[...]... assigning, sequencing and scheduling xii Online Storage Systems and Transportation Problems The book is aimed at practioners and scientists in operation research especially those interested in online optimization The target audience are readers interested in fast solutions of batch presorting and vehicle routing problems or software companies producing decision support systems Students and graduates in... (e.g., blue and yellow), for all (i.e., one blue and one yellow object already exist on each layer) Let the first four objects be Online Storage Systems and Transportation Problems 10 blue and the others yellow Suppose, with objective function value 8: has two optimal solutions 1 Three blue objects are assigned to the first layer and one to the second; one yellow object to the first layer and three to... only the coefficients and have value 1 14 Online Storage Systems and Transportation Problems Figure 2.2.5 The input sequence and the content of the layers before the assignment subject to Now consider subject to Batch Presorting Problems I Figure 2.2.6 15 The input sequence and the content of the layers after the assignment and (2.2.23)-(2.2.25) subject to (2.2.23)-(2.2.25) and (2.2.28)-(2.2.30) For... talks and discussions about the batch presorting problem Prof Dr Robert E Wilson (University of Florida), Steffen Rebennack (Universität Heidelberg) and Dr Anna Schreieck (BASF, Ludwigshafen) - for careful reading parts of this book And last but not least, my husband Josef Kallrath - for his positive spirit encouraging and supporting me never to give up xiv Online Storage Systems and Transportation Problems. .. real world optimization problems often share many common features, e.g., they have similar mathematical kernels such as flow, assignment or knapsack structures One further common feature of many real life decision problems is the online nature aspect, i.e., decision making is based on partial, insufficient 2 Online Storage Systems and Transportation Problems information or without any knowledge of... objects of and always have the colors of the variable i e., The colors of the objects in between are defined depending on the occurrence of variable in the clauses as follows: The values of the cost function storage) are defined for any (which reflects the content of the as: Online Storage Systems and Transportation Problems 18 Fig 2.3.7 illustrates these coefficients for an example with and In the... 20 Online Storage Systems and Transportation Problems With the same reasoning we can assume that So we only deal with cases where or Let us define a truth assignment by Furthermore, (2.2.1) tells us that as by construction Since (X, F) is unsatisfiable by assumption, there must be some clause which is not satisfied by Case 1: contains a non-negated literal Then and from (2.3.20) we know, that and. .. situations online optimization is recommended We can list a number of problems that were originally formulated as offline problems but which in many practical applications are used in their online versions: the bin packing problem, the list update problem, the problem, the vehicle routing problem, and the pickup and delivery problem to name a few Special optimization techniques for online applications. .. powerful technique to estimate the performance of online algorithms is the competitive analysis ( c f [11]) A good survey on online optimization and competitive analysis can be found in [4], [11], [30] Online optimization and competitive analysis are based on generic principles and can be beneficial in completely different areas such as the storage system and transportation problem considered in this book... practical applications, the total cost term of can be interpreted as a worst-case estimation of the performance and the total cost of analogously, represents the average performance over all colors 2.2.3.1 An Optimization Version of Since the objective is to minimize the maximal cost (2.2.11), we now formulate the decision problem as an optimization problem: 12 Online Storage Systems and Transportation Problems . U.S.A. Donald W. Hearn University of Florida, U.S.A. Online Storage Systems and Transportation Problems with Applications Optimization Models and Mathematical Solutions by Julia Kallrath ITWM,. life decision problems is the online nature aspect, i.e., decision making is based on partial, insufficient 2 Online Storage Systems and Transportation Problems information or without any knowledge. of general nature and thus can be em- bedded into any decision-support system involving assigning, sequencing and scheduling. xii Online Storage Systems and Transportation Problems The book is