Use of stochastic control theory to model a forest management system. (English) Zbl 0563.90056
A forest management problem due to O. Hellman [Eur. J. Oper. Res. 4, 16-18 (1979; Zbl 0418.90059)] has been modelled as a stochastic control problem with one state variable (inventory level) and one control variable (consumption rate of wood by the factories). The stochastic process governing the evolution of the inventory level is transformed into an Itô stochastic differential equation by approximating the compound Poisson process of wood arrivals into the depot as a Wiener process. The resulting stochastic control problem is solved by using the Hamilton-Jacobi-Bellman equation of stochastic dynamic programming. Two numerical examples illustrate the results.
MSC:
| 90B30 | Production models |
| 91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |
| 93E20 | Optimal stochastic control |
| 90B05 | Inventory, storage, reservoirs |
Keywords:
forest management; stochastic control; Itô stochastic differential equation; Wiener process; stochastic dynamic programmingCitations:
Zbl 0418.90059References:
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