International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 40, Pages 2567-2581

A series-type multistage production system with random demand

Ying-Chieh Chen

Department of Applied Statistics and Information Science, Ming Chuan University, 250 Chung Shan North Road, Section 5, Shihlin District, Taipei 111, Taiwan

Received 12 December 2001

Copyright © 2003 Ying-Chieh Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a mathematical model which considers the series-type product structure with n1 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.