Thesis (M.S. in Management (Material Logistics))--Naval Postgraduate School, December 1990. / Thesis Advisor(s): McMasters, Alan W. ; Weir, Maurice. "December 1990." Description based on title screen as viewed on April 2, 2010. DTIC Identifier(s): Inventory control, Navy, work load planning, stock points, warehouse management, theses. Author(s) subject terms: Work-load planning, Navy stock points, TQM, warehouse management. Includes bibliographical references (p. 153). Also available in print.

In two-location inventory systems, unidirectional transshipment policies are considered when an item is not routinely stocked at a location in the system. Unlike the past research in this area which has concentrated on the simple transshipment policies of complete pooling or no pooling, the research presented in this thesis endeavors to develop an understanding of a more general class of transshipment policy. The research considers two major approaches: a decomposition approach, in which the two-location system is decomposed into a system with independent locations, and Markov decision process approach. For the decomposition approach, the transshipment policy is restricted to the class of holdout transshipment policy. The first attempt to develop a decomposition approach assumes that transshipment between the locations occurs at a constant rate in order to decompose the system into two independent locations with constant demand rates. The second attempt modifies the assumption of constant rate of transshipment to take account of local inventory levels to decompose the system into two independent locations with non-constant demand rates. In the final attempt, the assumption of constant rate of transshipment is further modified to model more closely the location providing transshipments. Again the system is decomposed into two independent locations with non-constant demand rates. For each attempt, standard techniques are applied to derive explicit expressions for the average cost rate, and an iterative solution method is developed to find an optimal holdout transshipment policy. Computational results show that these approaches can provide some insights into the performance of the original system. A semi-Markov decision model of the system is developed under the assumption of exponential lead time rather than fixed lead time. This model is later extended to the case of phase-type distribution for lead time. The semi-Markov decision process allows more general transshipment policies, but is computationally more demanding. Implicit expressions for the average cost rate are derived from the optimality equation for dynamic programming models. Computational results illustrate insights into the management of the two-location system that can be gained from this approach.

Today, the competition between companies are very strong and fighted. In particular, small-medium size companies (SMEs) need to upgrade continuously in order to be in line with new technologies and new strategies that tends to develop companies in terms of productivity and quality. SMEs need, indeed, to be always competitive in a changeable market and to achieve competitive advantage through implementation of new technologies and theoretical methods or techniques. The implementation of those methods leads the company to increase its level of productivity and quality in order to achieve a competitive place within the market. The Gunasekaran framework is a tool which is useful in order to achieve a higher level of productivity and quality within a SME. This framework was studied and analyzed in order to be applied in a real life situation. This research focuses on the application of the same framework in a Mexican small company with the aim to develop and increase the level of productivity and quality of one department. Within the application of this framework, were applied the main concepts explained by the same Gunasekaran and they were analyzed in order to understand if a possible application could be useful to achieve success within the department.

In this thesis, we study large-scale dynamic optimization problems in the context of inventory management. We analyze inventory problems with constraints coupling the items or facility locations in the inventory systems, and we propose efficient solutions that are asymptotically optimal or empirically near-optimal. In Chapter 1, we analyze multi-item, single-location inventory systems with storage capacity limits which are formulated as both unconditional expected value constraints and unconditional probability constraints. We first show that problems with unconditional expected value constraints only can be solved to optimality through Lagrangian relaxation. Then, under an assumption on the correlation structure of the demands that is valid under most practical setting, we show that the original problem can be sandwiched between two other problems with expected value constraints only. One of these problems yields a feasible solution to the original problem that is asymptotically optimal as the number of items grows. In Chapter 2, we consider the same problem but with conditional probability constraints, that impose limits on overflow frequency for every possible state in each period. We construct an efficient feasible solution in two steps. First, we solve an unconditional expected value constrained problem with reduced capacity. Second, in each period, given the state information, we solve a single-period convex optimization problem with a conditional expected value constraint. We further show that the heuristic is asymptotically optimal as number of items I grows. In addition, we design another efficient method for moderate values of I, which works empirically well in an extensive numerical study. Moreover, we extract key managerial insights from the numerical study which are critical to decision making in real business problems. In Chapter 3, we analyze single-item, multi-location systems on inventory networks that can be described by directed acyclic graphs (DAG). We propose an innovative reformulation of the problem so that Lagrangian relaxation can still be applied, which, instead of decomposing the problem by facility location, aggregates the state information, leading to a tractable lower bound approximation for the problem. The Lagrange multiplier, which provides information on the value function from the lower bound dynamic program, is used in designing a feasible heuristic. An extensive numerical study is conducted which suggests that both the lower bound approximation and upper bound heuristic perform very well.

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.