The space-allocation problem arises when an architect tries to arrange rooms of fixed area but unspecified shape on a floor plan in such a way as to minimize a given linear combination of the distances between all pairs of rooms. In one dimension, this is the problem of ordering line segments along a simple axis or rooms along one side of a corridor. This paper devises an efficient branch-and-bound algorithm for finding the optimal ordering, and shows that the algorithm can solve one special type of facilities-to-locations assignment problem. Space allocation in two dimensions is also discussed briefly.

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This paper reviews the current status of the random-walk model as it applies to price-change sequences in common stocks, and examines certain striking dependencies in these sequences at the transaction level. In particular, successive transaction-price changes are seen to be negatively correlated, with each price change projecting its negative influence forward toward its successors in the sequence. The strength of this influence is diminished sharply by each nonzero price change that it is required to “penetrate,” but is only slightly weakened when projected across changes of zero magnitude. In the latter case, in fact, statistical dependency is shown to exist across intervals of as many as ten transactions or more.

This paper considers multi-product inventory problems which are subject to an order cost or setup cost hierarchy of the following form: all replenishment orders issued in any given scheduling period are filled in the next period, with the total setup cost of replenishing N different products in one period being S + s N. The values of N observed in the various periods, and therefore the expected setup cost per job, depend on the unknown lot sizes. This type of setup cost dependence can arise in simple inventory problems but is more commonly found in production environments in which the setup cost for a given job depends on the job immediately preceding it in the production schedule. Assuming demands to be random with known probability distributions, an iterative algorithm is presented for computing optimal lot sizes and reorder points for a set of heterogeneous products.

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