Title: Applied Inventory Management
Description: Supply chain management is one of the fundamental topics in the field of operations research, and a vast literature exists on the subject. Many recent developments in the field are rapidly narrowing the gap between the systems handled in the literature and the real-life problems companies need to solve on a day-to-day basis. However, there are certain features often observed in real-world systems that elude even these most recent developments. In this thesis, we consider a number of these features, and propose some new heuristics together with methodologies to evaluate their performance. In Chapter 2, we consider a general two-echelon distribution system consisting of a depot and multiple sales outlets which face random demands for a given item. The replenishment process consists of two stages: the depot procures the item from an outside supplier, while the retailers' inventories are replenished by shipments from the depot. Both of the replenishment stages are associated with a given facility-specific leadtime.

The depot as well as the retailers face a limited inventory capacity. We propose a heuristic for this class of dynamic programming models to obtain an upper bound on optimal costs, together with a new approach to generate lower bounds based on Lagrangian relaxation. We report on an extensive numerical study with close to 14,000 instances which evaluates the accuracy of the lower bound and the optimality gap of the various heuristic policies. Our study reveals that our policy performs exceedingly well almost across the entire parameter spectrum. In Chapter 3, we extend the model above to deal with distribution systems involving several items. In this setting, two interdependencies can arise between items that considerably complicate the problem. First, shared storage capacity at each of the retail outlets results in a trade-off between items; ordering more of one item means less space is available for another. Second, economies of scope can occur in the order costs if several items can be ordered from a single supplier, incurring only one fixed cost.

To our knowledge, our approach is the first that has been proposed to handle such complex, multi-echelon, multi-item systems. We propose a heuristic for this class of dynamic programming models, to obtain an upper bound on optimal costs, together with an approach to generate lower bounds. We report on an extensive numerical study with close to 1,200 instances that reveals our heuristic performs excellently across the entire parameter spectrum. In Chapter 4, we consider a periodic-review stochastic inventory control system consisting of a single retailer which faces random demands for a given item, and in which demand forecasts are dynamically updated (for example, new information observed in one period may affect our beliefs about demand distributions in future periods). Replenishment orders are subject to fixed and variable costs. A number of heuristics exist to deal with such systems, but to our knowledge, no general approach exists to find lower bounds on optimal costs therein. We develop a general approach for finding lower bounds on the cost of such systems using an information relaxation.

We test our approach in a model with advance demand information, and obtain good lower bounds over a range of problem parameters. Finally, in Appendix A, we begin to tackle the problem of using these methods in real supply chain systems. We were able to obtain data from a luxury goods manufacturer to inspire our study. Unfortunately, the methods we developed in earlier chapters were not directly applicable to these data. Instead, we developed some alternate heuristic methods, and we considered statistical techniques that might be used to obtain the parameters required for these heuristics from the data available.