MULTIPLE LOT-SIZING, AND VALUE OF PROBABILISTIC INFORMATION, IN PRODUCTION TO ORDER OF AN UNCERTAIN SIZE

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.