Production and distribution problems are usual in industry, specially if it has a big set of production that might be distributed for numerous clients in different places. This kind of problems are represented as optimization problems and solved using some techniques, as heuristics, that include tabu search, and genetic algorithms, and linear programming, that include LP rounding, primal dual method. This research studies heuristics and approximation algorithms to solve two problems of production and distribution, namely, the JRP (Joint Replenishment Problem) and the FLP (Facility Location Problem). We implement some of the algorithms to solve these problems and compare the results.