Commitment Under Uncertainty : Production-Inventory Policiesassociated with Environmental Considerations

We consider a manufacturer that produces in response to a stochastic demand and emits pollution during the production process. Industrial pollutants released into the air are characterized by spatial variability and special heterogeneity, and the precision of instruments for measuring stochastic pollution stocks varies widely across pollutants. Consequently, commitment (open-loop) strategies to control production and associated emissions are considered more practical than contingent (feedback) approaches when manufacturers are concerned about environmental consequences. In this paper, we derive an optimal control policy over a time horizon and show that such a policy induces asymptotic convergence of expected inventory and pollution stock trajectories to a unique steady state in terms of mean pollutant assimilation and assimilation volatility. Moreover, we find that the variance of the pollution stock also converges asymptotically to a unique steady state, which is critical for prevention of irreversible environment consequences. Notably, we show that the variance of the pollution stock increases with the volatility of pollutant assimilation while the level of the long-run expected pollution stock is not affected. On the other hand, environmental uncertainty does affect inventories, leading in the long run to lower expected steady-state inventory stocks