Tractable supply chain production planning, modeling nonlinear lead time and quality of service constraints

This paper addresses the task of coordinated planning of a supply chain (SC). Work in process (WIP) in each facility participating in the SC, finished goods inventory, and backlogged demand costs are minimized over the planning horizon. In addition to the usual modeling of linear material flow balance equations, variable lead time (LT) requirements, resulting from the increasing incremental WIP as a facility’s utilization increases, are also modeled. In recognition of the emerging significance of quality of service (QoS), that is, control of stockout probability to meet demand on time, maximum stockout probability constraints are also modeled explicitly. Lead time and QoS modeling require incorporation of nonlinear constraints in the production planning optimization process. The quantification of these nonlinear constraints must capture statistics of the stochastic behavior of production facilities revealed during a time scale far shorter than the customary weekly time scale of the planning process. The apparent computational complexity of planning production against variable LT and QoS constraints has long resulted in MRP-based scheduling practices that ignore the LT and QoS impact to the plan’s detriment. The computational complexity challenge was overcome by proposing and adopting a time-scale decomposition approach to production planning, where short-time-scale stochastic dynamics are modeled in multiple facility-specific subproblems that receive tentative targets from a deterministic master problem and return statistics to it. A converging and scalable iterative methodology is implemented, providing evidence that significantly lower cost production plans are achievable in a computationally tractable manner.