A newsboy problem with reactive production

This paper extends the classic newsboy problem by introducing reactive production. Production occurs in two stages, a anticipatory stage and a reactive stage. In the anticipatory stage, one determines a production level that anticipates the demand, all of which occurs in the reactive stage. There production takes place with full knowledge of the actual demand and, thus, can react to it. The reactive stage contains multiple sources of capacitated production. Demand is continuous and stochastic, and production, holding, and shortage costs are proportional. There are no fixed costs. Shortages are lost. Our model reduces to a single-period model with piecewise-linear convex costs. We obtain an analogue of the well-known critical fractile formula of the classic newsboy model. We also undertake a numerical study that compares our model with (i) the classic newsboy model, and (ii) a model which employs reactive production but uses classic newsboy formulas. Extensive computational experiments with normal demand problems suggest that the costs under our model can be substantially less than the costs under (i) and (ii).