Y. Gerchak et A. Grosfeldnir, MULTIPLE LOT-SIZING, AND VALUE OF PROBABILISTIC INFORMATION, IN PRODUCTION TO ORDER OF AN UNCERTAIN SIZE, International journal of production economics, 56-7, 1998, pp. 191-197
A make-to-order batch manufacturer knows that an order for items with
some particular specifications is forthcoming, but does not yet know t
he exact size of the order. Due to production lead times, work needs t
o start immediately. But some units produced may fail to meet required
tolerances; that is, the yield of each batch is random. Each new run
involves a costly setup, and each unit attempted involves material and
other variable costs. If a subjective probability distribution for th
e order size can be formed, the following related questions arise: (a)
What is the optimal run size? (b) When should production stop? To ans
wer these questions, this paper formulates a new model, whose main new
feature is the ability to handle uncertain demand within a multiple l
ot-sizing setting. It is proved that the optimal policy for this scena
rio is one of control limit - stop if and only if the stock of good un
its is larger than some critical value. A computer program was develop
ed for solving the problem for binomial yields, and optimal policies f
or several examples are reported. Due to the effort required to form a
nd communicate probabilistic forecasts, a common practice is to expres
s a forecast as a single number, corresponding, perhaps, to the mean o
r median of the unarticulated distribution. We compute the extra profi
t expected from forming, and using, probabilistic forecasts. We also s
how how to compute the profit's variance for any policy. (C) 1998 Else
vier Science B.V. All rights reserved.