Inventory-Constrained Throughput Optimization for Stochastic Customer Orders

Abstract

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. Note to Practitioners —Coordination of production and inventory is crucial for system efficiency improvement. In order to better operate the system and respond to customer demands, this paper explores such coordination for stochastic customer orders to achieve the maximum effective throughput. Particularly, we consider the case where production is constrained by material inventory. System bottlenecks for various cases are identified, which can facilitate system diagnosis and performance evaluation. Based on the bottleneck analysis, an optimization problem is formulated to provide the optimal throughput and policy. Several important practical cases are also discussed, including single product type, identical/uniform servers, and speed-identical/uniform product types. Besides, sensitivity analysis is conducted to show how the changes of parameters such as expected workload and server speed will affect throughput performance. In the future research, more complex production environments and cost-related constraints will be further considered to help practitioners achieve desirable system outputs.