Consider the problem of allocating multiple products by a distributor with limited capacity (truck size), who has a fixed sequence of customers (retailers) whose demands are unknown. Each time the distributor visits a customer, he gets information about the realization of the demand for this customer, but he does not yet know the demands of the following customers. The decision faced by the distributor is how much to allocate to each customer given that the penalties for not satisfying demand are not identical. In addition, we optimally solve the problem of loading the truck with the multiple products, given the limited storage capacity. This framework can also be used for the general problem of seat allocation in the airline industry. As with the truck in the distribution problem, the airplane has limited capacity. A critical decision is how to allocate the available seats between early and late reservations (sequence of customers), for the different fare classes (multiple products), where the revenues from discount (early) and regular (late) passengers are different.
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