Continuous-time production, distribution and financial planning with periodic liquidity balancing

Due to the inevitable focus on core competencies, even small- and medium-sized companies are increasingly forced to form supply chain (SC) networks. However, their specific situation is often characterized by a lack of equity and limited access to capital markets, so that bank loans must then be used to initiate production and distribution. Within a short-term multi-day planning horizon, both operations and finance must be scheduled precisely in order to obtain practical instructions for each network partner and the network managers. For this purpose, continuous-time modeling is required. Additionally, a coordination of monetary consequences resulting from both site-specific operational events and network-wide financial transactions is necessary to prevent insolvency. As bank overdrafts can be used to overcome financial imbalances during short periods (e.g., days or even hours), appropriate time intervals for liquidity management should be determined. The implementation of these intervals requires discrete-time modeling. In this context, the main challenge is to combine both of the aforementioned modeling techniques within a common decision model. To address this problem, a novel mixed-integer nonlinear program (MINLP) is developed, which enables exact planning and scheduling of SC operations as well as related financial transactions on the one hand, and periodic liquidity balancing on the other hand. A numerical analysis was based on a test scenario with randomly generated data. As we found out that even small problem instances of the MINLP, e.g., a three-stage supply chain with three sites in each stage, were not computable with high-performance hardware and a commercial nonlinear standard solver, we additionally propose an equivalent linearized version of the decision model. The latter could be optimized within acceptable computation time using the CPLEX solver.