Showing papers in "Annals of Operations Research in 2000"

Scenarios for Multistage Stochastic Programs

Abstract: A major issue in any application of multistage stochastic programming is the representation of the underlying random data process. We discuss the case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model. No assumptions on convexity with respect to the random parameters are required. We emphasize the notion of representative scenarios (or a representative scenario tree) relative to the problem being modeled.

Algorithms for the Set Covering Problem

Abstract: The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and mass-transit companies. In this survey, we focus our attention on the most recent and effective algorithms for SCP, considering both heuristic and exact approaches, outlining their main characteristics and presenting an experimental comparison on the test-bed instances of Beasley's OR Library.

The Optimal Control of a Train

Abstract: We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.

Single Machine Scheduling with Learning Effect Considerations

Abstract: In this paper we study a single machine scheduling problem in which the job processing times will decrease as a result of learning. A volume-dependent piecewise linear processing time function is used to model the learning effects. The objective is to minimize the maximum lateness. We first show that the problem is NP-hard in the strong sense and then identify two special cases which are polynomially solvable. We also propose two heuristics and analyse their worst-case performance.

Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty

Abstract: A dynamic (multi-stage) stochastic programming model for the weekly cost-optimal generation of electric power in a hydro-thermal generation system under uncertain demand (or load) is developed. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints coupling power units. It is assumed that the stochastic load process is given (or approximated) by a finite number of realizations (scenarios) in scenario tree form. Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single (thermal or hydro) unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the first stage (primal) decisions starting from the optimal (stochastic) multipliers is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 200 000 binary and 350 000 continuous variables, and more than 500 000 constraints.

An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems

Abstract: In this paper, we present an algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems involving (i) 0-1 integer variables, and, (ii) more than one parameter, bounded between lower and upper bounds, present on the right hand side (RHS) of constraints. The solution is approached by decomposing the mp-MILP into two subproblems and then iterating between them. The first subproblem is obtained by fixing integer variables, resulting in a multiparametric linear programming (mp-LP) problem, whereas the second subproblem is formulated as a mixed integer linear programming (MILP) problem by relaxing the parameters as variables.

Efficient algorithms for buffer space allocation

Abstract: This paper describes efficient algorithms for determining how buffer space should be allocated in a flow line. We analyze two problems: a primal problem, which minimizes total buffer space subject to a production rate constraint; and a dual problem, which maximizes production rate subject to a total buffer space constraint. The dual problem is solved by means of a gradient method, and the primal problem is solved using the dual solution. Numerical results are presented. Profit optimization problems are natural generalizations of the primal and dual problems, and we show how they can be solved using essentially the same algorithms.

Cyclic scheduling in robotic flowshops

Abstract: Fully automated production cells consisting of flexible machines and a material handling robot have become commonplace in contemporary manufacturing systems. Much research on scheduling problems arising in such cells, in particular in flowshop-like production cells, has been reported recently. Although there are many differences between the models, they all explicitly incorporate the interaction between the materials handling and the classical job processing decisions, since this interaction determines the efficiency of the cell. This paper surveys cyclic scheduling problems in robotic flowshops, models for such problems, and the complexity of solving these problems, thereby bringing together several streams of research that have by and large ignored one another, and describing and establishing links with other scheduling problems and combinatorial topics.

Multiple criteria linear programming model for portfolio selection

Abstract: The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model.

Selecting Portfolios with Fixed Costs and Minimum Transaction Lots

Abstract: The original Markowitz model of portfolio selection has received a widespread theoretical acceptance and it has been the basis for various portfolio selection techniques. Nevertheless, this normative model has found relatively little application in practice when some additional features, such as fixed costs and minimum transaction lots, are relevant in the portfolio selection problem. In this paper different mixed-integer linear programming models dealing with fixed costs and possibly minimum lots are introduced. Due to the high computational complexity of the models, heuristic procedures, based on the construction and optimal solution of mixed integer subproblems, are proposed. Computational results obtained using data from the Milan Stock Exchange show how the proposed heuristics yield very good solutions in a short computational time and make possible some interesting financial conclusions on the impact of fixed costs and minimum lots on portfolio composition.

SHADOC : a multi-agent model to tackle viability of irrigated systems

Abstract: The viability of irrigated systems in the Senegal River Valley is being brought into question today due to their under‐utilization. We assume that their viability depends largely on the way their different components behave and interact. We therefore sought to examine in greater depth today's knowledge of the structure of these systems and activities performed within them. This led to the development of a multi‐agent system model, a kind of virtual irrigated system, with a special focus on rules in use for access to credit, water allocation and cropping season assessment as well as organization and coordination of farmers. The purpose of this paper is to show how this kind of tool is relevant to the study of irrigated systems' viability. As an example it is used to examine the influence of existing social networks on the viability of irrigated systems.

A unified framework for pull control mechanisms in multi‐stage manufacturing systems

Abstract: This paper presents a unified framework for pull production control mechanisms in multi-stage manufacturing systems. A pull production control mechanism in a multi-stage manufacturing system is a mechanism that coordinates the release of parts into each stage of the system with the arrival of customer demands for final products. Four basic pull production control mechanisms are presented: Base Stock, Kanban, Generalized Kanban, and Extended Kanban. It is argued that on top of any of these basic coordination mechanisms, a local mechanism to control the work-in-process in each stage may be superimposed. Several cases of basic stage coordination mechanisms with stage work-in-process control are presented, and several production control systems that have appeared in the literature are shown to be equivalent to some of these cases.

Comparative Analysis of Artificial Neural Network Models: Application in Bankruptcy Prediction

Abstract: This study compares the predictive performance of three neural network methods, namely the learning vector quantization, the radial basis function, and the feedforward network that uses the conjugate gradient optimization algorithm, with the performance of the logistic regression and the backpropagation algorithm. All these methods are applied to a dataset of 139 matched-pairs of bankrupt and non-bankrupt US firms for the period 1983–1994. The results of this study indicate that the contemporary neural network methods applied in the present study provide superior results to those obtained from the logistic regression method and the backpropagation algorithm.

A Simulated Annealing Approach for Buffer Allocation in Reliable Production Lines

Abstract: We describe a simulated annealing approach for solving the buffer allocation problem in reliable production lines. The problem entails the determination of near optimal buffer allocation plans in large production lines with the objective of maximizing their average throughput. The latter is calculated utilizing a decomposition method. The allocation plan is calculated subject to a given amount of total buffer slots in a computationally efficient way.

The management of high seas fisheries

Abstract: The intergovernmental United Nations Conference on Highly Migratory and Straddling Stocks, initiated in 1993 and finished in 1995, addressed the conservation and management of fishery resources located both within the coastal state 200 mile Exclusive Economic Zone (EEZ) and the adjacent high seas. These types of marine resources continue to be a source for international conflicts and debates. The original United Nations Law of the Sea of 1982 failed to address transboundary fisheries in a proper way. In particular, the agreement did not recognize the emergence of the complicated “straddling stock” issue. In the new United Nations Law of the Sea agreement of 1995, a consensus was reached that the management of the straddling and highly migratory fish stocks should be carried out through regional fisheries management organizations. We present a review of the straddling stock issues in the international agreement emerging from the negotiations within the United Nations. The review is contrasted with and clarified by game theoretic analyses. We also discuss one international fishery exemplifying the case, the Norwegian spring‐spawning herring. The main conclusion is that the local problems, faced during the stage of setting up regional fisheries organizations for the management of straddling and highly migratory fish stocks, are expected to be much more complicated and difficult to solve as compared to the cases of “shared fish stocks”. In the current paper, we present two reasons for this increased complexity. The first is the larger number of players as compared to the case of “shared fish stocks” and the second is the possibility of new members entering the regional fisheries organizations.

Real-time dispatch of trams in storage yards

Abstract: Real-time dispatch problems arise when preparing and executing the daily schedule of local transport companies. We consider the daily dispatch of transport vehicles like trams in storage yards. Immediately on arrival, each tram has to be assigned to a location in the depot and to an appropriate round trip of the next schedule period. In order to achieve a departure order satisfying the scheduled demand, shunting of vehicles may be unavoidable. Since shunting takes time and causes operational cost, the number of shunting movements should be minimized without violation of operational constraints. As an alternative, we may serve some round trips with trams of type differing from the requested type. In practice, the actual arrival order of trams may differ substantially from the scheduled arrival order. Then, dispatch decisions are due within a short time interval and have to be based on incomplete information. For such real-time dispatch problems, we develop combinatorial optimization models and exact as well as heuristic algorithms. Computational experience for real-world and random data shows that the derived methods yield good (often optimal) solutions within the required tight time bounds.

Competitiveness of biomass-fueled electrical power plants.

Abstract: One way countries like the United States can comply with suggested rollbacks in greenhouse gas emissions is by employing power plants fueled with biomass. We examine the competitiveness of biomass‐based fuel for electrical power as opposed to coal using a mathematical programming structure. We consider fueling power plants from milling residues, whole trees, logging residues, switch grass, or short‐rotation woody crops. We do this using a combined model of the agricultural and forestry sectors. We find that the competitiveness of biomass depends in a key way upon the success of research in developing improved production methods for short‐rotation woody crops without great increases in costs.

Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks

Abstract: A catastrophe may affect different locations and produce losses that are rare and highly correlated in space and time. It may ruin many insurers if their risk exposures are not properly diversified among locations. The multidimentional distribution of claims from different locations depends on decision variables such as the insurer's coverage at different locations, on spatial and temporal characteristics of possible catastrophes and the vulnerability of insured values. As this distribution is analytically intractable, the most promising approach for managing the exposure of insurance portfolios to catastrophic risks requires geographically explicit simulations of catastrophes. The straightforward use of so-called catastrophe modeling runs quickly into an extremely large number of “what-if” evaluations. The aim of this paper is to develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision making on coverages of losses, profits, stability, and survival of insurers. We establish connections between ruin probability and the maximization of concave risk functions and we outline numerical experiments.

A decomposition method for analyzing inhomogeneous assembly/disassembly systems

Abstract: This paper presents a decomposition method for analyzing assembly/disassembly manufacturing systems with continuous material, exponential repair and failure time distributions, and processing times that differ from machine to machine. Decomposition equations are derived, an algorithm is developed, special cases are explored, and numerical results are discussed.

A statistical analysis of simulated annealing applied to the p-median problem

Abstract: We present a statistical analysis of simulated annealing applied to the p-median problem The algorithm we use combines elements of the vertex substitution method of Teitz and Bart with the general methodology of simulated annealing The cooling schedule adopted incorporates the notion of temperature adjustments rather than just temperature reductions Computational results are given for test problems ranging from 100 to 900 vertices, retrieved from Beasley's OR-Library for combinatorial problems Each problem was run for a maximum of 100 different streams of random numbers Optimal solutions were found for 26 of the 40 problems tested, although high optimum hitting rates were obtained for only 20 of them The worst gap in relation to the optimal solution was 162%, after all runs for each of the test problems were computed

Unit commitment in power generation – a basic model and some extensions

Abstract: For the unit commitment problem in the hydro-thermal power system of VEAG Vereinigte Energiewerke AG Berlin we present a basic model and discuss possible extensions where both primal and dual solution approaches lead to flexible optimization tools Extensions include staggered fuel prices, reserve policies involving hydro units, nonlinear start-up costs, and uncertain load profiles

A Survey of Reachability and Controllability for Positive Linear Systems

Abstract: This paper is a survey of reachability and controllability results for discrete-time positive linear systems. It presents a variety of criteria in both algebraic and digraph forms for recognising these fundamental system properties with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control, manpower planning, scheduling and other areas of operations research) but also in studying properties of reachable sets, in feedback control problems, and others. The paper highlights the intrinsic combinatorial structure of reachable/controllable positive linear systems and reveals the monomial components of such systems. The system matrix decomposition into monomial components is demonstrated by solving some illustrative examples.

A mathematical programming model applied to the study of water markets within the Spanish agricultural sector

Abstract: Spanish irrigated agriculture uses about 80% of all the nation's available water resources. The need to increase the economic efficiency of current uses of water in the agricultural sector is perceived as the top priority of the country's national water policy. In Spain surface water is centrally allocated among competing users based on allocation criteria dictated by the Water Law. The complete absence of price or market signals is a major obstacle to induce irrigators to use water more efficiently. Water markets within the agricultural sector is a promising, though scarcely analyzed in Spain, solution to increase its economic efficiency. This research is an attempt to evaluate probable water transfers among farmers and irrigation districts as well as water price equilibria resulting from different water market arrangements. Three interconnected mathematical programming models permit the simulation of water use at the farm level and water market arrangements in the Guadalquivir Valley (Spain). Results show that water markets would be highly dependent on the level of transaction costs and on the relative reductions of water allotments due to non‐overlapping drought cycles among water districts.

Optimal portfolio choice under a liability constraint

Abstract: The problem of characterizing the least expensive bond portfolio that enables one to meet his/her liability to pay C dollars K years from now is dealt with in this article. Bond prices are allowed to be either overpriced or underpriced at the purchase time, while at the sale time the bonds are suppose to be fairly priced. Assuming shifts in spot rates to occur instantly after the acquisition of a bond portfolio Z and to follow fairly general type of behavior described by the condition (2), we give both necessary and sufficient conditions for Z to solve the immunization problem above. Our model is general enough to cover situations with twists in the yield curve. Making use of the K-T conditions, we explain in remark 7 why we focus on search of an optimal portfolio in the class of barbell strategies. Finally, by means of the K-T conditions we find an optimal bond portfolio which solves the immunization problem.

Comparison among three pull control policies: kanban, base stock, and generalized kanban

Abstract: This paper is concerned with make‐to‐stock pull control policies. A classical policy is the kanban policy. Another policy, very easy to implement, is the base stock policy. These two policies contain one design parameter per stage. A general control policy, known as the generalized kanban policy, can also be used to implement the pull mechanism. The generalized kanban policy includes, as special cases, the kanban and the base stock policies. This policy uses two parameters for each stage of the production system. The aim of this paper is to provide qualitative and quantitative comparisons of these three policies. The results of our study will help to choose the policy to implement in order to control a production system. We give practical rules. We also show that if there is no delay in filling orders, all three policies have similar costs. However, for the systems studied, we show that, if there is a delay in filling orders, generalized kanban systems and base stock systems yield close to optimal costs, which are lower than costs of kanban systems for the same service quality.

Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems.

Abstract: We consider first nonlinear systems of the form x=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly We then show that the sequence converges Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space

Stochastic Nonstationary Optimization for Finding Universal Portfolios

Abstract: We apply ideas from stochastic optimization for defining universal portfolios. Universal portfolios are that class of portfolios which are constructed directly from the available observations of the stocks behavior without any assumptions about their statistical properties. Cover [7] has shown that one can construct such portfolio using only observations of the past stock prices which generates the same asymptotic wealth growth as the best constant rebalanced portfolio which is constructed with the full knowledge of the future stock market behavior.

Maximization of Manufacturing Yield of Systems with Arbitrary Distributions of Component Values

Abstract: This paper presents a general method for maximizing manufacturing yield when the realizations of system components are independent random variables with arbitrary distributions. Design specifications define a feasible region which, in the nonlinear case, is linearized using a first-order approximation. The method attempts to place the given tolerance hypercube of the uncertain parameters such that the area with higher yield lies in the feasible region. The yield is estimated by using the joint cumulative density function over the portion of the tolerance hypercube that is contained in the feasible region. A double-bounded density function is used to approximate various bounded distributions for which optimal designs are demonstrated on a tutorial example. Monte Carlo simulation is used to evaluate the actual yields of optimal designs.

Computational Discretization Algorithms for Functional Inequality Constrained Optimization

Abstract: In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is firstly converted into an optimization problem with a single nonsmooth equality constraint. Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smoothing techniques are used to approximate the equality constraint via a smooth inequality constraint. This leads to a sequence of approximate smooth optimization problems with one constraint. An adaptive scheme is incorporated into the method to facilitate the computation of the sum in the inequality constraint. The second method is to apply an adaptive scheme directly to the discretization problem. Thus a sequence of optimization problems with a small number of inequality constraints are obtained. Convergence analysis for both methods is established. Numerical examples show that each of the two proposed methods has its own advantages and disadvantages over the other.

Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex

Abstract: In this paper we study a method for global optimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. Some properties of the auxiliary subproblem are studied and a special algorithm for its solution is proposed. A cutting angle method based on this algorithm allows one to find an approximate solution of some problems of global optimization with 50 variables. Results of numerical experiments are discussed.