Using solution properties within an enumerative search to solve a sports league scheduling problem

This paper presents an enumerative approach for a particular sports league scheduling problem known as “Prob026” in CSPLib. Despite its exponential-time complexity, this simple method can solve all instances involving a number T of teams up to 50 in a reasonable amount of time while the best known tabu search and constraint programming algorithms are limited to T?40 and the direct construction methods available only solve instances where or T/2 is odd. Furthermore, solutions were also found for some T values up to 70. The proposed approach relies on discovering, by observation, interesting properties from solutions of small problem instances and then using these properties in the final algorithm to constraint the search process.     

Four solution techniques for a general one machine scheduling problem: A comparative study

Gelders and Kleindorfer suggested a generalized detailed scheduling cost structure, based on the sum of weighted tardiness and weighted flowtime. They solved the single-machine scheduling problem using a transportation scheme to obtain lower bounds in their branch and bound approach. Recently, Fisher, Baker, Rinnooy Kan and Srinivasan reported attractive computation times with general algorithms adapted to the total tardiness problem for the single-machine case. In this paper four algorithms are adapted to the generalized cost structure mentioned above and extensive computational results are presented.This investigation shows that much is to be expected from the dual approach for more complex scheduling problems while dynamic programming deserves a new research effort because of its efficiency in special structured problems and/or problems where a posteriori precedence relations (dominance criteria) can be developed.     

A tabu search tutorial based on a real-world scheduling problem

We apply a tabu search method to a scheduling problem of a company producing cables for cars: the task is to determine on what machines and in which order the cable jobs should be produced in order to save production costs. First, the problem is modeled as a combinatorial optimization problem. We then employ a tabu search algorithm as an approach to solve the specific problem of the company, adapt various intensification as well as diversification strategies within the algorithm, and demonstrate how these different implementations improve the results. Moreover, we show how the computational cost in each iteration of the algorithm can be reduced drastically from O(n ³) (naive implementation) to O(n) (smart implementation) by exploiting the specific structure of the problem (n refers to the number of cable orders).     

A new formulation and solution of the flowshop scheduling problem with no in-process waiting

To date, all models reported in the literature relating to the flowshop sequencing problem with no in-process waiting, have been based on single objective optimization. This paper presents a mixed integer goal programming model of the generalized N job, M machine standard flowshop problem with no in-process waiting, i.e. no intermediate queues. Instead of optimization being based on a single objective, the most satisfactory sequence is derived subject to user specified selection of the pre-emptive goals: makespan, flowtime, and machine idle time. Computational results of sample problems illustrating the advantage of a multiple criteria selection method are shown.     

Approximate solution of a resource-constrained scheduling problem

This paper is devoted to the approximate solution of a strongly NP-hard resource-constrained scheduling problem which arises in relation to the operability of certain high availability real time distributed systems. We present an algorithm based on the simulated annealing metaheuristic and, building on previous research on exact solution methods, extensive computational results demonstrating its practical ability to produce acceptable solutions, in a precisely defined sense. Additionally, our experiments are in remarkable agreement with certain theoretical properties of our simulated annealing scheme. The paper concludes with a short discussion on further research. This research was supported in part by Association Nationale de la Recherche Technique grant CIFRE-121/2004.     

The crane scheduling problem: models and solution approaches

In this paper, we study the crane scheduling problem for a vessel after the vessel is moored on a terminal and develop both exact and heuristic solution approaches for the problem. For small-sized instances, we develop a time-space network flow formulation with non-crossing constraints for the problem and apply an exact solution approach to obtain an optimal solution. For medium-sized instances, we develop a Lagrangian relaxation approach that allows us to obtain tight lower bounds and near-optimal solutions. For large-sized instances, we develop two heuristics and show that the error bounds of our heuristics are no more than 100%. Finally, we perform computational studies to show the effectiveness of our proposed solution approaches.     

An integer linear formulation for the file transfer scheduling problem

In this paper, we propose a new integer linear programming (ILP) formulation for solving a file transfer scheduling problem (FTSP), which is to minimize the overall time needed to transfer all files to their destinations for a given collection of various sized files in a computer network. Each computer in this network has a limited number of communication ports. The described problem is proved to be NP-hard in a general case. Our formulation enables solving the problem by standard ILP solvers like CPLEX or Gurobi. To prove the validity of the proposed ILP formulation, two new reformulations of FTSP are presented. The results obtained by CPLEX and Gurobi solvers, based on this formulation, are presented and discussed.     

A unified formulation of the machine scheduling problem

A wide class of machine scheduling problems can be formulated as ILP problems and solved by branch and bound using the out-of-kilter algorithm for the solution of the subproblems.     

An efficient solution approach for real-world driver scheduling problems in urban bus transportation

The driver scheduling problem in public transportation is defined in the following way. There is a set of operational tasks, and the goal is to define the sequence of these tasks as shifts in such a way that every task must be assigned to a shift without overlapping. In real-world situations several additional constraints need to be considered, which makes large practical problems challenging to be solved efficiently. In practice it is also an important request with respect to a public transportation scheduling system to offer several versions of quasi-optimal solutions. In this paper we present an efficient driver scheduling solution methodology which is flexible in the above sense.     

A network solution to a general vehicle scheduling problem

Dantzig and Fulkerson and later Bellmore et al. have shown that certain vehicle (tanker) scheduling problems can be formulated as minimum cost flow problems on a network. In this paper, the results of Dantzig and Fulkerson are extended to the case where more than one type of vehicle can be used in the determination of an optimal fleet. (In tanker scheduling terminology; how many small, medium and large tankers would form an optical fleet.) It is seen how the problem can be formulated as a modified transportation problem where flow in some arcs is conditioned to there being flow on certain other arcs. These “conditional” transportation problems were solved directly as linear programs and showed the peculiarity of terminating all integer in spite of having a constraint matrix, which does not satisfy the well known sufficient conditions for urimodularity. We discuss the implementation of the model and its empirical results.     

On the interactive solution to a multicriteria scheduling problem

Summary A mixed integer multiple criteria model is formulated for scheduling problems. Its solution is obtained by an interactive method based on the Tchebycheff-approximation. For solving greater problems some modifications are discussed at the end of the paper, which are essentially based on the notion of heuristic efficiency.

---

Zusammenfassung Da bei Ablaufplanungsproblemen häufig mehrere Zielsetzungen zu beachten sind, wird im folgenden Beitrag hierzu ein gemischt-ganzzahliges multikriterielles Entscheidungsmodell formuliert. Seine Lösung erfolgt mit Hilfe eines interaktiven Verfahrens. Zur numerischen Lösung größerer Problemstellungen sind einzelne Verfahrensmodifikationen erforderlich, die im wesentlichen auf dem im letzten Abschnitt eingeführten Begriff der heuristischen Effizienz aufbauen.

     

AFSCN scheduling: How the problem and solution have evolved

The Air Force Satellite Control Network (AFSCN) coordinates communications to more than 100 satellites via nine ground stations positioned around the globe. Customers request an antenna at a ground station for a specific time window along with possible alternative slots. Typically, 500 requests per day result in more than 100 conflicts, which are requests that cannot be satisfied because other tasks need the same slot. Scheduling access requests is referred to as the Satellite Range Scheduling Problem (SRSP).This paper presents an overview of three key issues: (1) how has the problem changed over the last 10 years, (2) what algorithms work best and (3) what objective function is appropriate for AFSCN. We compared data sets from 1992 and from 2002/2003 and found significant differences in the problems. Our evaluation of solutions focuses on three algorithms: local search, Gooley’s algorithm from AFIT, and the Genitor genetic algorithm. It can be shown that local search (and therefore metaheuristics based on local search) fail to compete with Gooley’s algorithm and Genitor. Finally, while all prior work on AFSCN minimizes request conflicts, we explore an alternative objective function. Because human schedulers must eventually schedule all requests, it might be better to optimize schedules for “repairability”. Our results suggest that minimizing schedule overlaps makes it easier to fit larger requests into the schedule.     

Self-similar solution of a tensile crack problem in a coupled formulation

Using a self-similar variables, an asymptotic investigation is carried out into the stress fields and the rates of creep deformations and degree of damage close to the tip of a tensile crack under creep conditions in a coupled (creep - damage) plane formulation of the problem. It is shown that a domain of completely damaged material (DCDM) exists close to the crack tip. The geometry of this domain is determined for different values of the material parameters appearing in the constitutive relations of the Norton power law in the theory of steady-state creep and a kinetic equation which postulates a power law for the damage accumulation. It is shown that, if the boundary condition at the point at infinity is formulated as the condition of asymptotic approximation to the Hutchinson–Rice-Rosengren solution [Hutchinson JW. Singular behaviour at the end of a tensile crack in a hardening material. J Mech Phys Solids 1968;16(1):13–31; Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids. 1968;16(1):1–12], then the boundaries of the DCDM, which are defined by means of binomial and trinomial expansions of the continuity parameter, are substantially different with respect to their dimension and shape. A new asymptotic of the for stress field, which determines the geometry of the DCDM and leads to close configurations of the DCDM constructed using binomial and trinomial asymptotic expansions of the continuity parameter, are established by an asymptotic analysis and a numerical solution of the non-linear eigenvalue problem obtained.     

Genetic algorithms for the bus driver scheduling problem: a case study

This paper describes an application of genetic algorithms to the bus driver scheduling problem. The application of genetic algorithms extends the traditional approach of Set Covering/Set Partitioning formulations, allowing the simultaneous consideration of several complex criteria. The genetic algorithm is integrated in a DSS but can be used as a very interactive tool or a stand-alone application. It incorporates the user's knowledge in a quite natural way and produces solutions that are almost directly implemented by the transport companies in their operational planning processes. Computational results with airline and bus crew scheduling problems from real world companies are presented and discussed.     

An effective mathematical formulation for the unidirectional cluster-based quay crane scheduling problem

The quay crane scheduling problem plays an important role in the paradigm of port container terminal management, due to the fact that it closely relates to vessel berthing time. In this paper, we focus on the study of a special strategy for the cluster-based quay crane scheduling problem that forces quay cranes to move unidirectionally during the scheduling. The scheduling problem arising when this strategy is applied is called the unidirectional quay crane scheduling problem in the literature. Different from other researches attempting to construct more sophisticated searching algorithms, in this paper, we seek for a more compact mathematical formulation of the unidirectional cluster-based quay crane scheduling problem that can be easily solved by a standard optimization solver. To assess the performance of the proposed model, commonly accepted benchmark suites are used and the results indicate that the proposed model outperforms the state-of-the-art algorithms designed for the unidirectional cluster-based quay crane scheduling problem.     

Iterative methods for the solution of a singular control formulation of a GMWB pricing problem

Discretized singular control problems in finance result in highly nonlinear algebraic equations which must be solved at each timestep. We consider a singular stochastic control problem arising in pricing a guaranteed minimum withdrawal benefit (GMWB), where the underlying asset is assumed to follow a jump diffusion process. We use a scaled direct control formulation of the singular control problem and examine the conditions required to ensure that a fast fixed point policy iteration scheme converges. Our methods take advantage of the special structure of the GMWB problem in order to obtain a rapidly convergent iteration. The direct control method has a scaling parameter which must be set by the user. We give estimates for bounds on the scaling parameter so that convergence can be expected in the presence of round-off error. Example computations verify that these estimates are of the correct order. Finally, we compare the scaled direct control formulation to a formulation based on a block version of the penalty method (Huang and Forsyth in IMA J Numer Anal 32:320?C351, 2012). We show that the scaled direct control method has some advantages over the penalty method.     

Heuristics for a coupled-operation scheduling problem

In this paper, we study a strongly NP-hard single machine scheduling problem in which each job consists of two operations that are separated by a time delay which lies within a specified range. The objective is to minimize the makespan. Determining the feasibility and, if applicable, makespan of any proposed permutation of the operations is non-trivial, requiring a longest path algorithm with O(n²) complexity for each permutation. Several heuristic algorithms are proposed: a deterministic and randomized construction algorithm, three descent algorithms and two reactive tabu search algorithms. The local search algorithms use a first improvement neighbourhood and mainly visit only feasible solutions within the search space. Results of extensive computational tests are reported, showing that the heavy computational burden of testing potential solutions renders the local search algorithms uncompetitive in comparison to the construction algorithms. The iterated descent algorithm performs least well.     

A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm

The Vehicle Routing Problem (VRP) is one of the most well studied problems in operations research, both in real life problems and for scientific research purposes. During the last 50 years a number of different formulations have been proposed, together with an even greater number of algorithms for the solution of the problem. In this paper, the VRP is formulated as a problem of two decision levels. In the first level, the decision maker assigns customers to the vehicles checking the feasibility of the constructed routes (vehicle capacity constraints) and without taking into account the sequence by which the vehicles will visit the customers. In the second level, the decision maker finds the optimal routes of these assignments. The decision maker of the first level, once the cost of each routing has been calculated in the second level, estimates which assignment is the better one to choose. Based on this formulation, a bilevel genetic algorithm is proposed. In the first level of the proposed algorithm, a genetic algorithm is used for calculating the population of the most promising assignments of customers to vehicles. In the second level of the proposed algorithm, a Traveling Salesman Problem (TSP) is solved, independently for each member of the population and for each assignment to vehicles. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the average quality is less than 1%. More specifically in the set with the 14 classic instances proposed by Christofides, the quality is 0.479% and in the second set with the 20 large scale vehicle routing problems, the quality is 0.826%. The algorithm is ranked in the tenth place among the 36 most known and effective algorithms in the literature for the first set of instances and in the sixth place among the 16 algorithms for the second set of instances. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the Expanding Neighborhood Search Strategy is used.