This paper studies an integration model of production planning, scheduling, and order- based inventory distribution control systems. It models supply-chain and production dynamics and employs process control to supply-chain operations and the production process and scheduling. It embeds generalized disjunctive programming (GDP) and branch-and-reduce algorithms to obtain an optimal solution. Generalized disjunctive programming reformulates the original mixed integer nonlinear programming (MINLP) model and solves the new model with a lower number of integer variables. Afterwards, the branch and reduce algorithm, which is strengthened with outer approximation (OA) cutting planes, is able to find optimal solutions with permissible optimality gaps. The results show that supply network size does not affect forecast accuracy; there is a forecast error rate of 12.9%. Similar figures are also shown for the inventory level, which is expected to be 32% of demand level, production changeover time at 0.58 days, inventory ramp-up period to meet the expected raw materials and final products inventory at 0.02 and 0.04 days respectively, and extra delivery time to meet a certain level of demand change at 1.1 days. The results show that the model is capable of controlling demand forecast, inventory level, and delivery quantity, so that the supply chain can avoid stock out at a minimal level of inventory, regardless of the size of supply-chain networks.
- branch and reduce
- generalized disjunctive programming
- mixed integer non-linear programming
- process control
- production planning