Some simple scheduling algorithms

This paper considers situations in which jobs require only one operation on a single machine, or on one of a set of identical machines. Penalty-free interruption is allowed. Some simple algorithms are given for finding optimum schedules to minimize maximum lateness and total delay, for the single-machine case, and maximum lateness for a restricted multi-machine case. A simple flow problem formulation permits minimizing maximum lateness for the more general multimachine case.     

A saddle-point theorem for a class of infinite games

In this paper, the existence of a saddle point for two-person zero-sum infinite games of a special type is proved. The games have continuous bilinear payoff functions and strategy sets which are convex, noncompact subsets of an infinite-dimensional vector space. The closures of the strategy sets are, however, compact. The payoff functions satisfy conditions which allow the use of dominance arguments to show that points in the closure of a strategy set are dominated by or are strategically equivalent to points in the strategy set itself. Combining the dominance arguments with a well-known existence theorem produces the main result of the paper. The class of games treated is an extension of a class studied by J. D. Matheson, who obtained explicit solutions for the saddle points by using necessary conditions.     

Structural models of award fee contracts

This paper describes the construction of a mathematical model structure in a particular area of management. In addition it is intended as an illustration of how appropriate levels of mathematics can be utilized in management research when original formulations lack sufficient precision for conducting quantitative analyses. The specific area studied deals with the formulation and analysis of contract types. In particular the award fee type contract is treated. At present mathematical structure models for other contract types have received considerable attention, but award fee types have not been structured in mathematical terms. The paper provides a discussion of model formulation for award fee contracts, develops a detailed example of such a structure, and illustrates that model by numerical examples indicating the application of such models to the formulation and analysis of award fee contracts.     

Toward a multi-stage information conversion model of the research and development process

Research and development activities in a business firm or government laboratory are portrayed as a multi-stage information generation and conversion process. A “basic research” phase generates opportunities, in the form of findings in a set of scientific disciplines, which are available for subsequent exploitation. It is assumed that increments to information in a subject area are stochastic, proportional to the amount of knowledge which already exists in the area, and have values which are randomly distributed. An “exploratory development” phase is viewed as a process of selecting a subset of alternative research opportunities, improving each opportunity in the direction of its applications, estimating the value of the improved opportunity and using these estimates to choose the exploratory development results to be implemented in engineering development. The “engineering development” phase makes the value of exploratory results realizable without changing value or risk. Engineering development costs are assumed to increase as value increases. If exploratory development is not successful, additional costs in engineering development must be incurred to bring the design up to a minimum desirable level. The model is intended as a step toward formulating and analyzing problems in management planning and control of the several interrelated stages of the research and development process.     

An integer programming algorithm for portfolio selection with fixed charges

A mean-variance portfolio selection model with limited diversification is formulated in which transaction and management costs are incorporated as the sum of a linear cost and a fixed cost. The problem is a fixed charge integer programming problem solved by hypersurface search using dynamic programming. Fathoming is performed in the forward pass of dynamic programming so that values of the state variable which correspond to infeasible solutions are eliminated from the tables. This logic permits the solution of problems with 20–30 possible investments.     

Cost analysis of pro rata and free-replacement warranties

This article examines the short run total costs and long run average costs of products under warranty. Formulae for both consumer cost under warranty and producer profit are derived. The results in the case of the pro rata warranty correct a mistake appearing in Blischke and Scheuer [5]. We also show that expected average cost to both the producer and the consumer of a product under warranty depends on both the mean of the product lifetime distribution and on its failure rate.     

Nonlinear integer programming for various forms of constraints

A theoretical and computational investigation is made of the performance of a dynamic-programming-based algorithm for nonlinear integer problems with various types of constraints. We include linear constraints, aggregated linear constraints, separable nonlinear constraints and constraints involving maxima and minima. Separability of the objective function is assumed. The new feature of the algorithm is that two types of fathoming or pruning are used to reduce the size of tables and number of computations: fathoming by bounds and fathoming by infeasibility.     

The logarithmic poisson gamma distribution: A model for leadtime demand

This paper considers an inventory system in which demand occurrences arise according to a stationary Poisson process, demand sizes at each occurrence follow a logarithmic distribution, and leadtimes are random variables with the gamma distribution. Both the exact and approximate distribution for leadtime demand are derived and computations are performed which compare the approximation to the exact distribution. The results have application to both repairable and consumable item inventory systems.     

Sequencing independent jobs with a single resource

This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well-known results for single-machine problems which can be applied with little or no modification to the corresponding variable-resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception.