Lessons from the healthy cities movement for social indicator development

The author investigates emerging developments of social indicators through the experience of a health planning initiative begun in 1986 under the coordination of the World Health Organization (Europe). By 1993 over 400 municipalities in first world countries had voluntarily committed themselves to participation. The paper results from interviews and reviews of some participants' programs and materials, with significant reliance upon material from Canada and the coordinating WHO office. The author divides indicator development into political and technical components, stressing the former. He makes nine principal conclusions relating to indicators' success: (1) three stages of indicator development are understanding, consensus and commitment; (2) indicators must be grounded in target population's reality; (3) indicators are historical artifacts; (4) programs must be in place that make indicator need apparent; (5) process is product; (6) new skills must be supplied; (7) indicators are client-driven; (8) good process protects indicators' integrity from inappropriate influence; and (9) quality is a culturally-derived value defying aggregation.     

Strengthening a linear reformulation of the 0-1 cubic knapsack problem via variable reordering

The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately leads to reduced overall solution times. In addition, we develop a simple heuristic method for obtaining good-quality CKP solutions that can be used to provide a warm start to the solver. Computational tests demonstrate the effectiveness of both our variable reordering strategy and heuristic method.