Economics Insights @ CBS

We consider the problem of scheduling n jobs, each with a specific processing requirement, release time and due date on m uniform parallel machines. It is shown that a feasible schedule can be obtained by determining the maximum flow in a network, thus permitting the use of standard network flow codes. Using a specialized maximum flow procedure, the complexity reduces to O(tn³) operations when t is the number of distinct machine types.

This paper presents an allocation model for a perishable product, distributed from a regional center to a given set of locations with random demands. We consider the combined problem of allocating the available inventory at the center while deciding how these deliveries should be performed. Two types of delivery patterns are analyzed: the first pattern assumes that all demand points receive individual deliveries; the second pattern subsumes the frequently occuring case in which deliveries in multistop routes traveled by a fleet of vehicles. Computational experience is reported.

For a collection of agents with von Neumann-Morgenstern preferences, a price-independent income distribution, and identical probability beliefs, there exists a von Neumann-Morgenstern approximate aggregator. The risk tolerance of the approximate aggregator is equal to the sum of the individual agent risk tolerances at prices which yield constant, "risk-free," contingent consumption. The application of the approximate aggregator to standard asset pricing models in finance is discussed briefly.

Some companies consistently enjoy share prices that exceed book value. Such value creators range from giants like Coca-Cola Co., IBM, and Procter & Gamble to less-known small and medium-sized companies like Pall and Shoney's. Other enterprises trade below book value year after year, in both bear and bull markets. Many managers believe that these differences in price to book ratio do not stem from real differences in competitive performance but rather from the capriciousness of the stock market.