Showing papers on "Solution set published in 1969"

Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems

Abstract: The paper shows that a broad class of problems can be formulated as minimizing a concave function over the solution set of a Leontief substitution system. The class includes deterministic single- and multi-facility economic lot size, lot-size smoothing, warehousing, product-assortment, batch-queuing, capacity-expansion, investment consumption, and reservoir-control problems with concave cost functions. Because in such problems an optimum occurs at an extreme point of the solution set, we can utilize the characterization of the extreme points given in a companion paper to obtain most existing qualitative characterizations of optimal policies for inventory models with concave costs in a unified manner. Dynamic programming recursions for searching the extreme points to find an optimal point are given in a number of cases. We only give algorithms whose computational effort increases algebraically (instead of exponentially) with the size of the problem.

Some algebraic properties of sets of stochastic matrices

Abstract: This paper presents some algebraic properties of some certain sets of stochastic matrices of probabilistic automata from the standpoint of their characteristic values. At first, a definite set and a quasidefinite set introduced by Paz (1965) , are algebraically investigated. Then we introduce new concepts, a periodic set and a quasiperiodic set, which are defined among stochastic matrices with a period t . The results obtained from a periodic set and a quasiperiodic set have a remarkable correspondence to those from a definite set and a quasidefinite set, respectively, and the formers in the case of the period t = 1 coincide with the latters. It is known that a definite set and a quasidefinite set are the special case and the extended concept of actual automata, respectively, and a definite set can be associated with a definite automaton. On the other hand, it is shown that a periodic set can be associated with a bounded transient automation which is constructed from autonomous and definite machines.

Closure of the Right-Hand-Side Set for Systems of Nonlinear Inequalities

Abstract: Consider the set of all vectors b such that the system gx ≦ b has a solution, where g: D → Rm, D ⊆ Rn. This paper presents necessary and sufficient conditions for this set to be closed, with special results on continuous and convex functions, and gives an application to mathematical programming.