As the CEO of ABC Motors, which is a major local automaker, an important part of John$$s job is to decide

the production capacity $($i$.$e$.$ how many cars to produce$)$ at the beginning of each production cycle. This

decision needs to be made well in advance of the actual sales season because many subsequent actions

will follow this decision: ordering of raw materials and parts, hiring of workforce, and physical process of

actual production. The challenge is that the demand is unknown at the production capacity decisionmaking time. The actual demand for the cars may be higher or lower than the produced quantities, and

the exact demand can only be known after the sales season. If the demand is higher than the production

quantity, then the potential profit is forgone due to unmet demand, and if the demand is lower, then the

unsold cars induce loss due to production costs already incurred.

The common practice to deal with demand uncertainty is demand forecasting. Although the demand

cannot be known exactly at the decision$-$making time, it can be treated as a random variable, and its

distribution can be characterized by looking at past demand data. With the knowledge of the distribution

of the demand, John needs to decide a production quantity that generates the highest expected profit

for the firm.