Dennis J. Sweeney

The reduced cost branch and bound algorithm for mixed integer programming

Abstract A different branch and bound algorithm for mixed integer programming is presented. Unlike standard linear programming based branch and bound algorithms, where a single fractional variable (or Special Ordered Set) is selected for problem separation, the proposed method selects groups of variables for separation on the basis of their reduced cost in an LP relaxation. The proposed method restricts a large portion of the integer variables to zero on one branch. The net effect is that the original integer program is solved by optimizing a series of smaller, more tightly restricted, integer programs. The authors have programmed the algorithm using the Extended Control Language of the IBM MPSX/370-MIP/370 mixed integer programming package. Computational results are presented that demonstrate the efficiency of the method on problems where the 0 1 variables are partitioned into multiple choice constraints containing special ordered sets of variables. While the computational results are limited to this class of problems the algorithm can, in theory, be applied to any mixed integer programming problem.

Toward a conceptual framework of the process of organized innovation technological within the firm

Abstract The literature concerning information flow and organizational design for technological innovation is summarized and a conceptual framework of the process of organized technological innovation within the firm is developed. The framework incorporates Rosenblooms premise that corporate strategy can serve to cut across both internal and external boundaries of the firm and is shown to be consistent with the relevant organizational and planning literatures. The potential for using mathematical models to represent a firms corporate strategy, budgeting and resource allocation activities is discussed. We argue that such models are needed to provide for policy analysis and could lead to a simulation capability that serves as a surrogate for real-life experimentation.

Finding an optimal dynamic advertising policy

In this paper a solution is presented to an important marketing problem : the timing of advertising expenditure. Using a differential equation to model the relationship between the sales and advertising rates and using profit as a criterion, a synthesis of the optimal dynamic advertising policy as a function of the current sales level and length of the campaign is derived. In addition, using profit as a criterion, the profitability under an optimal dynamic advertising policy is compared with the profits obtained using an optimal static policy. It is shown that a significant increase in profits can result from employing the optimal dynamic policy.