This paper investigates the assignment of tasks in a network of functionally similar computers. We formulate the problem by a periodic review model with Boolean variables. A computationally efficient, integer-generalized transportation model is applicable because of the existence of relative efficiencies of computers for jobs. Since a job is to be processed exclusively by one computer, we show that an optimal solution to this problem is a basic feasible solution to a slightly modified generalized transportation problem. A branch-and-bound solution procedure prevents possible splitting of a job among computers. We provide an algorithm and computational results.

Dedicated to Professor C. T. Rajagopal on his 65 th birthday Introduction J. R. Schue has shown in [4] that a separable infinite-dimensional simple L*-algebra is necessarily of one of three classical types A, B, C (the L*-types B, D coinciding). These L*-algebras are the analogues of the corresponding classes of simple Lie algebras. Each of the classical type L*-algebras occurs as an L*-subalgebra of the H*-algebra ofalt Hilbert-Schmidt operators on a separable Hilbert space 90-By replacing 9o by a Hilbert space ~ of arbitrary (infinite) dimension, we obtain analogously the general (i.e. not necessarily separable) simple L*-algebra of type A, or B, or C. However, in the non-separable case, it is not known whether these types exhaust all simple L*-algebras.The object of this paper is to study these general algebras which we shall refer to as "standard simple L*-algebras of classical type". We show that the types A, B, C are distinct in the sense of isomorphism, and prove that there exists, for each infinite cardinal N precisely one standard simple L*-algebra of (orthogonal) dimension N belonging to each of the three types. We also investigate the conjugacy problem for Cartan subalgebras in the case of these algebras. It turns out that for an L*-algebra of type A, or one of type C, any two Caftan subalgebras are conjugate under an L*-automorphism (which is even spatial in the sense of being implemented bY a unitary operator of the underlying Hilbert space). On the other hand, for a type B algebra, the Cartan subalgebras fall into two (conjugacy) classes such that any two in the same class are conjugate while no two from different classes are. The reason for this occurrence of two conjugacy classes in a type B algebra is related to the fact that a conjugation in an infinite-dimensional Hilbert space admits two kinds of representation (see Proposition 2). Finally, we apply the above results to determine the different conjugacy classes for all semi-simple L*-algebras belonging to a certain class which includes all separable algebras. We also deduce that, in the separable case, the conjugacy index (i.e. the number of conjugacy classes) is ~c + I, where ~ is the (cardinal) number of infinite-dimensional components of type B in the decomposition of L into its simple components.

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This paper investigates the problem of determining the optimal location of plants, and their respective production and distribution levels, in order to meet demand at a finite number of centers. The possible locations of plants are restricted to a finite set of sites, and the demands are allowed to be random. The cost structure of operating a plant is dependent on its location and is assumed to be a piecewise linear function of the production level, though not necessarily concave or convex. The paper is organized in three parts. In the first part, a branch and bound procedure for the general piecewise linear cost problem is presented, assuming that the demand is known. In the second part, a solution procedure is presented for the case when the demand is random, assuming a linear cost of production. Finally, in the third part, a solution procedure is presented for the general problem utilizing the results of the earlier parts. Certain extensions, such as capacity expansion or reduction at existing plants, and geopolitical configuration constraints can be easily incorporated within this framework.