Optimal production decision for a risk‐averse manufacturer faced with random yield and stochastic demand

Consider a risk‐averse manufacturer who produces a single product with a random yield to satisfy uncertain market demand. The manufacturer maximizes its expected profit subject to a chance constraint that requires the probability of the total profit below a target be less than a predetermined level. We show that due to the profit target constraint in the presence of random yield and stochastic demand, the manufacturer can neither produce too much nor too little irrespective of the predetermined probability level, depending solely on the profit target level. Further, the special case of uniform yield and uniform demand is examined and we obtain the manufacturer's optimal production quantity. In addition, two special cases of random yield rate and deterministic demand or deterministic yield rate and stochastic demand are considered. The opposite impacts of random yield and stochastic demand are revealed: the random yield induces a minimum production quantity that may cause the manufacturer to increase its production quantity, while the stochastic demand induces a maximum production quantity that may cause the manufacturer to decrease its production quantity. By comparing the solutions of the above‐mentioned special cases with the case of both random yield and stochastic demand, it is demonstrated that the existence of both random yield and stochastic demand results in a more constrained production requirement for the manufacturer (a larger minimum production quantity and a smaller maximum production quantity). That is, the opposite impacts of random yield and stochastic demand will not offset, but enhance each other.