Inventory-Constrained Throughput Optimization for Stochastic Customer Orders

Inventory-production coordination for customer orders is becoming increasingly important for companies to increase customer responsiveness and achieve economic purposes. In this paper, the joint optimization of inventory and production is considered for stochastic customer orders to maximize the throughput. Demands of customer orders dynamically arrive at the inventory department, and each incoming order consists of multiple product types with random workloads. To process the workloads, certain amounts of a common raw material are required and need to be drawn from the inventory department. A customer order will be lost if there do not exist enough raw materials in the inventory department. With the necessary materials, workloads of accepted orders will be assigned to a set of unrelated parallel servers to be processed in the production department. This paper intends to maximize the effective throughput through proper coordination of the inventory and the production departments. For this problem, system bottlenecks are identified and analyzed, and mathematical programming models are developed to determine the optimal throughput and the corresponding inventory and production policies. Several special cases are also explored to provide intuitive insights into the relationship between the system parameters and optimal throughput. Relationships between key model parameters and effective throughput are identified through sensitivity analysis and further validated by the results of computational experiments.