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Optimal control approach to two-stage inventory system in steel cold rolling production

This paper studies a two-stage inventory problem arising from cold rolling production process in the steel industry. The problem is to find a optimal inventory level which satisfies the order demand and ensures the continuity of production via controlling the production rate. Consider ring “transport of batch” to different sales center, we assume that the realization of the demand depends on the corresponding inventory level. We propose an optimal control model for this problem by relaxing some complex constraints of the practical technological requirements. To solve the two-stage inventory problem, the maximum principle is used and we obtain three optimal production rate: full production, no production and singular production in different conditions. Finally, a numerical example is provided to illustrate our method, where the experimental data is collected from a certain steel company.