Reliable Computing 4: 63–69, 1998.
1998 Kluwer Academic Publishers. Printed in the Netherlands.
Reliable Optimal Production Control with
ZHIHUI HUEY HU
Texas A&M University, College Station, TX 77841, USA, e-mail: email@example.com
(Received: 3 December 1995; accepted: 16 February 1997)
Abstract. Production is the most fundamental activity in our economy. In this paper, a Cobb-Douglas
production function is used as the mathematical model to describe the relationship among production,
labor and capital. Two reliable production optimal control problems are studied. Algorithms to ﬁnd
dynamic optimal control intervals are provided with interval parameter presentations and interval
1. Optimal Production Control with Cobb-Douglas Model: Traditional
Production. Every day, various products are produced to meet different demands
in our society. Production is truly one of the most fundamental activities in our
Every producing ﬁrm wants to maximize its proﬁts:
In an equilibrium market, where the amount produced is more or less ﬁxed (by
the demand and by the ﬁrm’s market share), in order to maximize proﬁts, the
ﬁrm needs to minimize production costs.
In a seller’s market, in which the supply of a product is smaller than the demand
for it, maximizing proﬁts means producing the maximum amount within the
available production costs.
Production function. In both cases, to optimize production, we must know how
the output Q depends on the production costs. The dependence of Q on controllable
parameters is called a production function.
One of the most widely used production functions was proposed by Cobb and
Douglas and has the following form (see, e.g., ):
Q = A
where L is labor (measured in certain units), K is capital,andA,
(constant) parameters; these parameters depend on the ﬁrm, on the produced unit,
etc., and have to be determined experimentally.
Comment. In many real-life situations,
= 1. This equality has a simple
economic interpretation: if we increase both labor and capital twofold, we will thus