Dynamic Capacity and Inventory Management with Renewable Resource

Problem definition: We consider a production system where a certain resource is used as the key raw material. The firm needs to decide the production quantity in each period facing stochastic demand and subject to the resource capacity constraint. The resource is self-renewable, and the growth rate depends on the existing capacity level. Such a system is commonly seen in, for example, the fishing industry.Methodology/results: We model the self-renewal of resource using a generating function and formulate the production optimization problem as a dynamic program. We analyze both the structural properties of the optimal production policy and the long-run dynamics of the resource capacity. We explore two special cases to obtain deeper insights on the interplay between the dynamics of resource capacity and the production operations. For the system with deterministic demand, we show that it could be optimal to produce more than demand and hold inventory in order to prevent overpopulation when resource is self-renewable. For the system with fully-perishable products, we show that the newsvendor cost structure has a significant impact on the long-run sustainability of resource. We conduct numerical experiments, using real salmon population data, to test the robustness of our findings under general systems with stochastic demand and nonperishable products. Through system performance comparisons, we show the importance of modeling the self-renewal of resource and the advantage of the optimal production policy over simple heuristic policies that ignore the renewability of resource.Managerial implications: Many resources in the agricultural and energy sectors are renewable. Our modeling and analysis highlight the relationship between production-inventory operations (and operational-cost structures) and the dynamics of resource capacity. The results and insights on the interplay between profitability and sustainability can be meaningful to both production firms and environment regulators