The goal of this dissertation is the study of optimization models that integrate production, inventory and transportation decisions, in search of opportunities to improve the performance of a supply chain network. We estimate the total costs of a given design of a general supply chain network, including production, inventory and transportation costs. We consider production and transportation costs to be of fixed charge type. Fixed charge cost functions are linear functions with a discontinuity at the origin.; The main focus of this dissertation is the development of solution procedures for these optimization models. Their computational complexity makes the use of heuristics solution procedures advisable. One of the heuristics we propose is a Multi-Commodity Dynamic Slope Scaling Procedure (MCDSSP). This heuristic makes use of the fact that when minimizing a concave function over a convex set, an extreme point optimal solution exists. The same holds true for linear programs. Therefore, the concave cost function is approximated by a linear function and the corresponding linear program is solved. The slope of the linear function is updated iteratively until no better solution is found. The MCDSSP can be used to solve any multi-commodity network flow problem with fixed charge cost functions.; We also develop a Lagrangean decomposition based heuristic. The subproblems from the decomposition have a special structure. One of the subproblems is the multi-facility lot-sizing problem that we study in detail in Chapter 2. The multi-facility lot-sizing problem is an extension of the economic lot-sizing problem. We add a new dimension to the classical problem, the facility selection decision. We provide the following heuristic approaches to solve this problem: dynamic programming, a primal-dual method, a cutting plane method and a linear programming based algorithm. We propose a set of valid inequalities and show that they are facet defining. We tested the performance of the heuristics on a wide range of randomly generated problems.; We also studied other extensions of the multi-facility lot-sizing problem. In Chapter 3 we analyze and provide solution approaches to the multi-commodity and multi-retailer (single-commodity) versions of the problem.
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