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.

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.

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

2007 Annual Report of the Iowa Railway Finance Authority

The Iowa Railway Finance Authority (IRFA) was created in 1980 by the 68th General Assembly to provide for the financing of rail facilities, and to enhance and continue the operation of essential rail facilities. IRFA was authorized to offer financial assistance for the acquisition, rehabilitation, construction, refinancing, extension, replacement, maintenance, repair or leasing of any rail facility. The 2005 legislative session amended Iowa Code 327H.20 by assigning all repayments of IRFA and other Iowa DOT rail assistance loans to the Rail Revolving Loan and Grant Fund. In 2006, a state appropriation of $235,000 was added to the program. In 2007, $2 million was appropriated to support rail development and job growth.

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.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

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.

2008 Annual Report of the Iowa Railway Finance Authority

The Iowa Railway Finance Authority (IRFA) was created in 1980 by the 68th General Assembly to provide for the financing of rail facilities and to enhance and continue the operation of essential rail facilities. IRFA was authorized to offer financial assistance for the acquisition, rehabilitation, construction, refinancing, extension, replacement, maintenance, repair, or leasing of any rail facility. Rail Revolving Loan and Grant Program The 2005 legislative session amended Iowa Code 327H.20 by assigning all repayments of IRFA and other Iowa Department of Transportation (Iowa DOT) rail assistance loans to the Rail Revolving Loan and Grant Program (RRLGP). In addition, the following annual appropriations were allocated to the fund: • FY 2007: $235,000 • FY 2008: $2 million • FY 2009: $2 million Since the creation of the RRLGP in 2005, IRFA has awarded funding to 23 projects totaling over $7.2 million in grants and loans in its three rounds of competitive funding. These projects have pledged to create 1,672 jobs within two years of project completion and 1,361 jobs have been retained. Funded projects are associated with over $2 billion in total private capital investment. In 2008, the IRFA Board directed all available funds be used to help repair railroads devastated by summer flooding. On July 31, $3.9 million in deferred payment loans were offered to seven Iowa based railroads to allow for immediate repair of rail beds, including the cost of materials, labor and equipment.

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.

Réanimation cardio-pulmonaire et travail en équipe : réflexion autour du concept aéronautique de "Crew Resource Management"

La prise en charge intra-hospitalière des arrêts cardio-respiratoires s'appuie sur une application précoce des gestes de base de la réanimation cardio- pulmonaire (massage cardiaque, ventilation pulmonaire, défibrillation) par les soignants. À l'heure actuelle, les formations à la réanimation cardio-pulmonaire impliquent uniquement l'apprentissage de gestes techniques et de connaissances théoriques, mais omettent totalement les aspects relationnels, ainsi que les problèmes de communication et de travail en équipe. Au travers d'une revue critique de la littérature médicale et aéronautique, nous proposons une nouvelle piste de formation dans le domaine de la réanimation cardio-pulmonaire. En s'appuyant sur les travaux réalisés dans l'aviation, dans les domaines de l'erreur humaine et du travail en équipe, nous offrons finalement une adaptation du "Crew Resource Management" ainsi qu'une série de recommandations, visant à intégrer les éléments relationnels et le facteur humain dans les cours de réanimations cardio-pulmonaires.

Method to assess and optimise dependability of complex macro-systems: application to a railway signalling system

Achieving a high degree of dependability in complex macro-systems is challenging. Because of the large number of components and numerous independent teams involved, an overview of the global system performance is usually lacking to support both design and operation adequately. A functional failure mode, effects and criticality analysis (FMECA) approach is proposed to address the dependability optimisation of large and complex systems. The basic inductive model FMECA has been enriched to include considerations such as operational procedures, alarm systems. environmental and human factors, as well as operation in degraded mode. Its implementation on a commercial software tool allows an active linking between the functional layers of the system and facilitates data processing and retrieval, which enables to contribute actively to the system optimisation. The proposed methodology has been applied to optimise dependability in a railway signalling system. Signalling systems are typical example of large complex systems made of multiple hierarchical layers. The proposed approach appears appropriate to assess the global risk- and availability-level of the system as well as to identify its vulnerabilities. This enriched-FMECA approach enables to overcome some of the limitations and pitfalls previously reported with classical FMECA approaches.

Linking Real Time and Location in Scheduling Demand-Responsive Transit, September 1996

The role of rural demand-responsive transit is changing, and with that change is coming an increasing need for technology. As long as rural transit was limited to a type of social service transportation for a specific set of clients who primarily traveled in groups to common meal sites, work centers for the disabled, or clinics in larger communities, a preset calendar augmented by notes on a yellow legal pad was sufficient to develop schedules. Any individual trips were arranged at least 24 to 48 hours ahead of time and were carefully scheduled the night before in half-hour or twenty-minute windows by a dispatcher who knew every lane in the service area. Since it took hours to build the schedule, any last-minute changes could wreak havoc with the plans and raise the stress level in the dispatch office. Nevertheless, given these parameters, a manual scheduling system worked for a small demand-responsive operation.