enforcing service equity among different customers at the expense of a deterioration in the global fill-rate.