Analyses of approximate optimization of logistic problems.

The thesis focuses on methods of mathematical optimization for logistic planning with applications to the location of facilities and inventory of products. Algebraic models of location on networks are presented in increasing order of complexity and realism emphasizing the presence of elemental models as building blocks of larger logistic systems. The thesis examines two small, well-known logistic problem formulations. For both applications, optimization programs are presented for which a classical solution approach is to find approximate optima because the representation encapsulates either combinatorial or functional complexities. Mathematical expressions of these approximations enable the calculation of their variations with the model parameters. Thus, constraint specifications of mathematical programs ease both the analysis of fast approximation and the analysis of variation of the optimal value as a function of each parameter of the model. Starting with the uncapacitated facility location model, a simple heuristic for the location of facilities is compared with previous heuristics and exact algorithms and shown to yield an acceptable level of accuracy with respect to previous measures of quality. In a study of capacity planning patterned after a traditional model of inventory control, a (Q,r) inventory system is analysed. The underlying mathematical model serves as a base for sensitivity analysis. As in the previous chapter, an approximation yields sufficient insight to predict the variation of optimal policies under varying conditions