Inventory management has always been a major component of the field of operations research and numerous models derived from the industry aroused the interest of both the researchers and the practitioners. Within this framework, our work focuses on several classical inventory problems, for which no tractable method is known to compute an optimal solution. Specifically, we study deterministic models, in which the demands of the customers are known in advance, and we propose approximation techniques for each of the corresponding problems that build feasible approximate solutions while remaining computationally tractable. We first consider continuous-time models with a single facility when demand and holding costs are time-dependent. We present a simple technique that balances the different costs incurred by the system and we use this concept to build approximation methods for a large class of such problems. The second part of our work focuses on a discrete time model, in which a central warehouse supplies several retailers facing the final customers demands. This problem is known to be NP-hard, thus finding an optimal solution in polynomial time is unrealistic unless P=NP. We introduce a new decomposition of the system into simple subproblems and a method to recombine the solutions to these subproblems into a feasible solution to the original problem. The resulting algorithm has a constant performance guarantee and can be extended to several generalizations of the system, including more general cost structures and problems with backlogging or lost-sales.
Approximation algorithms for inventory control models