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.

Purpose: Cycle time reduction is important for order fulling process but often subject to resource constraints. This study considers an unrelated parallel machine environment where orders with random demands arrive dynamically. Processing speeds are controlled by resource allocation and subject to diminishing marginal returns. The objective is to minimize long-run expected order cycle time via order schedule and resource allocation decisions.Design/methodology/approach: A stochastic optimization algorithm named CAP is proposed based on particle swarm optimization framework. It takes advantage of derived bound information to improve local search efficiency. Parameter impacts including demand variance, product type number, machine speed and resource coefficient are also analyzed through theoretic studies. The algorithm is evaluated and benchmarked with four well-known algorithms via extensive numerical experiments.Findings: First, cycle time can be significantly improved when demand randomness is reduced via better forecasting. Second, achieving processing balance should be of top priority when considering resource allocation. Third, given marginal returns on resource consumption, it is advisable to allocate more resources to resource-sensitive machines.Originality/value: A novel PSO-based optimization algorithm is proposed to jointly optimize order schedule and resource allocation decisions in a dynamic environment with random demands and stochastic arrivals. A general quadratic resource consumption function is adopted to better capture diminishing marginal returns.