Synthesis of experimental designs of maneuvering captive-model tests with a large number of factors

An approach to synthesizing D-optimized experimental designs for an arbitrary number of factors was developed and tested on a third-order polynomial regression model with 5–8 factors. Three options were envisaged for the internal optimization procedure: an exhaustive search, a quasirandom search with the help of the Sobol sequences, and a genetic algorithm. The calculations performed have shown the pronounced superiority of the variant involving a genetic algorithm. Captive-model tests with a catamaran model with varying Froude number, drift angle, rate of yaw, sinkage, trim, and heel are presented as an example of the practical synthesis of the experimental design. The linear regression model constructed is a third-order 5-factor polynomial with respect to all factors except the Froude number. The influence of the latter is accounted for by representing the polynomials regression coefficients as functions of the Froude number represented as a truncated Fourier series with a linear term added.     

Supplying a single location from heterogeneous sources

This paper studies how items with different characteristics, and being demanded at different rates from a finite number of supply points, should be transported to a common destination. The items may differ in size and value, and the origins may differ in their spatial distribution, the kind of items they produce and the production rate. Depending on the application context, the common destination can represent a warehouse, a factory, a military base, a break-bulk terminal, a port or another kind of transportation terminal. Different kinds of items may call for separate transportation treatment if, for example, the items have sharply different inventory carrying costs or their origins are not equally scattered. On the other hand, if their characteristics are not very different, they may be transported together more cheaply because of existing economies of scale. In fact, in most applications it should be optimal to use only a few transportation systems because the economies of scale are quite strong. The paper essentially shows that origins can be ranked according to a simple criterion, and that if two origins are served together, the ones ranked in between should be served with them. A simple method for determining the optimal number of transportation systems and the sources served by each is developed. The technique is illustrated with a numerical example. The results of the paper are developed assuming that supply points do not cluster together by type and that the density of suppliers is slowly varying. In any practical application in which these assumptions are not reasonable approximations, the results of this paper should not be applied too literally. Nevertheless, they can still be used as guidelines in the search for an optimum supply strategy.     

Physical distribution from a warehouse: Vehicle coverage and inventory levels

This paper studies the costs involved in distributing items from a warehouse or depot to randomly scattered customers on a day-to-day basis. Two trade-offs are explored simultaneously. The first one arises because by accumulating large inventories at the depot it is possible to build more efficient distribution tours. This trade-off has already been explored for both distribution of goods (Burns et al., 1983) and passengers (Daganzo et al., 1977; Hendrickson, 1978). Another tradeoff, which involves the length of individual vehicle tours (Clarens and Hurdle, 1975), balances the inventory inside the vehicles against the transportation cost. Banks et al. (1982) have considered both of these tradeoffs simultaneously in the context of passenger transportation, but used a somewhat unrealistic model for vehicle routing. This paper is similar to the latter reference but uses a different routing strategy. It also illustrates how the nature of the objects carried (cheap goods, expensive goods, people, etc.) affects the optimal configuration of the distribution system and the overall distribution costs. Usually there is an optimum partitioning of the service area into districts and an optimum dispatching frequency in each district. The results can vary tremendously, depending on factors such as: the inventory carrying cost per item per unit time, the transportation costs, the demand per unit area and unit time, the average distance from the depot, the average vehicle speed and the time per stop.As an illustration of the ideas, a hypothetical limousine service from an airport is analyzed. The example is used to demonstrate how dramatically the optimal system configuration depends on the nature of the items carried.