Rollout Algorithms for Stochastic Scheduling Problems

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.     

Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period

In this article, we consider the single machine scheduling problem with one planned setup period, with the aim of minimizing the weighted sum of the completion times. We study the WSPT and MWSPT heuristics and we show that the worst-case performance ratio is 3 for the two heuristics in some cases and it is unbounded otherwise. We also show that these worst-case performance ratios are tight.     

Pareto optimality and a class of set covering heuristics

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.     

Crossdocking—JIT scheduling with time windows

In this paper, we study a problem central to crossdocking that aims to eliminate or minimize storage and order picking activity using JIT scheduling. The problem is modelled naturally as a machine scheduling problem. As the problem is NP-hard, and for real-time applications, we designed and implemented two heuristics. The first uses Squeaky Wheel Optimization embedded in a Genetic Algorithm and the second uses Linear Programming within a Genetic Algorithm. Both heuristics offer good solutions in experiments where comparisons are made with the CPLEX solver.     

Generalized Pinwheel Problem

This paper studies a non-preemptive infinite-horizon scheduling problem with a single server and a fixed set of recurring jobs. Each job is characterized by two given positive numbers: job duration and maximum allowable time between the job completion and its next start. We show that for a feasible problem there exists a periodic schedule. We also provide necessary conditions for the feasibility, formulate an algorithm based on dynamic programming, and, since this problem is NP-hard, formulate and study heuristic algorithms. In particular, by applying the theory of Markov Decision Process, we establish natural necessary conditions for feasibility and develop heuristics, called frequency based algorithms, that outperform standard scheduling heuristics.     

New solution methods for single machine bicriteria scheduling problem: Minimization of average flowtime and number of tardy jobs

We consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine. This problem, which is known to be NP-hard, is important in practice, as the former criterion conveys the customer’s position, and the latter reflects the manufacturer’s perspective in the supply chain. We propose four new heuristics to solve this multiobjective scheduling problem. Two of these heuristics are constructive algorithms based on beam search methodology. The other two are metaheuristic approaches using a genetic algorithm and tabu-search. Our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature.     

A hybrid scatter search/electromagnetism meta-heuristic for project scheduling

In the last few decades, several effective algorithms for solving the resource-constrained project scheduling problem have been proposed. However, the challenging nature of this problem, summarised in its strongly NP-hard status, restricts the effectiveness of exact optimisation to relatively small instances. In this paper, we present a new meta-heuristic for this problem, able to provide near-optimal heuristic solutions for relatively large instances. The procedure combines elements from scatter search, a generic population-based evolutionary search method, and from a recently introduced heuristic method for the optimisation of unconstrained continuous functions based on an analogy with electromagnetism theory. We present computational experiments on standard benchmark datasets, compare the results with current state-of-the-art heuristics, and show that the procedure is capable of producing consistently good results for challenging instances of the resource-constrained project scheduling problem. We also demonstrate that the algorithm outperforms state-of-the-art existing heuristics.     

A Neural Network Application in Personnel Scheduling

In this paper, we present and evaluate a neural network model for solving a typical personnel-scheduling problem, i.e. an airport ground staff rostering problem. Personnel scheduling problems are widely found in servicing and manufacturing industries. The inherent complexity of personnel scheduling problems has normally resulted in the development of integer programming-based models and various heuristic solution procedures. The neural network approach has been admitted as a promising alternative to solving a variety of combinatorial optimization problems. While few works relate neural network to applications of personnel scheduling problems, there is great theoretical and practical value in exploring the potential of this area. In this paper, we introduce a neural network model following a relatively new modeling approach to solve a real rostering case. We show how to convert a mixed integer programming formulation to a neural network model. We also provide the experiment results comparing the neural network method with three popular heuristics, i.e. simulated annealing, Tabu search and genetic algorithm. The computational study reveals some potential of neural networks in solving personnel scheduling problems.     

Heuristics for unrelated machine scheduling with precedence constraints

In this paper, we consider the problem of scheduling tasks on unrelated parallel machines. Precedence constraints between the tasks form chains of tasks. We propose a number of heuristics in order to find near optimal solutions to the problem. Empirical results show that the heuristics are able to find very good approximate solutions.     

Efficient Batch Job Scheduling in Grids Using Cellular Memetic Algorithms

Computational grids are an important emerging paradigm for large-scale distributed computing. As grid systems become more wide-spread, techniques for efficiently exploiting the large amount of grid computing resources become increasingly indispensable. A key aspect in order to benefit from these resources is the scheduling of jobs to grid resources. Due to the complex nature of grid systems, the design of efficient grid schedulers becomes challenging since such schedulers have to be able to optimize many conflicting criteria in very short periods of time. This problem has been tackled in the literature by several different metaheuristics, and our main focus in this work is to develop a new highly competitive technique with respect to the existing ones. For that, we exploit the capabilities of cellular memetic algorithms (cMAs), a kind of memetic algorithm with structured population, for obtaining efficient batch schedulers for grid systems, and the obtained results will be compared versus the state of the art. A careful design of the cMA methods and operators for the problem yielded to an efficient and robust implementation. Our experimental study, based on a known static benchmark for the problem, shows that this heuristic approach is able to deliver very high quality planning of jobs to grid nodes and thus it can be used to design efficient dynamic schedulers for real grid systems. Such dynamic schedulers can be obtained by running the cMA-based scheduler in batch mode for a very short time to schedule jobs arriving in the system since the last activation of the cMA scheduler. This work has been partially funded by the Spanish MEC and FEDER under contract TIN2005-08818-C04-01 (the OPLINK project: ).     

Single Machine Scheduling with Learning Effect Considerations

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.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

Parallel multiobjective evolutionary algorithms for batch scheduling in heterogeneous computing and grid systems

This article presents six parallel multiobjective evolutionary algorithms applied to solve the scheduling problem in distributed heterogeneous computing and grid systems. The studied evolutionary algorithms follow an explicit multiobjective approach to tackle the simultaneous optimization of a system-related (i.e. makespan) and a user-related (i.e. flowtime) objectives. Parallel models of the proposed methods are developed in order to efficiently solve the problem. The experimental analysis demonstrates that the proposed evolutionary algorithms are able to efficiently compute accurate results when solving standard and new large problem instances. The best of the proposed methods outperforms both deterministic scheduling heuristics and single-objective evolutionary methods previously applied to the problem.     

Parallel machine scheduling problems with a single server

In this paper, we consider the problem of scheduling jobs on parallel machines with setup times. The setup has to be performed by a single server. The objective is to minimize the schedule length (makespan), as well as the forced idle time. The makespan problem is known to be NP-hard even for the case of two identical parallel machines. This paper presents a pseudopolynomial algorithm for the case of two machines when all setup times are equal to one. We also show that the more general problem with an arbitrary number of machines is unary NP-hard and analyze some list scheduling heuristics for this problem. The problem of minimizing the forced idle time is known to be unary NP-hard for the case of two machines and arbitrary setup and processing times. We prove unary NP-hardness of this problem even for the case of constant setup times. Moreover, some polynomially solvable cases are given.     

Minimizing makespan in a two-stage hybrid flow shop scheduling problem with open shop in one stage

This paper considers a scheduling problem in two-stage hybrid flow shop, where the first stage consists of two machines formed an open shop and the other stage has only one machine. The objective is to minimize the makespan, i.e., the maximum completion time of all jobs. We first show the problem is NP-hard in the strong sense, then we present two heuristics to solve the problem. Computational experiments show that the combined algorithm of the two heuristics performs well on randomly generated problem instances.     

Optimization models for assessing the peak capacity utilization of intelligent transportation systems

With limited economic and physical resources, it is not feasible to continually expand transportation infrastructure to adequately support the rapid growth in its usage. This is especially true for traffic coordination systems where the expansion of road infrastructure has not been able to keep pace with the increasing number of vehicles, thereby resulting in congestion and delays. Hence, in addition to striving for the construction of new roads, it is imperative to develop new intelligent transportation management and coordination systems. The effectiveness of a new technique can be evaluated by comparing it with the optimal capacity utilization. If this comparison indicates that substantial improvements are possible, then the cost of developing and deploying an intelligent traffic system can be justified. Moreover, developing an optimization model can also help in capacity planning. For instance, at a given level of demand, if the optimal solution worsens significantly, this implies that no amount of intelligent strategies can handle this demand, and expanding the infrastructure would be the only alternative. In this paper, we demonstrate these concepts through a case study of scheduling vehicles on a grid of intersecting roads. We develop two optimization models namely, the mixed integer programming model and the space-time network flow model, and show that the latter model is substantially more effective. Moreover, we prove that the problem is strongly NP-hard and develop two polynomial-time heuristics. The heuristic solutions are then compared with the optimal capacity utilization obtained using the space-time network model. We also present important managerial implications.     

Market-based pricing in grids: On strategic manipulation and computational cost

Grid technologies and the related concepts of utility computing and cloud computing enable the dynamic sourcing of computer resources and services, thus allowing enterprises to cut down on hardware and software expenses and to focus on key competencies and processes. Resources are shared across administrative boundaries, e.g. between enterprises and/or business units. In this dynamic and inter-organizational setting, scheduling and pricing become key challenges. Market mechanisms show promise for enhancing resource allocation and pricing in grids. Current mechanisms, however, are not adequately able to handle large-scale settings with strategic users and providers who try to benefit from manipulating the mechanism. In this paper, a market-based heuristic for clearing large-scale grid settings is developed. The proposed heuristic and pricing schemes find an interesting match between scalability and strategic behavior.     

Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times

In this paper we study the problem of scheduling n jobs on a single machine with availability constraints. The objective is to minimize total weighted job completion times. We show that the problem is NP-hard in the strong sense. Then we consider two intractable special cases, namely, proportional weight case, and single availability constraint case. We propose two heuristics for these cases and analyze their worst-case error bounds.     

Single Machine Scheduling with a Common Delivery Window

In this paper we consider the single machine scheduling problem of minimizing the mean absolute deviation (MAD) of job completion times from a restricted common delivery window. This problem is NP-hard. A Lagrangian relaxation procedure is proposed to solve the problem. Two efficient heuristics are also proposed. An experimental study on randomly generated problems is carried out to test the performance of the proposed methods. The computational results show that the obtained lower bounds are very good and the proposed heuristics generate near-optimal solutions.     

No-wait flowshops with bicriteria of makespan and total completion time

We consider the m-machine no-wait flowshop scheduling problem with the objective of minimizing a weighted sum of makespan and total completion time. For the two-machine problem, we develop a dominance relation and embed it within a proposed branch-and-bound algorithm. For the m-machine problem, we propose a heuristic. Computational experiments show that the proposed heuristic outperforms the best existing multi-criteria heuristics and the best single criterion heuristics for makespan and total completion time. The efficiency of the dominance relation and branch-and-bound algorithm is also investigated and shown to be effective.