Showing papers in "Annals of Operations Research in 2001"

Project Scheduling with Multiple Modes: A Genetic Algorithm

Abstract: In this paper we consider the resource-constrained project scheduling problem with multiple execution modes for each activity and makespan minimization as objective. We present a new genetic algorithm approach to solve this problem. The genetic encoding is based on a precedence feasible list of activities and a mode assignment. After defining the related crossover, mutation, and selection operators, we describe a local search extension which is employed to improve the schedules found by the basic genetic algorithm. Finally, we present the results of our thorough computational study. We determine the best among several different variants of our genetic algorithm and compare it to four other heuristics that have recently been proposed in the literature. The results that have been obtained using a standard set of instances show that the new genetic algorithm outperforms the other heuristic procedures with regard to a lower average deviation from the optimal makespan.

A Robust Genetic Algorithm for Resource Allocation in Project Scheduling

Abstract: Genetic algorithms have been applied to many different optimization problems and they are one of the most promising metaheuristics However, there are few published studies concerning the design of efficient genetic algorithms for resource allocation in project scheduling In this work we present a robust genetic algorithm for the single-mode resource constrained project scheduling problem We propose a new representation for the solutions, based on the standard activity list representation and develop new crossover techniques with good performance in a wide sample of projects Through an extensive computational experiment, using standard sets of project instances, we evaluate our genetic algorithm and demonstrate that our approach outperforms the best algorithms appearing in the literature

An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization

Abstract: Recently, we propose a nonlinear conjugate gradient method, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the weak Wolfe conditions. In this paper, we will study methods related to the new nonlinear conjugate gradient method. Specifically, if the size of the scalar β k with respect to the one in the new method belongs to some interval, then the corresponding methods are proved to be globally convergent; otherwise, we are able to construct a convex quadratic example showing that the methods need not converge. Numerical experiments are made for two combinations of the new method and the Hestenes–Stiefel conjugate gradient method. The initial results show that, one of the hybrid methods is especially efficient for the given test problems.

Simulated Annealing for Multi-Mode Resource-Constrained Project Scheduling

Abstract: In this paper the resource-constrained project scheduling problem with multiple execution modes for each activity and the makespan as the minimization criterion is considered. A simulated annealing approach to solve this problem is presented. The feasible solution representation is based on a precedence feasible list of activities and a mode assignment. A comprehensive computational experiment is described, performed on a set of standard test problems constructed by the ProGen project generator. The results are analyzed and discussed and some final remarks are included.

A Competitive Heuristic Solution Technique for Resource-Constrained Project Scheduling

Abstract: In this work a new heuristic solution technique for the Resource-Constrained Project Scheduling Problem (RCPSP) is proposed This technique is a hybrid multi-pass method that combines random sampling procedures with a backward–forward method The impact of each component of the algorithm is evaluated through a step-wise computational analysis which in addition permits the value of their parameters to be specified Furthermore, the performance of the new technique is evaluated against the best currently available heuristics using a well known set of instances The results obtained point out that the new technique greatly outperforms both the heuristics and metaheuristics currently available for the RCPSP being thus competitive with the best heuristic solution techniques for this problem

Analysis of Scheduling Schemes and Heuristic Rules Performance in Resource-Constrained Multiproject Scheduling

Abstract: Frequently, the availability of resources assigned to a project is limited and not sufficient to execute all the concurrent activities. In this situation, decision making about their schedule is necessary. Many times this schedule supposes an increase in the project completion time. Additionally, companies commonly manage various projects simultaneously, sharing a pool of renewable resources. Given these resource constraints, we often can only apply heuristic methods to solve the scheduling problem. In this work the effect of the schedule generation schemes – serial or parallel – and priority rules – MINLFT, MINSLK, MAXTWK, SASP or FCFS – with two approaches – multi-project and single-project – are analysed. The time criteria considered are the mean project delay and the multiproject duration increase. Through an extensive computational study, results show that with the parallel scheduling generation scheme and the multi-project approach the project manager can obtain a good multiproject schedule with the time criterion selected: minimising mean project delay or minimising multiproject duration increase. New heuristics – based on priority rules with a two-phase approach – that outperform classical ones are proposed to minimise mean project delay with a multi-project approach. Finally, the best heuristics analysed are evaluated together with a representative sample of commercial project management software.

Global Convergence of Conjugate Gradient Methods without Line Search.

Abstract: Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC 1 objective function; (2) The Polak–Ribiere method and the Conjugate Descent method applied to a general, not necessarily convex, LC 1 objective function.

Topological design of survivable mesh-based transport networks

Abstract: A method of designing a telecommunications network, the method comprising the steps of A) for all working demand flows required to be routed in the telecommunications network, finding an initial topology of spans between nodes in the telecommunications network that is sufficient for routing all working demand flows, while attempting to minimize the cost of providing the spans; B) given the initial topology of spans identified in step A, finding a set of additional spans that ensures restorability of working demand flows that are required to be restored in case of failure of any span in the initial topology of spans, while attempting to minimize the cost of providing additional spans; and C) starting with the initial topology of spans and the additional spans identified in step B, finding a final topology of spans between nodes in the telecommunications network that attempts to minimize the total cost of the final topology of spans, while routing all working demand flows and ensuring restorability of working demand flows required to be restored in case of failure of any span in the final topology of spans. A network so designed may be implemented in whole or in part.

Proximity Function Minimization Using Multiple Bregman Projections, with Applications to Split Feasibility and Kullback–Leibler Distance Minimization

Abstract: Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets The simultaneous multiprojection algorithm of Censor and Elfving for solving the CFP, in which different generalized projections may be used at the same time, has been shown to converge for the case of nonempty intersection; still open is the question of its convergence when the intersection of the closed convex sets is empty Motivated by the geometric alternating minimization approach of Csiszar and Tusnady and the product space formulation of Pierra, we derive a new simultaneous multiprojection algorithm that employs generalized projections of Bregman to solve the convex feasibility problem or, in the inconsistent case, to minimize a proximity function that measures the average distance from a point to all convex sets We assume that the Bregman distances involved are jointly convex, so that the proximity function itself is convex When the intersection of the convex sets is empty, but the closure of the proximity function has a unique global minimizer, the sequence of iterates converges to this unique minimizer Special cases of this algorithm include the “Expectation Maximization Maximum Likelihood” (EMML) method in emission tomography and a new convergence result for an algorithm that solves the split feasibility problem

Using Genetic Algorithms and Heuristics for Job Shop Scheduling with Sequence-Dependent Setup Times

Abstract: The importance of job shop scheduling as a practical problem has attracted the attention of many researchers. However, most research has focused on special cases such as single machine, parallel machine, and flowshop environments due to the “hardness” of general job shop problems. In this paper, a hybrid algorithm based on an integration of a genetic algorithm and heuristic rules is proposed for a general job shop scheduling problem with sequence-dependent setups (Jm|sjk|Cmax ). An embedded simulator is employed to implement the heuristic rules, which greatly enhances the flexibility of the algorithm. Knowledge relevant to the problem is inherent in the heuristic rules making the genetic algorithm more efficient, while the optimization procedure provided by the genetic algorithm makes the heuristic rules more effective. Extensive numerical experiments have been conducted and the results have shown that the hybrid approach is superior when compared to recently published existing methods for the same problem.

Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows

Abstract: In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in- and out-flows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it.

Optimal Base Station Positioning and Channel Assignment for 3G Mobile Networks by Integer Programming

Abstract: In this paper, discrete mathematical programming approaches are used to solve the frequency allocation and cell site selection problem in an integrated setup Both CDMA (code division multiple access) and FD/TDMA (frequency/time division multiple access) technologies will be important for 3rd generation mobile systems If all users share the same bandwidth, base transmitter stations should be placed such that a maximum of traffic can be carried at low interference rates The expected traffic is represented by spatially scattered weighted nodes The problem to select an optimal set of base station locations from a given pool of configurations is formulated as an integer linear program and solved by combinatorial optimization methods For systems which employ FD/TDMA schemes, the cell site optimization process depends on the assignment of channels We suggest an integrated linear programming approach to solve both objectives in a single planning step Because of the problems' tremendous complexity, special branch-and-bound procedures are developed as exact and approximate solution methods An examples is given for a typical urban scenario with base transmitters below roof tops

How Airlines and Airports Recover from Schedule Perturbations: A Survey

Abstract: The explosive growth in air traffic as well as the widespread adoption of Operations Research techniques in airline scheduling has given rise to tight flight schedules at major airports. An undesirable consequence of this is that a minor incident such as a delay in the arrival of a small number of flights can result in a chain reaction of events involving several flights and airports, causing disruption throughout the system. This paper reviews recent literature in the area of recovery from schedule disruptions. First we review how disturbances at a given airport could be handled, including the effects of runways and fixes. Then we study the papers on recovery from airline schedule perturbations, which involve adjustments in flight schedules, aircraft, and crew. The mathematical programming techniques used in ground holding are covered in some detail. We conclude the review with suggestions on how singular perturbation theory could play a role in analyzing disruptions to such highly sensitive schedules as those in the civil aviation industry.

An Exact Procedure for the Resource-Constrained Weighted Earliness–Tardiness Project Scheduling Problem

Abstract: In this paper we study the resource-constrained project scheduling problem with weighted earliness–tardinesss penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness–tardinesss penalty cost of the project subject to the finish–start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in-time environments. We introduce a depth-first branch-and-bound algorithm which makes use of extra precedence relations to resolve resource conflicts and relies on a fast recursive search algorithm for the unconstrained weighted earliness–tardinesss problem to compute lower bounds. The procedure has been coded in Visual C++, version 4.0 under Windows NT. Both the recursive search algorithm and the branch-and-bound procedure have been validated on a randomly generated problem set.

Two Issues in Setting Call Centre Staffing Levels

Abstract: Motivated by a problem facing the Police Communication Centre in Auckland, New Zealand, we consider the setting of staffing levels in a call centre with priority customers. The choice of staffing level over any particular time period (e.g., Monday from 8 am–9 am) relies on accurate arrival rate information. The usual method for identifying the arrival rate based on historical data can, in some cases, lead to considerable errors in performance estimates for a given staffing level. We explain why, identify three potential causes of the difficulty, and describe a method for detecting and addressing such a problem.

A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks

Abstract: Due to the practical importance of stochastic project networks (PERT-networks), many methods have been developed over the past decades in order to obtain information about the random project completion time. Of particular interest are methods that provide (lower and upper) bounds for its distribution, since these aim at balancing efficiency of calculation with accuracy of the obtained information.

Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints

Abstract: A family of parameter dependent optimal control problems is considered The problems are subject to higher-order inequality type state constraints It is assumed that, at the reference value of the parameter, the solution exists and is regular Regularity conditions are formulated under which the original problems are locally equivalent to some other problems subject to equality type constraints only The classical implicit function theorem is applied to these new problems to investigate Frechet dif ferentiability of the stationarity points with respect to the parameter

Discrete Cost Multicommodity Network Optimization Problems and Exact Solution Methods

Abstract: We first introduce a generic model for discrete cost multicommodity network optimization, together with several variants relevant to telecommunication networks such as: the case where discrete node cost functions (accounting for switching equipment) have to be included in the objective; the case where survivability constraints with respect to single-link and/or single-node failure have to be taken into account. An overview of existing exact solution methods is presented, both for special cases (such as the so-called single-facility and two-facility network loading problems) and for the general case where arbitrary step-increasing link cost-functions are considered. The basic discrete cost multicommodity flow problem (DCMCF) as well as its variant with survivability constraints (DCSMCF) are addressed. Several possible directions for improvement or future investigations are mentioned in the concluding section.

An Integrated Optimization Model for Train Crew Management

Abstract: Train crew management involves the development of a duty timetable for each of the drivers (crew) to cover a given train timetable in a rail transport organization. This duty timetable is spread over a certain period, known as the roster planning horizon. Train crew management may arise either from the planning stage, when the total number of crew and crew distributions are to be determined, or from the operating stage when the number of crew at each depot is known as input data. In this paper, we are interested in train crew management in the planning stage. In the literature, train crew management is decomposed into two stages: crew scheduling and crew rostering which are solved sequentially. We propose an integrated optimization model to solve both crew scheduling and crew rostering. The model enables us to generate either cyclic rosters or non-cyclic rosters. Numerical experiments are carried out over data sets arising from a practical application.

A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization

Abstract: Quasi-Newton equations play a central role in quasi-Newton methods for optimization and various quasi-Newton equations are available. This paper gives a survey on these quasi-Newton equations and studies properties of quasi-Newton methods with updates satisfying different quasi-Newton equations. These include single-step quasi-Newton equations that use only gradient information and that use both gradient and function value information in one step, and multi-step quasi-Newton equations that use the gradient information in last m steps. Main properties of quasi-Newton methods with updates satisfying different quasi-Newton equations are studied. These properties include the finite termination property, invariance, heredity of positive definite updates, consistency of search directions, global convergence and local superlinear convergence properties.

Portfolio Selection Problem with Minimax Type Risk Function

Abstract: The investor's preference in risk estimation of portfolio selection problems is important as it influences investment strategies. In this paper a minimax risk criterion is considered. Specifically, the investor aims to restrict the standard deviation for each of the available stocks. The corresponding portfolio optimization problem is formulated as a linear program. Hence it can be implemented easily. A capital asset pricing model between the market portfolio and each individual return for this model is established using nonsmooth optimization methods. Some numerical examples are given to illustrate our approach for the risk estimation.

A Representational Paradigm for Dynamic Resource Transformation Problems

Abstract: There are a host of complex operational problems arising in transportation and logistics which are characterized by dynamic information processes, complex operational characteristics and decentralized control structures. Yet, they are also optimization problems. The optimization community has made outstanding progress in the solution of large optimization problems when information processes are static (we do not model the arrival of new information) and when the entire problem can be viewed as being part of a single control structure. Not surprisingly, this technology has been extremely successful in applications such as planning airline operations which meet these requirements. This paper has grown out of the challenges we faced modeling complex operational problems arising in freight transportation and logistics, which are characterized by highly dynamic information processes, complex operational characteristics and decentralized control structures. Whereas people solve more traditional problems have struggled with the development of effective algorithms, we have struggled with the more basic challenge of simply modeling the problem. We feel that our ability to solve these problems is limited by the languages that we use to express them. Classical mathematical paradigms do not provide an easy and natural way to represent the optimization of these problems in the presence of dynamic information processes, or to capture the complexities of large scale operations. In particular, models do not capture the organization and flow of information in large organizations, preferring instead to assume the presence of a single, all-knowing decision-maker. As a result, most dynamic models posed in the literature are myopic or deterministic. The characteristics of more complex operations has spawned an extensive literature presenting models that are unique to a particular industry. For example, we solve airline fleet assignment problems (Hane et al. [22]), railroad car distribution problems (Jordan and Turnquist [26], Mendiratta and Turnquist [27], Haghani [21], and Herren [23], for example), the load matching problem of truckload trucking (Powell [33], Powell [34], Schrijver [40]), routing and scheduling problems in less-than-truckload trucking (Powell [32], Crainic and Roy [12]), the flow management problem in air traffic control (Andreatta and Romanin-Jacur [2] and Odoni [29]) and the management of ocean containers (Crainic, Gendreau and Dejax [11]). Even within an industry, rail car distribution is dif

Supply Chain Optimisation in the Paper Industry

Abstract: We describe the formulation and development of a supply-chain optimisation model for Fletcher Challenge Paper Australasia (FCPA). This model, known as Paper Industry Value Optimisation Tool (PIVOT), is a large mixed integer program that finds an optimal allocation of supplier to mill, product to paper machine, and paper machine to customer, while at the same time modelling many of the supply chain details and nuances which are peculiar to FCPA. PIVOT has assisted FCPA in solving a number of strategic and tactical decision problems, and provided significant economic benefits for the company.

Uncertainty Modelling in Software Development Projects (With Case Study)

Abstract: A project scheduling model tailored specifically for software development projects is proposed in this study. The model incorporates uncertainties related to activity durations and network topology. The first type of uncertainty exists due to error-prone coding which might result in elongated task durations caused by validation and debugging sessions. Furthermore, in practice, macro-activities represent groups of sub-tasks in order to simplify the planning and monitoring of the project. Due to the aggregation, it is more difficult to be precise on the duration of a macro-activity. The uncertainty related to the network topology is due to common database design issues or program modules shared among parallel tasks in the project network. These tasks become associated with each other through uncertain Start-to-Start (SS) precedence relationships. On the other hand, SS lags may also be the outcome of technological precedence relationships among pairs of activities. However, the imprecision underlying the work content of a predecessor activity leads to uncertain SS lags. Software development projects are human-intensive projects and hence, the duration of a task depends on the skill of the person assigned to the job as well as his/her learning rate. Thus, a task may be realized by alternative staff members which results in different expected task durations. Hence, a realistic model proposed for software development projects should incorporate staff assignment features under the uncertainties discussed above. In this study, we develop a mathematical model for software development projects and propose heuristic solution methods to be used by the project co-ordinator in preparing the project plan. The heuristic algorithms developed here are tested on real data provided by a consulting firm undertaking software development projects from manufacturing companies in Turkey.

Maximizing the Net Present Value of a Project Under Resource Constraints Using a Lagrangian Relaxation Based Heuristic with Tight Upper Bounds.

Abstract: Resource-constrained project scheduling under a net present value objective attracts growing interest Because this is an NP-hard problem, it is unlikely that optimum solutions can be computed for large instances within reasonable computation time Thus, heuristics have become a popular research field Up to now, however, upper bounds are not well researched Therefore, most researchers evaluate their heuristics on the basis of a best known lower bound, but it is unclear how good the performance really is With this contribution we close this gap and derive tight upper bounds on the basis of a Lagrangian relaxation of the resource constraints We also use this approach as a basis for a heuristic and show that our heuristic as well as the cash flow weight heuristic proposed by Baroum and Patterson yield solutions very close to the optimum result Furthermore, we discuss the proper choice of a test-bed and emphasize that discount rates must be carefully chosen to give realistic instances

Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases

Abstract: In many large-scale project scheduling problems, multiple projects are either taking place at the same time or scheduled into a tight sequence in order to efficiently share a common resource. One example of this is the computing resource allocation at an Application Service Provider (ASP) which provides data processing services for multiple paying customers. Typical services provided by ASPs are data mining, payroll processing, internet-based storage backup services and Customer Relation Management (CRM) services. The processing mode of an ASP can be either batch or concurrent, depending on the type service rendered. For example, for CPU intensive or long processing time required services, it would be more economical to processes one customer request at a time in order to minimize the context switching overhead. While the data transaction processes within a service request are subject to certain precedence relationships, the requests from different customers to an ASP are independent of each other, and the total time required to process a service request depends on the computing resource allocated to that request. The related issue of achieving an optimal use of resources at ASPs leads to problem of project scheduling with controllable project duration.

Log-Sigmoid Multipliers Method in Constrained Optimization

Abstract: In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for con- strained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augmented Lagrangian techniques. We established convergence of the LS type penalty method under very mild assumptions on the input data and estimated the rate of convergence of the LS multipliers method under the standard second order optimality condition for both exact and nonexact minimization. Some important properties of the dual function and the dual problem, which are based on the LS Lagrangian, were discovered and the primal-dual LS method was introduced.

Modeling and Solving an Airline Schedule Generation Problem

Abstract: Since opening a new flight connection or closing an existing flight has a great impact on the revenues of an airline, the generation of the flight schedule is one of the fundamental problems in airline planning processes. In this paper we concentrate on a special case of the problem which arises at charter companies. In contrast to airlines operating on regular schedules, the market for charter airlines is well-known and the schedule is allowed to change completely from period to period. Thus, precise adjustments to the demands of the market have a great potential for minimizing operating costs. We present a capacitated network design model and propose a combined branch-and-cut approach to solve this airline schedule generation problem. To tighten the linear relaxation bound, we add cutting planes which adjust the number of aircraft and the spill of passengers to the demand on each itinerary. For real-world problems from a large European charter airline we obtain solutions within a very few percent of optimality with running times in the order of minutes on a customary personal computer for most of the data sets.

The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality

Abstract: Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: the geometric programming formulation (of the generalized geometric programming type), the parametric programming formulation (of the generalized Rockafellar-perturbation type), and the ordinary Lagrangian formulation (of the generalized Falk type). The relative strengths and weaknesses of these three duality formulations are described herein, as are the fundamental relations between them. As a theoretical application, the basic duality between Fenchel's hypothesis and the existence of recession directions in convex programming is established and then expressed within each of these three duality formulations

Modified Block SSOR Preconditioners for Symmetric Positive Definite Linear Systems

Abstract: A class of modified block SSOR preconditioners is presented for the symmetric positive definite systems of linear equations, whose coefficient matrices come from the hierarchical-basis finite-element discretizations of the second-order self-adjoint elliptic boundary value problems. These preconditioners include a block SSOR iteration preconditioner, and two inexact block SSOR iteration preconditioners whose diagonal matrices except for the (1,1)-block are approximated by either point symmetric Gauss–Seidel iterations or incomplete Cholesky factorizations, respectively. The optimal relaxation factors involved in these preconditioners and the corresponding optimal condition numbers are estimated in details through two different approaches used by Bank, Dupont and Yserentant (Numer. Math. 52 (1988) 427–458) and Axelsson (Iterative Solution Methods (Cambridge University Press, 1994)). Theoretical analyses show that these modified block SSOR preconditioners are very robust, have nearly optimal convergence rates, and especially, are well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.