Multi-item capacitated lot-sizing problems with setup times and pricing decisions

We study a multi-item capacitated lot-sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot-sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch-and-price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65027/1/20394_ftp.pd

Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches

Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinational optimization problems. We review the various meta-heuristics that have been specifically developed to solve lot sizing problems, discussing their main components such as representation, evaluation neighborhood definition and genetic operators. Further, we briefly review other solution approaches, such as dynamic programming, cutting planes, Dantzig-Wolfe decomposition, Lagrange relaxation and dedicated heuristics. This allows us to compare these techniques. Understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms. Finally, we discuss general guidelines for computational experiments and illustrate these with several examples

Avoiding redundant columns by adding classical Benders cuts to column generation subproblems

This is the author accepted manuscript. The final version is available fro,m Elsevier via the DOI in this recordWhen solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column generation, columns might be generated that are not needed to express any integer optimal solution. Such columns are called strongly redundant and the dual bound obtained by solving the LP relaxation is potentially stronger if these columns are not generated. We introduce a sufficient condition for strong redundancy that can be checked by solving a compact LP. Using a dual solution of this compact LP we generate classical Benders cuts for the subproblem so that the generation of strongly redundant columns can be avoided. The potential of these cuts to improve the dual bound of the column generation master problem is evaluated computationally using an implementation in the branch-price-and-cut solver GCG. While their efficacy is limited on classical problems, the benefit of applying the cuts is demonstrated on structured models to which a temporal decomposition can be applied.Engineering and Physical Sciences Research Council (EPSRC

Integrated machine learning and optimization approaches

This dissertation focuses on the integration of machine learning and optimization. Specifically, novel machine learning-based frameworks are proposed to help solve a broad range of well-known operations research problems to reduce the solution times. The first study presents a bidirectional Long Short-Term Memory framework to learn optimal solutions to sequential decision-making problems. Computational results show that the framework significantly reduces the solution time of benchmark capacitated lot-sizing problems without much loss in feasibility and optimality. Also, models trained using shorter planning horizons can successfully predict the optimal solution of the instances with longer planning horizons. For the hardest data set, the predictions at the 25% level reduce the solution time of 70 CPU hours to less than 2 CPU minutes with an optimality gap of 0.8% and without infeasibility. In the second study, an extendable prediction-optimization framework is presented for multi-stage decision-making problems to address the key issues of sequential dependence, infeasibility, and generalization. Specifically, an attention-based encoder-decoder neural network architecture is integrated with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions. The proposed framework is demonstrated to tackle the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing and multi-dimensional knapsack. The results show that models trained on shorter and smaller-dimension instances can be successfully used to predict longer and larger-dimension problems with the presented item-wise expansion algorithm. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. The proposed framework can be advantageous for solving dynamic mixed-integer programming problems that need to be solved instantly and repetitively. In the third study, a deep reinforcement learning-based framework is presented for solving scenario-based two-stage stochastic programming problems, which are computationally challenging to solve. A general two-stage deep reinforcement learning framework is proposed where two learning agents sequentially learn to solve each stage of a general two-stage stochastic multi-dimensional knapsack problem. The results show that solution time can be reduced significantly with a relatively small gap. Additionally, decision-making agents can be trained with a few scenarios and solve problems with a large number of scenarios. In the fourth study, a learning-based prediction-optimization framework is proposed for solving scenario-based multi-stage stochastic programs. The issue of non-anticipativity is addressed with a novel neural network architecture that is based on a neural machine translation system. Furthermore, training the models on deterministic problems is suggested instead of solving hard and time-consuming stochastic programs. In this framework, the level of variables used for the solution is iteratively reduced to eliminate infeasibility, and a heuristic based on a linear relaxation is performed to reduce the solution time. An improved item-wise expansion strategy is introduced to generalize the algorithm to tackle instances with different sizes. The results are presented in solving stochastic multi-item capacitated lot-sizing and stochastic multi-stage multi-dimensional knapsack problems. The results show that the solution time can be reduced by a factor of 599 with an optimality gap of only 0.08%. Moreover, results demonstrate that the models can be used to predict similarly structured stochastic programming problems with a varying number of periods, items, and scenarios. The frameworks presented in this dissertation can be utilized to achieve high-quality and fast solutions to repeatedly-solved problems in various industrial and business settings, such as production and inventory management, capacity planning, scheduling, airline logistics, dynamic pricing, and emergency management

Simultaneous lotsizing and scheduling - extensions and solution approaches

The present thesis focuses on simultaneous lotsizing and scheduling. A comprehensive review of the literature is presented in which the historical development of the subject and the current research gaps are, based on a classification scheme, described. Additionally, a review focusing on so-called secondary resources (e.g., setup operators or raw materials), which are considered alongside the primary production resource, is provided. The insights on different types of secondary resources help to develop a new model formulation generalizing and extending the currently used approaches, which are specific to certain settings. Some illustrative examples demonstrate the functional principle and flexibility of this new formulation which can thus be used in a wide range of applications. Finally, a new heuristic to solve large-scaled simultaneous lotsizing and scheduling problems is presented. The heuristic creates a modified multi-line master problem by aggregating products into groups. The resulting problem is less complex and its solution can be used to define single-line sub problems. These sub problems are solved by heuristics present in the literature and the results are then combined to form a solution to the original problem. Numerical tests show the applicability of the aforementioned approach to solve problems of practical relevance.Die vorliegende Ausarbeitung betrachtet das Thema der simultanen Losgrößen- und Reihenfolgeplanung tiefergehend. Ein ausführlicher Literaturüberblick zeigt unter Zuhilfenahme eines Klassifizierungsschemas den Entwicklungsverlauf und aktuelle Forschungslücken in diesem Bereich auf. Weiterhin wird ein auf zusätzliche Ressourcen (sogenannte secondary resources) fokussierter Literaturüberblick erstellt. Diese Ressourcen (z.B. Personal zur Umrüstung oder Rohmaterial) werden zusätzlich zu der primären Produktionsressource benötigt. Die Erkenntnisse zu den verschiedenen Typen von zusätzlichen Ressourcen werden verwendet, um ein generelles Modell zu entwickeln, welches die bisherigen, auf bestimmte Anwendungsfälle spezialisierten, Formulierungen abbildet und erweitert. Testläufe mit Beispielszenarien demonstrieren die Funktionalität und die Flexibilität der neuen Modellformulierung welche für einen Vielzahl von Anwendungsfällen verwendet werden kann. Abschließend wird eine neue Heuristik zum Lösen von simultanen Losgrößen- und Reihenfolgeplanungsproblemen praxisrelevanter Größen vorgestellt. Innerhalb der Heuristik wird durch Produktaggregation ein modifiziertes Mehrlinien-Masterproblem generiert. Das resultierende Problem ist weniger komplex und die dafür gefundene Lösung kann zum Erstellen von Einlinien-Teilproblemen verwendet werden. Diese Teilprobleme werden mit aus der Literatur bekannten Heuristiken gelöst. Die Ergebnisse werden zu einer Lösung für das ursprüngliche Problem zusammengefasst. Numerische Tests belegen die Tauglichkeit des Verfahrens zum Lösen von praxisrelevanten Problemen

Operational performance of two-stage food production systems : process interactions and capacitated storage

The food sector has seen several important developments in recent years. First, competition has become fiercer because of the increased market power of food retailing. Secondly, quality legislation has become more stringent due to a growing concern for food safety throughout the society. Third, sustainable production has become more important, and organizations are held responsible for the environmental performance of their production system. In this thesis, several aspects of these developments are studied from an Operations Management perspective. Specific questions that are addressed are: * What are the implications of capacity- and time-constrained intermediate storage on production performance? * What are the performance implications of demand characteristics like high product mix variability and lead time reductions? * How do planning decisions and process configurations influence the realization of product losses The results provide insight in the operational performance of two-stage food production systems with intermediate storage. This performance not only entails competitiveness (through the insights on lead time performance), but also sustainability (through the insight in realization of product losses).