## A series-type multistage production system with random demand.(English)Zbl 1039.90013

Summary: We propose a mathematical model which considers the series-type product structure with $$n-1$$ predecessors. Our objective is to obtain the optimal production functions, in the planning horizon $$[0,T]$$, based on the assumptions (1) that the cost of production unit is a linear function of production quantity in a time unit, (2) that sales of finished goods occur at the end of planning horizon, and (3) that product demand is a random variable. Then the phenomenon of optimal solution is discussed.

### MSC:

 90B30 Production models 90B05 Inventory, storage, reservoirs 49N90 Applications of optimal control and differential games
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