A decomposition algorithm for robust lot sizing problem with remanufacturing option

In this paper, we propose a decomposition procedure for constructing robust optimal production plans for reverse inventory systems. Our method is motivated by the need of overcoming the excessive computational time requirements, as well as the inaccuracies caused by imprecise representations of problem parameters. The method is based on a min-max formulation that avoids the excessive conservatism of the dualization technique employed by Wei et al. (2011). We perform a computational study using our decomposition framework on several classes of computer generated test instances and we report our experience. Bienstock and Özbay (2008) computed optimal base stock levels for the traditional lot sizing problem when the production cost is linear and we extend this work here by considering return inventories and setup costs for production. We use the approach of Bertsimas and Sim (2004) to model the uncertainties in the input

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

Polynomial policies in supply chain networks

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 63-64).This thesis aims to solve the periodic-reviewed inventory control problem in supply chain networks with uncertain demand so as to minimize the overall cost of the system over a fixed planning time horizon. In such problems, one seeks to optimally determine ordering quantities at different stages in time. We investigate the class of polynomial policies, where the control policy is directly parametrized polynomially in the observed uncertainties of previous stages. We use sum-of-square relaxations to reformulate the problem into a single semidefinite optimization problem for a specific polynomial degree. We consider both robust and stochastic approaches in order to address the uncertainties in demand. In extensive numerical studies, we find that polynomial policies exhibit better performance over basestock policies across a variety of networks and demand distributions under the mean and standard deviation criteria. However, when the uncertainty set turns out to be larger than planned, basestock policies start outperforming polynomial policies. Comparing the policies obtained under the robust and stochastic frameworks, we find that they are comparable in the average performance criterion, but the robust approach leads to better tail behavior and lower standard deviation in general.by Liwei He.S.M

Applications of robust optimization to queueing and inventory systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 105-111).This thesis investigates the application of robust optimization in the performance analysis of queueing and inventory systems. In the first part of the thesis, we propose a new approach for performance analysis of queueing systems based on robust optimization. We first derive explicit upper bounds on performance for tandem single class, multiclass single server, and single class multi-server queueing systems by solving appropriate robust optimization problems. We then show that these bounds derived by solving deterministic optimization problems translate to upper bounds on the expected steady-state performance for a variety of widely used performance measures such as waiting times and queue lengths. Additionally, these explicit bounds agree qualitatively with known results. In the second part of the thesis, we propose methods to compute (s,S) policies in supply chain networks using robust and stochastic optimization and compare their performance. Our algorithms handle general uncertainty sets, arbitrary network topologies, and flexible cost functions including the presence of fixed costs. The algorithms exhibit empirically practical running times. We contrast the performance of robust and stochastic (s,S) policies in a numerical study, and we find that the robust policy is comparable to the average performance of the stochastic policy, but has a considerably lower standard deviation across a variety of networks and realized demand distributions. Additionally, we identify regimes when the robust policy exhibits particular strengths even in average performance and tail behavior as compared with the stochastic policy.by Alexander Anatolyevich Rikun.Ph.D

Robust Counterparts of Inequalities Containing Sums of Maxima of Linear Functions

This paper adresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with general uncertainty. In the literature, often the reformulation that is exact when there is no uncertainty is used. However, in robust optimization this reformulation gives an inferior solution and provides a pessimistic view. We observe that in many papers this conservatism is not mentioned. Some papers have recognized this problem, but existing solutions are either too conservative or their performance for different uncertainty regions is not known, a comparison between them is not available, and they are restricted to specific problems. We provide techniques for general problems and compare them with numerical examples in inventory management, regression and brachytherapy. Based on these examples, we give tractable recommendations for reducing the conservatism.robust optimization;sum of maxima of linear functions;biaffine uncertainty;robust conic quadratic constraints

Designing a robust production system for erratic demand environments.

Production systems must have the right type of material in the right quantities when required for production. They must minimize the work in progress while ensuring no stock-outstock-out occurs. While these twin opposing goals are achievable when demand is stable, they are difficult to realize under an erratic demand pattern. This dissertation aims to develop a production system that can meet erratic demands with minimal costs or errors. After a detailed introduction to the problem considered, we review the relevant literature. We then conduct a numerical analysis of current production systems, identify their deficiencies, and then present our solution to address these deficiencies via the ARK (Automated Replenishment System) technique. This technique is applied to a real-world problem at Methode Engineering ©. We conclude by detailing the scientific benefit of our technique and proposing ideas for future research

A framework for creating production and inventory control strategies

In multiproduct manufacturing systems, it is difficult to assure that an optimised setting of a pull production control strategy will be able to maintain its service level and inventory control performances. This is because the competition for resources among products is liable to make them affect the service levels of one another. By comparing different pull strategies, this research has observed that tightly coupled strategies are able to maintain lower amount of inventory than decoupled strategies, but they do so at the detriment of service level robustness. As a result, tightly coupled strategies are better suited to manufacturing environments with low variability, while decoupled strategies are more robust in high variability environments. Here, robustness is a measure of how well a strategy is able to minimise the drop below its original optimised service level when the initial system conditions change. Furthermore, the Kanban allocation policy applied under a strategy plays a major role in its ability to manage the performances of multiple products. Experimental results show that the Shared Kanban Allocation Policy (SKAP) keeps a lower amount of inventory than the Dedicated Kanban Allocation Policy (DKAP), but it is more susceptible to the variability in the demand or processing times of one product impacting the service level of another. Therefore, a Hybrid Kanban allocation policy (HKAP) that combines both the DKAP and the SKAP has been implemented. This approach considers products’ demand and processing time attributes before categorising them into the same Kanban sharing group. The results of the implementation of the HKAP show that it can keep as low inventory as the SKAP and avoid products impacting the service levels of one another. Additionally, it offers a better approach to managing large multiproduct systems, as the performances of product groups can be differentially managed through the combination of Kanban sharing and dedication policies. Lastly, the observations on the performances of strategies and policies under different system conditions can be used as a framework through which line designers select strategies and policies to suit their manufacturing system