An exact policy for enhancing buyer-supplier linkage in supply chain system

Kim S.L. and Ha D. [2003. A JIT lot-splitting model for supply chain management: Enhancing buyer-supplier linkage. International Journal of Production Economics 86, 1-10] proposed a novel cooperative method for synchronizing supply with actual customer demand in a just-in-time scenario. However, all decision variables obtained using their model may not be integers, making it difficult to be implemented in fixed-cycle applications (i.e., a planning horizon of one time period). In addition, their model can only be used to solve joint optimization for single buyer and single supplier. Furthermore, problems arise when resource constraints are added to their model because traditional inventory models do not allow constraints to be added by the decision maker arbitrarily. To improve the practical utility of the model of Kim and Ha (2003), we derive a mixed-integer optimization approach, which not only can be applied to the joint optimization for the multi-buyer and single supplier, but also all decision variables obtained are executable integers for the planning horizon of one time period. To suit real-world situations, infinite planning horizon scenario is also considered in this study. In addition, illustrative examples are included to demonstrate the usefulness of the proposed models in which the integrated purchase policy being superior to independent optimization can be clearly seen. Moreover, the analytical superiority of the proposed models in terms of execution time can be seen, through a computational experiment conduced on a set of logical number of buyers in the multi-buyer and single-supplier problem. Finally, the performance of various approaches (i.e., proposed models and genetic algorithm) is also examined to provide valuable insight into the practical problem.