Multiship Crane Sequencing with Yard Congestion Constraints

Crane sequencing in container terminals determines the order of ship discharging and loading jobs that quay cranes (QCs) perform, so that the duration of a vessel's stay is minimized. The ship's load profile, berthing time, number of available bays, and QCs are considered. More important, clearance and yard congestion constraints need to be included, which, respectively, ensure that a minimum distance between adjacent QCs is observed and yard storage blocks are not overly accessed at any point in time. In sequencing for a single ship, a mixed-integer programming (MIP) model is proposed, and a heuristic approach based on the model is developed that produces good solutions. The model is then reformulated as a generalized set covering problem and solved exactly by branch and price (B&P). For multiship sequencing, the yard congestion constraints are relaxed in the spirit of Lagrangian relaxation, so that the problem decomposes by vessel into smaller subproblems solved by B&P. An efficient primal heuristic is also designed. Computational experiments reveal that large-scale problems can be solved in a reasonable computational time

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Decisional Conflict and User Acceptance of Multicriteria Decision-Making Aids *

Despite the development of increasingly sophisticated and refined multicriteria decision-making (MCDM) methods, an examination of the experimental evidence indicates that users most often prefer relatively unsophisticated methods. In this paper, we synthesize theories and empirical findings from the psychology of judgment and choice to provide a new theoretical explanation for such user preferences. Our argument centers on the assertion that the MCDM method preferred by decision makers is a function of the degree to which the method tends to introduce decisional conflict. The model we develop relates response mode, decision strategy, and the salience of decisional conflict to user preferences among decision aids. We then show that the model is consistent with empirical results in MCDM studies. Next, the role of decisional conflict in problem formulation aids is briefly discussed. Finally, we outline future research needed to thoroughly test the theoretical mechanisms we have proposed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73461/1/j.1540-5915.1991.tb00371.x.pd

A Reverse Logistics Network Model for Handling Returned Products

58827Due to the emergence of e-commerce and the proliferation of liberal return policies, product returns have become daily routines for many companies. Considering the significant impact of product returns on the company’s bottom line, a growing number of companies have attempted to streamline the reverse logistics process. Products are usually returned to initial collection points (ICPs) in small quantities and thus increase the unit shipping cost due to lack of freight discount opportunities. One way to address this issue is to aggregate the returned products into a larger shipment. However, such aggregation increases the holding time at the ICP, which in turn increases the inventory carrying costs. Considering this logistics dilemma, the main objectives of this research are to minimize the total cost by determining the optimal location and collection period of holding time of ICPs; determining the optimal location of a centralized return centre; transforming the nonlinear objective function of the proposed model formulation by Min et al. (2006a) into a linear form; and conducting a sensitivity analysis to the model solutions according to varying parameters such as shipping volume. Existing models and solution procedures are too complicated to solve real-world problems. Through a series of computational experiments, we discovered that the linearization model obtained the optimal solution at a fraction of the time used by the traditional nonlinear model and solution procedure, as well as the ability to handle up to 150 customers as compared to 30 in the conventional nonlinear model. As such, the proposed linear model is more suitable for actual industry applications than the existing models.S

A two-phase approach for real-world train unit scheduling

A two-phase approach for the train unit scheduling problem is proposed. The first phase assigns and sequences train trips to train units temporarily ignoring some station infrastructure details. Real-world scenarios such as compatibility among traction types and banned/restricted locations and time allowances for coupling/ decoupling are considered. Its solutions would be near-operable. The second phase focuses on satisfying the remaining station detail requirements, such that the solutions would be fully operable. The first phase is modeled as an integer fixed-charge multicommodity flow (FCMF) problem. A branch-and-price approach is proposed to solve it. Experiments have shown that it is only capable of handling problem instances within about 500 train trips. The train company collaborating in this research operates over 2400 train trips on a typical weekday. Hence, a heuristic has been designed for compacting the problem instance to a much smaller size before the branch-and-price solver is applied. The process is iterative with evolving compaction based on the results from the previous iteration, thereby converging to near-optimal results. The second phase is modeled as a multidimensional matching problem with a mixed integer linear programming (MILP) formulation. A column-and-dependentrow generation method for it is under development