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This paper extends the notion of convex programming with set-inclusive constraints as set forth by Soyster [Opns. Res. 21, 1154-1157 (1973)] by replacing the objective vector c with a convex set C and formulating a dual problem. The primal problem to be considered is (I) [Multiple line equation(s) cannot be represented in ASCII text] where the sets {K[sub j]} are convex activity sets, K(b) is a polyhedral resource set, C is a convex set of objective vectors, and the binary operation + refers to addition of sets. Any feasible solution to the dual problem provides an upper bound to (I) and, at optimality conditions, the value of (I) is equal to the value of the dual. Furthermore, the optimal solution of the dual problem can be used to reduce (I) to an ordinary linear programming problem. [ABSTRACT FROM AUTHOR]

The problem is that of locating a facility in a region, so as to minimize the weighted sum of distances between customers and facility. This note shows that a subregion containing half or more of the total 'customer-weight,' if it obeys an additional restrictive hypothesis, must include at least one optimal location for the facility. Thus the search for an optimal location can be limited to such a subregion, once identified. [ABSTRACT FROM AUTHOR]

This paper presents an approach, similar to penalty functions, for solving arbitrary mathematical programs. The surrogate mathematical program is a lesser constrained problem that, in some cases, may be solved with dynamic programming. The paper deals with the theoretical development of this surrogate approach. [ABSTRACT FROM AUTHOR]

This paper analyzes priority rules that are mixtures of preemption and postponable rules. Whether a preemption occurs is made to depend on some factor in addition to priority class; dependence on the completed portion of service (age) of the lower-priority customer in service and the number of prior preemptions of the lower-priority customer in service are each considered. The stochastic model (without priorities) is that of the M/G/1 queue. The paper obtains first-moment expressions (e.g., expected number of customers in the system) in the steady-state case for each priority class as a function of the particular factor being considered. It then introduces a linear cost model that is a function of expected waiting time and expected number of preemptions, and formulates the problem of finding an optimal rule from each class by considering a parametric class of rules determined by each factor. In each case, conditions are sought for the global optimality of a rule over a class of rules, but results are obtained only after restrictions (e.g., monotone failure rates) on service distributions are imposed. [ABSTRACT FROM AUTHOR]

This paper presents two algorithms for targeting strikes in a lines-of-communication (LOC) network. The LOCs are represented by a network of nodes and directed arcs. It is assumed that the user of the LOCs is attempting to achieve a circulation flow at minimum cost, a very general goal that includes, as special cases, maximizing flow between two points, meeting required flows between two points at minimum cost, and combinations of these two. The algorithms presented here attempt to make such costs as large as possible over time when the effect of targeting strikes is to increase arc-cost functions and decrease arc capacities for a given period of time. The first algorithm treats the situation where arc costs are linear functions of flow; the second treats the situation where arc costs are piecewise linear functions of flow with one break point. [ABSTRACT FROM AUTHOR]

This paper introduces a generalization of the frequently discussed problem of finding the optimum redundancy that maximizes the reliability of a network of components. Past work has restricted consideration to arrangements of redundant components called series-parallel networks. This paper allows a much broader class of arrangements called series-parallelseries networks. It is important to consider such arrangements for realistic situations in which components have more than one failure mode, or the combination of parallel paths introduces a failure probability. A dynamic programming algorithm is used to solve the more general problem for the case in which there are no constraints on the optimum solution. The algorithm is extended to handle multiple constraints using dominance and a variety of elimination methods to reduce the storage required in a compurer implementation of the algorithm. Problems with as many as 15 serial components and three constraints have been solved with reasonable digital computer computation times. [ABSTRACT FROM AUTHOR]

This paper considers an efficient algorithm for finding the optimal design of a module under a special set of circumstances that prevail in the design of a module for logistical applications. The method is based on primal-dual relations between generalized polynomial minimization and its quasi dual. [ABSTRACT FROM AUTHOR]

A certain class of integer programming problems, called asymptotic or steady-state, has been shown by GOMORY to be cost equivalent to a group-optimization problem. This paper extends the algebraic characterization by demonstrating that there are cost-equivalent group problems for all integer programming problems. Finally, the result is interpreted from the viewpoint of dynamic programming, and this provides the turnpike theorem. [ABSTRACT FROM AUTHOR]

This paper presents computational algorithms for the solution of a clam of stochastic programming problems. Let z and y represent the decision and state vectors, and suppose that x must be chosen from some set K and that p is a linear function of both x and an additive random vector ξ. If y is uniquely determined once z is chosen and ξ is observed, we say that the problem has simple recourse. The algorithms presented apply, e.g., when the preference functions h(x) and g(y) are convex, and continuously differentiable, K is a convex polytope, ξ has a distribution that satisfies mild convergence conditions, and the objective is to minimize the expectation of the sum of the two preference functions. An illustrative example of an inventory problem is formulated, and the special ease when p is asymmetric, quadratic, and separable is presented in detail to illustrate the calculations involved. [ABSTRACT FROM AUTHOR]

This paper gives general conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the subproblems be sequentially nested. Conditions are given under which inactive constraints may be dropped after each subproblem. Procedures for generating cutting-planes include those of KELLEY, CHENEY AND GOLDSTEIN, and a generalization of the one used by both ZOUTENDIJK and VEXNoTT. For algorithms with nested constraint sets, these conditions reduce to a special case of those of ZANGWILL for such problems and include as special cases the algorithms of Kelley, Cheney and Goldstein, and Veinott. Finally, the paper gives an arithmetic convergence rate. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm, based on a recently proposed method due to D.D. Morrison, for solving constrained optimization problems, and shows that it compares favorably with existing methods in several examples. [ABSTRACT FROM AUTHOR]

The article presents a study which dealt with the use of optimum preventive maintenance policies when immediate detection of system failure is uncertain. The authors mention that in the derivation of preventive maintenance policies it is generally believed that system failure are detected and repaired immediately. In connection to this, the authors state that the study aims to develop the preventive maintenance schedule that will optimize system performance when immediate detection or repair failures are not assured. They added that the study showed that even for exponential failure rates, optimum preventive maintenance schedule exist.

The paper considers two-person zero-sum game. Let B be an arbitrary positive real number and let &b.Theta; be a real number between zero and one. First player chooses a number, t1, with t1 ranging between 0 to B+1. Second player chooses a number, t2, with t2 ranging between 0 to B. The pay-off function, &b.Theta, which specifies the amount the first player receives from second player, is given in the article. If &b.Theta; were continuous, it would be known that these two numbers are equal and hence the game would have a well-determined value. However, the pay-off function considered here is not continuous and this standard theorem cannot be applied. It should be clear that the optimal strategies for first player and second player are not unique.

This paper is an extension of previously published work by Bernard O. Koopman to the general case of any number of tasks and any effect function. A systematic method for the numerical calculation of the maximum effect and its corresponding optimum distribution is presented in a form which is also suitable for solution on an automatic digital computer. For the special case of additive returns which saturate, a special graphical or numerical method for any number of tasks is presented with an example worked out in detail A similar method for multiplicative effects is sketched. [ABSTRACT FROM AUTHOR]

The article considers the use of sub-optimization to solve operations research problems. The reason why operations researchers have to sub-optimize is because it is so frequently impossible, either in principle or more frequently in practice, to calculate the consequences of any given action in terms of the appropriate high level criteria. The three classes of sub-optimizations are: those in which there is a one-dimensional objectives function; those in which the objectives function is multi-dimensional; and those which are partial in that objectives which are known to be important are left out because they are not subject to quantitative analysis. The article also provides examples of criterion problem which is simplest in industrial operations research.

The article presents mathematical research and an algorithm for solving linear programs with variable binaries. This research was based on the prior work of E. L. Lawler and M. D. Bell. The algorithm which is presented is based on the idea of monotonically increasing functions and uses many of the properties of this type of function, according to the author. The article presents several mathematical examples and notes the uniqueness of this approach to solving linear programs with variable binaries. According to the author, this approach eliminates about 40% of vectors that were previously necessary in order to derive solutions to an auxiliary problem that is necessary to the solution of many linear programs with variable binaries. The author mentions questions for further research.

This paper deals with a model in which Poisson events in fixed time periods are recorded with probability a and left to accumulate into the succeeding period with probability 1-α. The distribution of number of events recorded is obtained, together with its mean, variance, and generating function. [ABSTRACT FROM AUTHOR]

The article deals with the use of a unified algorithm for solving some network-programming problems. The author states that hydraulic and mechanical analogues for the problems discussed in this section are useful in explaining the nature of the solution-process to some whose physical intuition is stronger than their mathematical background. The author also mentions that acquaintance with the studies discussed here will enable the reader to modify the methods for the case where the variable x are restricted to be integers.