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ABSTRACTGeometric programming is a mathematical programming technique that is designed to determine the constrained minimum value of a generalized polynomial objective function. To date, most applications of the technique have been restricted to certain classes of engineering problems.This paper presents a brief summary of geometric programming and then illustrates its application to managerial problems by applying it to three well‐known inventory models.

ABSTRACTThe nucleolus linear programming (LP) method for allocating joint costs associated with a shared resource often stops short of uniquely specifying all savings allocations. Barton [1] recently presented the minimum total propensity to disrupt (MTPD) as a secondary criterion for uniquely determining those allocations not provided by the initial LP solution. Barton demonstrated the uniqueness of his solution on a specific example with a four‐entity grand coalition. We show a practical approach for implementing Barton's two‐step procedure. Our purpose is to make the nucleolus/MTPD model readily accessible to a wide range of practitioners using commonly available spreadsheet tools. We also demonstrate the global optimality of the allocations that the model provides.

AbstractThis article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment‐type constraints along with other constraints. Several unresolved questions of a number‐theoretic nature are mentioned at the conclusion of the article.

ABSTRACTThirty empirically assessed utility functions on changes in wealth or return on investment were examined for general features and susceptability to fits by linear, power, and exponential functions. Separate fits were made to below‐target data and above‐target data. The usual "target" was the no‐change point.The majority of below‐target functions were risk seeking; the majority of above‐target functions were risk averse; and the most common composite shape was convex‐concave, or risk seeking in losses and risk averse in gains. The least common composite was concave‐concave. Below‐target utility was generally steeper than above‐target utility with a median below‐to‐above slope ratio of about 4.8. The power and exponential fits were substantially better than the linear fits. Power functions gave the best fits in the majority of convex below‐target and concave above‐target cases, and exponential functions gave the best fits in the majority of concave below‐target and convex above‐target cases. Several implications of these results for decision making under risk are mentioned.

The number partitioning problem has proven to be a challenging problem for both exact and heuristic solution methods. We present a new modeling and solution approach that consists of recasting the problem as an unconstrained quadratic binary program that can be solved by efficient metaheuristic methods. Our approach readily accommodates both the common two-subset partition case as well as the more general case of multiple subsets. Preliminary computational experience is presented illustrating the attractiveness of the method.

AbstractA cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.

ABSTRACTLearning effects play an important role in certain resource allocation problems, and several authors have proposed models for these problems that capture the relevant relationships. However, the models may be difficult to implement or have shortcomings in the prescribed solution procedures. In this paper, we selectively review the work to date and present a simple reformulation that facilitates solution by off‐the‐shelf software.