A decision problem associated with the production of the same goods under several labels is anticipating how much to produce under each label. In some settings a portion of the goods is left unlabeled so that subsequent excess demand can be filled by labeling these goods held in “bright storage”. This adds another decision variable to the problem and introduces some new alternatives. Attached to these alternatives facing the decision maker are several different kinds of costs depending upon the nature of the errors made in forecasting the demand for each of the labels. These costs, when associated with discrete probability distributions for the demand variables, lead to an optimization problem with nonnegative variables with objective of minimizing the decision maker's expected cost. Minor restrictions on the costs make this objective function, convex. By introducing new variables the entire problem can be reformulated as a linear program. If the demand variables can take only integer values, then there is an integer, optimal solution to the bright storage problem.
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