Knowledge that Transforms

Given is a vertical market structure (VMS) which consists of producers, one intermediary level and consumers. In most of the literature on VMS either equilibrium behavior is studied without consideration of objectives or some objective function is being optimized without taking into account behavior of intermediaries. This paper is a modest attempt to bring the two approaches together. The decision variables are consumer advertising, intermediary advertising and markup offered by producers to intermediaries. Behavior of intermediaries is incorporated through the use of a pseudodecision variable, the equilibrium number of middlemen in the VMS.

Group theory is used to integrate a wide variety of integer programming methods into a common computational process. Included are group optimization algorithms, Lagrangian methods, the cutting plane method, and the method of surrogate constraints. These methods are controlled by a supervisor which performs four main functions: set-up, directed search, subproblem analysis, and prognosis. Some computational experience is given. One appendix contains an algorithm for dynamically solving unconstrained group problems. A second appendix gives an algorithm for solving zero-one group problems.