A simple optimised search heuristic for the job-shop scheduling problem

This paper presents a simple Optimised Search Heuristic for the Job Shop Scheduling problem that combines a GRASP heuristic with a branch-and-bound algorithm. The proposed method is compared with similar approaches and leads to better results in terms of solution quality and computing times.

A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

Solving two production scheduling problems with sequence-dependent set-up times

In today’s competitive markets, the importance of goodscheduling strategies in manufacturing companies lead to theneed of developing efficient methods to solve complexscheduling problems.In this paper, we studied two production scheduling problemswith sequence-dependent setups times. The setup times areone of the most common complications in scheduling problems,and are usually associated with cleaning operations andchanging tools and shapes in machines.The first problem considered is a single-machine schedulingwith release dates, sequence-dependent setup times anddelivery times. The performance measure is the maximumlateness.The second problem is a job-shop scheduling problem withsequence-dependent setup times where the objective is tominimize the makespan.We present several priority dispatching rules for bothproblems, followed by a study of their performance. Finally,conclusions and directions of future research are presented.

The crew-scheduling module in the GIST system

The public transportation is gaining importance every year basically duethe population growth, environmental policies and, route and streetcongestion. Too able an efficient management of all the resources relatedto public transportation, several techniques from different areas are beingapplied and several projects in Transportation Planning Systems, indifferent countries, are being developed. In this work, we present theGIST Planning Transportation Systems, a Portuguese project involving twouniversities and six public transportation companies. We describe indetail one of the most relevant modules of this project, the crew-scheduling module. The crew-scheduling module is based on the application of meta-heuristics, in particular GRASP, tabu search and geneticalgorithm to solve the bus-driver-scheduling problem. The metaheuristicshave been successfully incorporated in the GIST Planning TransportationSystems and are actually used by several companies.

ILS-ESP An efficient, simple, and parameter-free algorithm for solving the permutation flow-shop problem

From a managerial point of view, the more effcient, simple, and parameter-free (ESP) an algorithm is, the more likely it will be used in practice for solving real-life problems. Following this principle, an ESP algorithm for solving the Permutation Flowshop Sequencing Problem (PFSP) is proposed in this article. Using an Iterated Local Search (ILS) framework, the so-called ILS-ESP algorithm is able to compete in performance with other well-known ILS-based approaches, which are considered among the most effcient algorithms for the PFSP. However, while other similar approaches still employ several parameters that can affect their performance if not properly chosen, our algorithm does not require any particular fine-tuning process since it uses basic "common sense" rules for the local search, perturbation, and acceptance criterion stages of the ILS metaheuristic. Our approach defines a new operator for the ILS perturbation process, a new acceptance criterion based on extremely simple and transparent rules, and a biased randomization process of the initial solution to randomly generate different alternative initial solutions of similar quality -which is attained by applying a biased randomization to a classical PFSP heuristic. This diversification of the initial solution aims at avoiding poorly designed starting points and, thus, allows the methodology to take advantage of current trends in parallel and distributed computing. A set of extensive tests, based on literature benchmarks, has been carried out in order to validate our algorithm and compare it against other approaches. These tests show that our parameter-free algorithm is able to compete with state-of-the-art metaheuristics for the PFSP. Also, the experiments show that, when using parallel computing, it is possible to improve the top ILS-based metaheuristic by just incorporating to it our biased randomization process with a high-quality pseudo-random number generator.

Optimised search heuristic combining valid inequalities and tabu search

This paper presents an Optimised Search Heuristic that combines a tabu search method with the verification of violated valid inequalities. The solution delivered by the tabu search is partially destroyed by a randomised greedy procedure, and then the valid inequalities are used to guide the reconstruction of a complete solution. An application of the new method to the Job-Shop Scheduling problem is presented.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Metaheuristics for the bus-driver scheduling problem

We present new metaheuristics for solving real crew scheduling problemsin a public transportation bus company. Since the crews of thesecompanies are drivers, we will designate the problem by the bus-driverscheduling problem. Crew scheduling problems are well known and severalmathematical programming based techniques have been proposed to solvethem, in particular using the set-covering formulation. However, inpractice, there exists the need for improvement in terms of computationalefficiency and capacity of solving large-scale instances. Moreover, thereal bus-driver scheduling problems that we consider can present variantaspects of the set covering, as for example a different objectivefunction, implying that alternative solutions methods have to bedeveloped. We propose metaheuristics based on the following approaches:GRASP (greedy randomized adaptive search procedure), tabu search andgenetic algorithms. These metaheuristics also present some innovationfeatures based on and genetic algorithms. These metaheuristics alsopresent some innovation features based on the structure of the crewscheduling problem, that guide the search efficiently and able them tofind good solutions. Some of these new features can also be applied inthe development of heuristics to other combinatorial optimizationproblems. A summary of computational results with real-data problems ispresented.

Solving a concrete sleepers production scheduling by genetic algorithms

PRECON S.A is a manufacturing company dedicated to produce prefabricatedconcrete parts to several industries as rail transportation andagricultural industries.Recently, PRECON signed a contract with RENFE,the Spanish Nnational Rail Transportation Company to manufacturepre-stressed concrete sleepers for siding of the new railways of the highspeed train AVE. The scheduling problem associated with the manufacturingprocess of the sleepers is very complex since it involves severalconstraints and objectives. The constraints are related with productioncapacity, the quantity of available moulds, satisfying demand and otheroperational constraints. The two main objectives are related withmaximizing the usage of the manufacturing resources and minimizing themoulds movements. We developed a deterministic crowding genetic algorithmfor this multiobjective problem. The algorithm has proved to be a powerfuland flexible tool to solve the large-scale instance of this complex realscheduling problem.

Note on the blocking flow shop problem

We present some results attained with different algorithms for the Fm|block|Cmax problem using as experimental data the well-known Taillard instances.

A hybrid algorithm combining metaheuristic with Monte Carlo simulation for solving the Stochastic Flow Shop problem

In this paper, a hybrid simulation-based algorithm is proposed for the StochasticFlow Shop Problem. The main idea of the methodology is to transform the stochastic problem into a deterministic problem and then apply simulation to the latter. In order to achieve this goal, we rely on Monte Carlo Simulation and an adapted version of a deterministic heuristic. This approach aims to provide flexibility and simplicity due to the fact that it is not constrained by any previous assumption and relies in well-tested heuristics.

A hybrid algorithm combining metaheuristic with Monte Carlo simulation for solving the Stochastic Flow Shop problem

In this paper, a hybrid simulation-based algorithm is proposed for the StochasticFlow Shop Problem. The main idea of the methodology is to transform the stochastic problem into a deterministic problem and then apply simulation to the latter. In order to achieve this goal, we rely on Monte Carlo Simulation and an adapted version of a deterministic heuristic. This approach aims to provide flexibility and simplicity due to the fact that it is not constrained by any previous assumption and relies in well-tested heuristics.