A convex property of an ordered flow shop sequencing problem

A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.     

A manpower planning/capital budgeting model (MAPCAB)

A deterministic resource allocation model is developed to optimize defense effectiveness subject to budget, manpower, and risk constraints. The model consists of two major submodels connected by a heuristic. The first is a mathematical program which optimizes the multiperiod weapon mix subject to the constraint set. The second is a manpower supply model based on a transition matrix in which individual transitions are functions of personnel related budgets and historical transition rates. The heuristic marries the submodels through an iterative process leading to improved solutions. An example is provided which demonstrates how systems are undercosted and overprocured if manpower supply is not properly reflected relative to manpower demand.     

Optimal search using two nonconcurrent sensors

Search for a stationary target is considered for a situation in which two sensors are available, but cannot be used simultaneously. The cost (in time) of switching from one sensor to the other is ignored, and each sensor is assumed to have perfect discrimination. For a specified class of searches an optimal allocation of search effort is obtained. In the case of a circular normal prior target location distribution, an example is presented in which one sensor is assumed to have a fixed sweep width and the other a stochastic sweep width. An optimal plan is found for this example. This plan produces an allocation of search effort which is expended in a disk by one sensor and in a bounding annulus by the other.     

A defense allocation problem with development costs

In this paper, the mathematical model for the allocation of resources among a general mix of percentage vulnerable and of numerically vulnerable weapon systems is presented and solved. Percentage vulnerable systems consist of mobile weapons which are difficult to locate, but relatively easy to destroy once located; numerically vulnerable systems comprise easily located fixed base weapons which are difficult to destroy. The distinguishing feature of this analysis is the inclusion of development costs. The theory of max-min is extended as necessary to solve this problem. References are provided to a sequence of earlier versions of this problem.     

Maximization of long-run average rate-of-return by stochastic approximation

Suppose that an individual has a surplus stock of wealth and a fixed set of risky investment opportunities over a sequence of time periods. Assuming the criterion of maximal long-run average rate-of-return, the individual may select portfolios sequentially via a modified stochastic approximation procedure. This approach yields optimal asymptotic investment results under minimal assumptions.     

A heuristic network procedure for the assembly line balancing problem

Proposed is a Heuristic Network (HN) Procedure for balancing assembly lines. The procedure uses simple heuristic rules to generate a network which is then traversed using a shortest route algorithm to obtain a heuristic solution. The advantages of the HN Procedure are: a) it generally yields better solutions than those obtained by application of the heuristics, and b) sensitivity analysis with different values of cycle time is possible without having to regenerate the network. The rationale for its effectiveness and its application to problems with paralleling are presented. Computational experience with the procedure on up to 50 task test problems is provided.     

Probabilistic formulations of the multifacility weber problem

The problem considered is to locate one or more new facilities relative to a number of existing facilities when both the locations of the existing facilities, the weights between new facilities, and the weights between new and existing facilities are random variables. The new facilities are to be located such that expected distance traveled is minimized. Euclidean distance measure is considered; both unconstrained and chance-constrained formulations are treated.     

Multiproduct lot-size scheduling with proportional product demands

In this paper we consider the multiproduct, multiperiod production-scheduling model of Manne under the assumption that, across products, demands are interrelated over time. When demand requirements are proportional we show that the solution has a specific structure determined by the ratio of setup to production-run time of each product. This structure holds for any length horizon and may permit a substantial (time) savings for column generation solution procedures.     

An exact branch-and-bound procedure for the quadratic-assignment problem

The quadratic-assignment problem is a difficult combinatorial problem which still remains unsolved. In this study, an exact branch-and-bound procedure, which is able to produce optimal solutions for problems with twelve facilities or less, is developed. The method incorporates the concept of stepped fathoming to reduce the effort expended in searching the decision trees. Computational experience with the procedure is presented.     

A three-echelon,multi-item model for recoverable items

The main objective of this paper is to develop a mathematical model for a particular type of three-echelon inventory system. The proposed model is being used by the Air Force to evaluate inventory investment requirements for alternative logistic structures. The system we will model consists of a group of locations, called bases, and a central depot. The items of concern in our analysis are called recoverable items, that is, items that can be repaired when they fail. Furthermore, each item has a modular or hierarchical design. Briefly, the model is used to determine the stock levels at each location for each item so as to achieve optimum inventory-system performance for a given level of investment. An algorithm for the computation of stock levels for each item and location is developed and illustrated. Some of the ways the model can be used are illustrated with Air Force data.