The crew timetabling problem: An extension of the crew scheduling problem

In some urban transportation companies driving periods are short when compared with the total duty time, leading to long non-driving periods that can be used as cover time. This paper presents the Crew Timetabling Problem, an extension of the Crew Scheduling Problem in which crew timetables are obtained by levelling the cover crew resources. An objective function for this problem is proposed in order to balance the number of driving and cover crews. A Lisbon Underground case study is used to illustrate the Crew Timetabling Problem. The problem is represented in a multigraph and solved by a tabu search-based heuristic.     

A constructive approach to Noether's problem

A general method is developed to attack Noether's Problem constructively by trying to find minimal bases consisting of rational invariants which are quotients of polynomials of small degrees. This approach turns out to be successful for many small groups and for most of the classical groups with their natural representations. The applications include affirmative answers to Noether's Problem for the conformal symplectic groups CSp _2n (q), for the simple subgroups Ω _n (q) of the orthogonal groups forn andq odd, for some other subgroups of orthogonal groups and for the special unitary groups SU _n (q ²). The author was supported by the Graduate College “Modelling and Scientific Computing in Mathematics and Science” during this work     

A constraint programming-based approach to the crew scheduling problem of the Taipei mass rapid transit system

This paper addresses the crew scheduling problem for a mass rapid transit (MRT) system. The problem is to find a minimum number of duties to cover all tasks while satisfying all the hard and soft scheduling rules. Such rules are complicated in real-world operations and difficult to follow through optimization methods alone. In this paper, we propose a constraint programming (CP)-based approach to solve the problem. The approach involves a CP model for duty generation, a set covering problem model for duty optimization, and alternative ways to identify the final solution in different situations. We applied the proposed CP-based approach to solve a case problem for the Taipei MRT. Case application results using real-world data showed that our approach is capable of reducing the number of daily duties from 58 to 55 and achieving a 5.2 % savings in labor costs. We also incorporated the soft rule considerations into the CP model in order to generate alternative optimum solutions that would improve the workload balance. The coefficient of variation of the work time distribution improves significantly, falling from 21 % to approximately 5 %. Given the CP model’s comprehensive coverage of various scheduling rules, our proposed approach and models would also be applicable to other MRT systems.     

An evolutionary approach to rehabilitation patient scheduling: A case study

Focusing on real settings, this study aimed to develop an evolutionary approach based on genetic algorithm for solving the problem of rehabilitation patient scheduling to increase service quality by reducing patient waiting time and improve operation efficiency by increasing the therapy equipment utilization. Indeed, due to partial precedence constraints of rehabilitation therapies, the problem can be structured as a hybrid shop scheduling problem that has received little attention to date. In addition, a mixed integer programming model was also constructed as a benchmark to validate the solution quality with small problems. Based on empirical data from a Medical Center in Taiwan, several experiments were conducted to estimate the validity of the proposed algorithm. The results showed that the proposed algorithm can reduce patient waiting time and enhance resource utilization and thus demonstrated the practicality of the proposed algorithm. Indeed, a decision support system embedded with the developed algorithm has been implemented in this medical center.     

A solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew scheduling problem and we propose a solution approach consisting of solving a sequence of optimization problems. Furthermore, we explain why it is useful to consider such a dynamic approach and compare it with a static one. Moreover, we perform a sensitivity analysis on our main assumption that the travel times of the trips are known exactly a certain amount of time before actual operation.We provide extensive computational results on some real-world data instances of a large public transport company in the Netherlands. Due to the complexity of the vehicle and crew scheduling problem, we solve only small and medium-sized instances with such a dynamic approach. We show that the results are good in the case of a single depot. However, in the multiple-depot case, the dynamic approach does not perform so well. We investigate why this is the case and conclude that the fact that the instance has to be split in several smaller ones, has a negative effect on the performance.     

A constructive approach to the problem of program correctness

As an alternative to methods by which the correctness of given programs can be established a posteriori, this paper proposes to control the process of program generation such as to produce a priori correct programs. An example is treated to show the form that such a control might then take. This example comes from the field of parallel programming; the way in which it is treated is representative of the way in which a whole multiprogramming system has actually been constructed.     

An evolutionary approach for the target allocation problem

We propose an evolutionary approach for target allocation in tactical level land combat. The purpose is to assign friendly military units to enemy units such that the total weapon effectiveness used is minimised while the attrition goals set for the enemy units are satisfied. A repair algorithm is developed to ensure feasibility with respect to the attrition goal constraints. A tightness measure is devised to determine the population size of the genetic algorithm as a function of constraint tightness. Also, a local improvement algorithm is used to further improve the solution quality. Experimental results indicate that the genetic algorithm can find solutions with acceptable quality in reasonable computation time. Although the approach is developed for the target allocation problem, it can be adapted for other assignment problems.     

Solving the short-term electrical generation scheduling problem by an adaptive evolutionary approach

In this paper, we introduce an adaptive evolutionary approach to solve the short-term electrical generation scheduling problem (STEGS). The STEGS is a hard constraint satisfaction optimization problem. The algorithm includes various strategies proposed in the literature to tackle hard problems with constraints such as: the representation used a non-binary coding scheme that drastically reduces the search space compared with the traditional evolutionary approaches. Specialized operators are especially designed for this problem and for this kind of representation, which also includes a local search procedure. Furthermore, the algorithm is guided by an adaptive parameter control strategy. We used some very well known benchmarks for STEGS to evaluate our approach. The results are very encouraging and we have obtained new better values for all the systems tested. Our aim here is to show that evolutionary approaches can be considered as good techniques to be used to solve real-world highly constrained problems.     

A partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases

Crew scheduling for airlines requires an optimally scheduled coverage of flights with regard to given timetables. We consider the crew scheduling and assignment process for airlines, where crew members are stationed unevenly among home bases. In addition, their availability changes dynamically during the planning period due to pre-scheduled activities, such as office and simulator duties, vacancy, or requested off-duty days.We propose a partially integrated approach based on two tightly coupled components: the first constructs chains of crew pairings spaced by weekly rests, where crew capacities at different domiciles and time-dependent availabilities are considered. The second component rearranges parts of these pairing chains into individual crew schedules with, e.g., even distribution of flight time. Computational results with real-life data from an European airline are presented.     

Subgraph ejection chains and tabu search for the crew scheduling problem

The tabu search algorithms for the Crew Scheduling Problem (CSP) reported in this paper are part of a decision support system for crew scheduling management of the Lisbon Underground. The CPS is formulated as the minimum number of duties necessary to cover a pre-defined timetable under a set of contractual rules. An initial solution is constructed following a traditional run-cutting approach. Two alternative improvement algorithms are subsequently used to reduce the number of duties in the initial solution. Both algorithms are embedded in a tabu search framework: Tabu-crew takes advantage of a form of strategic oscillation for the neighbourhood search while the run-ejection algorithm considers compound moves based on a subgraph ejection chain method. Computational results are reported for a set of real problems.     

A constructive approach to the finite congruence lattice representation problem

A finite lattice is representable if it is isomorphic to the congruence lattice of a finite algebra. In this paper, we develop methods by which we can construct new representable lattices from known ones. The techniques we employ are sufficient to show that every finite lattice which contains no three element antichains is representable. We then show that if an order polynomially complete lattice is representable then so is every one of its diagonal subdirect powers. Received August 30, 1999; accepted in final form November 29, 1999.     

A hybrid evolutionary algorithm to solve the job shop scheduling problem

This paper presents a Hybrid Evolutionary Algorithm (HEA) to solve the Job Shop Scheduling Problem (JSP). Incorporating a tabu search procedure into the framework of an evolutionary algorithm, the HEA embraces several distinguishing features such as a longest common sequence based recombination operator and a similarity-and-quality based replacement criterion for population updating. The HEA is able to easily generate the best-known solutions for 90 % of the tested difficult instances widely used in the literature, demonstrating its efficacy in terms of both solution quality and computational efficiency. In particular, the HEA identifies a better upper bound for two of these difficult instances.     

A subproblem-centric model and approach to the nurse scheduling problem

The number of hospitals in Japan exceeds 10,000, and every month nurses are scheduled to shifts in about 30,000 units in total. There is serious demand for automating this scheduling task. In this paper, we introduce a mathematical programming formulation of the nurse scheduling problem in Japan, and develop a meta-heuristic approach to solve the problem. This scheduling problem is a hard combinatorial problem due to tight constraints involving such factors as the skill level of a team, the need to balance workload among nurses, and the consideration of nurses' preferences, even though the number of the nurses to be scheduled is not large, at between 20 and 40. The performance of our approach is demonstrated by the successful solution of data taken from actual scheduling problems. The proposed model and approach can be adapted for the majority of hospitals in Japan, as well as for some hospitals in other countries, and is likely applicable to many other scheduling problems in the fields of business and logistics. Key words.nurse scheduling – block-angular problem – subproblem – integer programming – relaxation – tabu search – branch-and-boundMathematics Subject Classification (1991):20E28, 20G40, 20C20     

A filter-and-fan approach to the job shop scheduling problem

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure. Our new search method, based on a filter-and-fan (F&F) procedure, uses the SBP as a subroutine to generate a starting solution and to enhance the best schedules produced. The F&F approach is a local search procedure that generates compound moves by a strategically abbreviated form of tree search. Computational results carried out on a standard set of 43 benchmark problems show that our F&F algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best of these algorithms.     

Improvement heuristic for the flow-shop scheduling problem: An adaptive-learning approach

We propose an improvement-heuristic approach for the general flow-shop problem (n/m/C_max) based on the idea of adaptive learning. The approach employs a one-pass heuristic to give a good starting solution in the search space and uses a weight parameter to perturb the data of the original problem to obtain improved solutions. The weights are then adjusted employing a learning strategy which involves reinforcement and backtracking. The learning is similar to that in neural networks. The random perturbation allows a non-deterministic local search. We apply the improvement-heuristic approach in conjunction with three well-known heuristics in the literature, namely, Palmer’s Slope Index, CDS and NEH. We test our approach on several benchmark problem sets including Taillard’s, Carlier’s, Heller’s and Reeves’. We compare our results to the best-known upper-bound solutions and find that for many problems we match the best-known upper bound. For one problem we discover a new upper bound.     

A hybrid rank-based evolutionary algorithm applied to multi-mode resource-constrained project scheduling problem

We consider the multi-mode resource-constrained project scheduling problem (MRCPSP), where a task has different execution modes characterized by different resource requirements. Due to the nonrenewable resources and the multiple modes, this problem is NP-hard; therefore, we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan.     

A constructive solution to a problem of ranking tournaments

A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd?s and J. W. Moon. By probabilistic methods, the existence of ?? ?? unrankable” tournaments was proved. On the other hand, they also mentioned the problem of explicit constructions. However, there seems to be only a few of explicit constructions of such tournaments. In this note, we give a construction of many such tournaments by using skew Hadamard difference sets which have been investigated in combinatorial design theory.     

Variational approach to a non-local identification problem related to non-linear ion transport

A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H¹-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem

This paper investigates the construction of an automatic algorithm selection tool for the multi-mode resource-constrained project scheduling problem (MRCPSP). The research described relies on the notion of empirical hardness models. These models map problem instance features onto the performance of an algorithm. Using such models, the performance of a set of algorithms can be predicted. Based on these predictions, one can automatically select the algorithm that is expected to perform best given the available computing resources. The idea is to combine different algorithms in a super-algorithm that performs better than any of the components individually. We apply this strategy to the classic problem of project scheduling with multiple execution modes. We show that we can indeed significantly improve on the performance of state-of-the-art algorithms when evaluated on a set of unseen instances. This becomes important when lots of instances have to be solved consecutively. Many state-of-the-art algorithms perform very well on a majority of benchmark instances, while performing worse on a smaller set of instances. The performance of one algorithm can be very different on a set of instances while another algorithm sees no difference in performance at all. Knowing in advance, without using scarce computational resources, which algorithm to run on a certain problem instance, can significantly improve the total overall performance.