Showing papers by "David Pisinger published in 2014"

A Base Integer Programming Model and Benchmark Suite for Liner-Shipping Network Design

Abstract: The liner-shipping network design problem is to create a set of nonsimple cyclic sailing routes for a designated fleet of container vessels that jointly transports multiple commodities. The objective is to maximize the revenue of cargo transport while minimizing the costs of operation. The potential for making cost-effective and energy-efficient liner-shipping networks using operations research OR is huge and neglected. The implementation of logistic planning tools based upon OR has enhanced performance of airlines, railways, and general transportation companies, but within the field of liner shipping, applications of OR are scarce. We believe that access to domain knowledge and data is a barrier for researchers to approach the important liner-shipping network design problem. The purpose of the benchmark suite and the paper at hand is to provide easy access to the domain and the data sources of liner shipping for OR researchers in general. We describe and analyze the liner-shipping domain applied to network design and present a rich integer programming model based on services that constitute the fixed schedule of a liner shipping company. We prove the liner-shipping network design problem to be strongly NP-hard. A benchmark suite of data instances to reflect the business structure of a global liner shipping network is presented. The design of the benchmark suite is discussed in relation to industry standards, business rules, and mathematical programming. The data are based on real-life data from the largest global liner-shipping company, Maersk Line, and supplemented by data from several industry and public stakeholders. Computational results yielding the first best known solutions for six of the seven benchmark instances is provided using a heuristic combining tabu search and heuristic column generation.

A matheuristic for the liner shipping network design problem

Abstract: We present an integer programming based heuristic, a matheuristic, for the liner shipping network design problem. This problem consists of finding a set of container shipping routes defining a capacitated network for cargo transport. The objective is to maximize the revenue of cargo transport, while minimizing the cost of operating the network. Liner shipping companies publish a set of routes with a time schedule, and it is an industry standard to have a weekly departure at each port call on a route. A weekly frequency is achieved by deploying several vessels to a single route, respecting the available fleet of container vessels. The matheuristic is composed of four main algorithmic components: a construction heuristic, an improvement heuristic, a reinsertion heuristic, and a perturbation heuristic. The improvement heuristic uses an integer program to select a set of improving port insertions and removals on each service. Computational results are reported for the benchmark suite LINER-LIB 2012 following the industry standard of weekly departures on every schedule. The heuristic shows overall good performance and is able to find high quality solutions within competitive execution times. The matheuristic can also be applied as a decision support tool to improve an existing network by optimizing on a designated subset of the routes. A case study is presented for this approach with very promising results.

A Combined Stochastic Programming and Optimal Control Approach to Personal Finance and Pensions

Abstract: We combine a dynamic programming approach (stochastic optimal control) with a multi-stage stochastic programming approach (MSP) in order to solve various problems in personal finance and pensions. Stochastic optimal control produces an optimal policy that is easy to understand and implement. However, explicit solution may not exist, especially when we want to deal with constraints, such as limits on portfolio composition, limits on the sum insured, an inclusion of transaction costs or taxes on capital gains, which are important issues regularly mentioned in the literature. Both optimization methods are integrated into one MSP formulation, and in a short computational time produce a solution, which takes into account the entire lifetime of an individual with a focus on the practical constraints during the first years of a contract. Two applications are considered: (A) optimal investment, consumption and sum insured for an individual maximizing the expected utility of consumption and bequest, and (B) optimal investment for a pension saver who wishes to maximize the expected utility of retirement benefits. Numerical results show that among the considered practical constraints, the presence of taxes affects the optimal controls the most. Furthermore, the individual's preferences, such as impatience level and risk aversion, have even a higher impact on the controlled processes than the taxes on capital gains.

A Branch-and-Price Framework for Railway Rolling Stock Rescheduling During Disruptions

Abstract: Rescheduling rolling stock during a disruption is a passenger railway optimization problem. In current practice this is typically optimized manually despite the high complexity and high runtime requirements of the task. In this paper we propose a path-based mathematical formulation that is solved using column generation in a complete Branch-and-Price framework. In contrast to flow-based approaches our formulation is more easily extended to handle certain families of constraints, such as train unit maintenance restrictions. We benchmark the framework against real-life instances provided by the suburban railway operator in Copenhagen (DSB S-tog). In combination with a lower bound method we show that near-optimal solutions can be found within a few seconds during a disruption. In addition we show that framework is also able to find solution within a few minutes for non-disturbed timetables. Acknowledgements: The Danish Council for Strategic Research and DSB S-tog

Bunker purchasing with contracts

Abstract: The cost for bunker fuel represents a major part of the daily running costs of liner shipping vessels. The vessels, sailing on a fixed roundtrip of ports, can lift bunker at these ports, having differing and fluctuating prices. The stock of bunker on a vessel is subject to a number of operational constraints such as capacity limits, reserve requirements and sulphur content. Contracts are often used for bunker purchasing, ensuring supply and often giving a discounted price. A contract can supply any vessel in a period and port, and is thus a shared resource between vessels, which must be distributed optimally to reduce overall costs. The Bunker Purchasing with Contracts Problem has been formulated as a mixed integer programme, which has been Dantzig-Wolfe decomposed. To solve it, a novel column generation algorithm has been developed. The algorithm has been run on a series of real-world instances with up to 500+ vessels and 500+ contracts, and provide near optimal solutions. This makes it possible for a major liner shipping company to plan bunker purchasing on a global level, and provides an efficient tool for assessing new contracts.

Optimal Retirement Planning with a Focus on Single and Joint Life Annuities

Abstract: We optimize the asset allocation, consumption and bequest decisions of an investor with uncertain lifetime and under time-varying investment opportunities. The asset menu is given by stocks, zero coupon bonds and pure endowments with different maturities. The latter are contingent on either a single or a joint life, and pay fixed or variable benefits. We further include transaction costs on stocks and bonds, and surrender charges on pure endowments. We show that despite high surrender charges, annuities are the primary asset class in a portfolio, and that annuity income is never fully consumed, but used for rebalancing purposes. We argue that the optimal retirement product for a household is much more complex than any of those available in the market. Every household should be offered an annuity tailored to its needs, using a unique combination of assets and mortality protection levels.

A matheuristic for the liner shipping network design problem

Abstract: We present an integer programming based heuristic, a matheuristic, for the liner shipping network design problem. This problem consists of finding a set of container shipping routes defining a capacitated network for cargo transport. The objective is to maximize the revenue of cargo transport, while minimizing the cost of operating the network. Liner shipping companies publish a set of routes with a time schedule, and it is an industry standard to have a weekly departure at each port call on a route. A weekly frequency is achieved by deploying several vessels to a single route, respecting the available fleet of container vessels. The matheuristic is composed of four main algorithmic components: a construction heuristic, an improvement heuristic, a reinsertion heuristic, and a perturbation heuristic. The improvement heuristic uses an integer program to select a set of improving port insertions and removals on each service. Computational results are reported for the benchmark suite LINER-LIB 2012 following the industry standard of weekly departures on every schedule. The heuristic shows overall good performance and is able to find high quality solutions within competitive execution times. The matheuristic can also be applied as a decision support tool to improve an existing network by optimizing on a designated subset of the routes. A case study is presented for this approach with very promising results.

Optimization-based guidelines to retirement planning and pension product design

Abstract: Pension systems differ across countries and are subject to country specific regulations. In addition, various countries offer different types of pension plans to their citizens. In some pension plans individuals have a lot of flexibility regarding managing their savings; in others, pension funds or life insurers manage the members' savings without taking into account the individuals' preferences. Nevertheless, in most of the pension plans individuals face some challenges. They have to decide on the investment and consumption of their retirement savings either by choosing a pension provider and a specific pension product, or by choosing a particular annuity, and, possibly, a life insurance policy. In some countries they have to make decisions as soon as they are employed; in other countries, not until they approach the time of retirement. To help individuals make the right decisions regarding their retirement savings, this thesis presents some optimization techniques that could be applied by pension providers and financial advisers to provide individuals with such guidelines. For a given objective function and a number of constraints, we search for the optimal solution, which indicates, for example, how to invest the savings, which annuity to purchase, and which level of death benefit to choose. In most of the papers we follow a classical approach and maximize the expected CRRA utility of either the final wealth, or the consumption and bequest amount. Scholars refer to the aforementioned decisions as the consumption-investment problems. A classical approach to solving these problems is stochastic optimal control (SOC), which aims to find a closed-form solution to a given problem. However, as the explicit solution exists only for relatively simple models, this approach cannot be applied to the problems considered in this thesis. Therefore, in this thesis we use a multi-stage stochastic programming (MSP) approach that is known for its practical applications and thus broadly used in operations research. In a few chapters of the thesis we apply a mixed approach, i.e., a combination of the MSP and SOC approaches, and in one of the chapters we apply Monte Carlo simulations. Each chapter of the thesis focuses on different challenges that individuals face, given a different set of constraints, determined either by national regulations or by individuals' personal preferences. The first two chapters deal with defined contribution pension plans, where an individual makes the consumption, investment, and life insurance decisions, both before and after retirement. Our results indicate that retirement savings management differs for each individual, and that it should not only depend on the individual's degree of risk aversion or time left to retirement, but also characteristics such as current wealth, expected income before and after retirement, expected pension contributions, impatience factor, lifetime expectancy, and preferences regarding portfolio composition and the level of death benefit. Consequently, pension providers should offer variable life annuities that are tailored to the individuals' needs in terms of the underlying asset allocation, the payout profile, and the level of death benefit.The next three chapters discuss the purchase of the right annuity. We start with investigating whether individuals should wait until retirement to purchase a life annuity providing fixed payments, whether they should invest in this annuity already some years before retirement by purchasing a deferred annuity with the same fixed payments, or whether they should invest their savings in stocks and bonds. Despite simple model assumptions, our findings indicate that individuals should invest part of their savings in deferred annuities. The proportion in these products increases with the degree of risk aversion and the expected lifetime, and decreases with the bequest motive. Afterwards, we investigate the optimal annuity choice under inflation risk, which is often ignored both by practitioners advising on the retirement planning and by scholars investigating the consumption-investment problems. We search for an optimal level of retirement income in real terms, given investment opportunities in inflation-linked, nominal, and variable annuities, as well as in stocks and bonds. Our findings show that real annuities are a crucial asset in every portfolio, and that trying to hedge inflation without investing in inflation-linked products leads to a lower and more volatile retirement income. In the last chapter discussing the annuity purchase, we differentiate between a wide variety of annuities. In addition to stocks and bonds with different maturities, we search for the optimal investment in annuities contingent on a single and joint lifetime, with fixed and variable payments, with immediate and deferred payments, and with temporary and life long payments. We conclude that the optimal portfolio for a single and a two-person household not only requires frequent rebalancing, but also consists of too many different assets. Accordingly, we argue that despite so many annuities available in the market, the products that individuals need the most are not available. Finally, in the last chapter of this thesis we apply Monte Carlo simulations to investigate the value of the interest rate guarantee incorporated in the Danish with-profit products. In these products the pension provider offers its members a guaranteed interest rate as well as some bonus rate that depends on the pension provider's realized investment returns. We argue that with-profit products with such a bonus mechanism often provide lower returns than pure unit-linked products without any guarantee because, to meet the solvency requirements, the pension provider has to invest individuals' assets more conservatively.

Interactive Cost Configuration Over Decision Diagrams

Abstract: In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrack-free user interaction online. In particular,binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDD-based configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multi-valued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is non-additive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiple-cost configuration is NP-hard in the input MDD. However, for solving two-cost configuration we develop a pseudo-polynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over real-world configuration models and product-catalogue datasets. Response times are generally within a fraction of a second even for very large instances.

Optimal Annuity Portfolio Under Inflation Risk

Abstract: The paper investigates the importance of inflation-linked annuities to individuals facing inflation risk. Given the investment opportunities in nominal, real, and variable annuities, as well as cash and stocks, we investigate the consumption and investment decisions under two different objective functions: 1) maximization of the expected CRRA utility function, and 2) minimization of squared deviations from an inflation-adjusted target. To find the optimal decisions we apply a multi-stage stochastic programming approach. Our findings indicate that independently of the considered objective function and risk aversion, real annuities are a crucial asset in every portfolio. In addition, without investing in real annuities, the retiree has to rebalance the portfolio more frequently, and still obtains the lower and more volatile real consumption.