Duration automation in scheduling program for a cluster computer system

The rise of the engine remanufacturing industry has resulted in increased possibilities of energy conservation during the remanufacturing process, and scheduling could exert significant effects on the energy performance of manufacturing systems. However, only a few studies have specifically addressed energy-efficient scheduling for remanufacturing. Considering the uncertain processing time and routes and the operation characteristics of remanufacturing, we used the crankshaft as an illustrative case and built a fuzzy job-shop scheduling model to minimize the energy consumption during remanufacturing. An improved adaptive genetic algorithm was developed by using the hormone modulation mechanism to deal with the scheduling problem that simultaneously involves parallel machines, batch machines, and uncertain processing routes and time. The algorithm demonstrated superior performance in terms of optimal value, run time, and convergent generation in comparison with other algorithms. Computational results indicated that the optimal scheduling scheme is expected to generate 1.7 kW · h of energy saving for the investigated problem size. In addition, the scheme could improve the energy efficiency of the crankshaft remanufacturing process by approximately 5%. This study provides a basis for production managers to improve the sustainability of remanufacturing through energy-aware scheduling.

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time (1+varepsilon )-approximation algorithm that yields an (e+varepsilon )-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with optimal cost at 1+varepsilon speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most log n many classes. This algorithm allows the jobs even to have up to log n many distinct release dates. All proposed quasi-polynomial time algorithms require the input data to be quasi-polynomially bounded.

In this thesis, we study the theoretical approach on energy-efficient scheduling problems arising in demand response management in the modern electrical smart grid. Consumers send in power requests with flexible feasible timeslots during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. We study the smart grid scheduling problem in different models. For the offline model, we prove the problem is NP-hard for the general case. We propose a polynomial time algorithm for special input where jobs have unit power request and unit time duration. By adapting the polynomial time algorithm for unit-size jobs, we propose an approximation algorithm for more general input. On the other hand, we also present an exact algorithm to find the optimal schedule for the problem with general input. For the online model, we propose an online algorithm for jobs with jobs with arbitrary power request, arbitrary time duration, and arbitrary contiguous feasible intervals. We also show a lower bound of the competitive ratio for the smart grid scheduling problem with unit height and arbitrary width. For special cases, we design different online algorithms with better competitive ratios. Finally, we look at other optimization problems and show how to solve them by adapting our techniques. We prove that our online algorithm can solve the machine minimization problem with an asymptotically optimal competitive ratio. We also show that our exact algorithm can be adapted to solve other demand response management problems.

This paper presents a predictive robust and stable approach for a two-machine flow shop scheduling problem with machine disruption and uncertain job processing time. Indeed, a general approach is proposed that can be used for robustness and stability optimization in an m-machine flow shop or job shop scheduling problem. The robustness measure is the total expected realized completion time. The expected sum of squared aberration between each jobs’ completion time in the realized and initial schedules is the stability measure. We proposed and compared two methods to deal with such an NP-hard problem; a method based on decomposing the problem into sub-problem and solving each sub-problem, and a theorem-based method. The extensive computational results indicated that the second method has a better performance in terms of robustness and stability, especially in large-sized problems. In other words, the second method is preferable because of the better manufacturer responsiveness to the customer and the production staff satisfaction enhancement.

Two-station single-track railway scheduling problem with trains of equal speed

The flow set with partial order is a mixed-integer set described by a budget on total flow and a partial order on the arcs that may carry positive flow. This set is a common substructure of resource allocation and scheduling problems with precedence constraints and robust network flow problems under demand/capacity uncertainty. We give a polyhedral analysis of the convex hull of the flow set with partial order. Unlike for the flow set without partial order, cover-type inequalities based on partial order structure are a function of a lifting sequence. We study the lifting sequences and describe structural results on the lifting coefficients for general and simpler special cases. We show that all lifting coefficients can be computed in polynomial time by solving maximum weight closure problems in general. For the special case of induced-minimal covers, we give a sequence-dependent characterization of the lifting coefficients. We prove, however, if the partial order is defined by an arborescence, then lifting is sequence-independent and all lifting coefficients can be computed in linear time. Moreover, if the partial order is defined by a path (total order), then the coefficients can be expressed explicitly. We also give a complete polyhedral description of the flow set with partial order for the polynomially-solvable total order case. We show that finding an optimal lifting order for a given induced-minimal cover and a given fractional solution is a submodular optimization problem, which is solved greedily. Finally, we present preliminary computational results with a cutting-plane algorithm based on the lifting and separation results.

Cell association is a significant research issue in future mobile communication systems due to the unacceptably large computational time of traditional schemes. This article proposes a polynomial-time cell association scheme which not only completes the association in polynomial time but also fits for a generic optimization objective function. On the one hand, traditional cell association as a non-deterministic polynomial (NP) hard problem with a generic utility function is heuristically transformed into a 2-dimensional assignment optimization and solved by a certain polynomial-time algorithm, which significantly saves computational time. On the other hand, the scheme jointly considers utility maximization and load balancing among multiple base stations (BSs) by maintaining an experience pool storing a set of weighting factor values and their corresponding performances. When an association optimization is required, a suitable weighting factor value is taken from the pool to calculate a long square utility matrix and a certain polynomial-time algorithm will be applied for the association. Comparing with several representative schemes, the proposed scheme achieves large system capacity and high fairness within a relatively short computational time.

We consider the problem of scheduling jobs on a batching machine to minimize maximum lateness. Two batch processing modes, serial batch (s-batch) and parallel batch (p-batch), are considered. We first describe the exact algorithms for the s-batch and p-batch scheduling problems. We then present a robust extension to classical problems in which uncertain processing times are represented by a budgeted uncertainty set. Given a solution, we demonstrate efficient algorithms to evaluate the solution under its worst-case scenario for both s-batch and p-batch robust scheduling problems. For the s-batch robust scheduling problem, we propose an exact algorithm that has the same time complexity as the classical problem. For the p-batch robust scheduling problem, we design a heuristic algorithm that provides both upper and lower bounds on the optimal value. Computational results show that the proposed heuristic performs satisfactorily.

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, when we attempt to formulate job shop scheduling problems which closely describe and represent the real world problem, various factors involved are often imprecisely or ambiguously known to the analyst. Also, in the real situations, machines are not continuously available due to preventive maintenance activity. Besides, in the production system, there are many users and machines in various priorities. Often, user satisfactions, machine stability and schedule itself are in conflict. By considering the imprecise or fuzzy nature of the data in real world problem, job shop scheduling with uncertain processing time and machine available constraint is introduced. Under the fuzzy circumstance, we attempt to make a feasible solution for flexible job shop scheduling problem (FJSSP) based on a hybrid optimization approach with multi-objective which not only to minimize the makespan, but also maximize the user satisfaction and machine stability. In the experiment, we make the comparisons with some other algorithms, such as genetic algorithm, to demonstrate the hybrid approach is much better on efficient search and stability with three benchmark examples. Sensitivity analysis is conducted to study the impact, in term of total objective, when the proportion of machine stability is varied.

We consider the classic scheduling problem of minimizing the total weighted flow-time on a single machine (min-WPFT), when preemption is allowed. In this problem, we are given a set of $n$ jobs, each job having a release time $r_j$, a processing time $p_j$, and a weight $w_j$. The flow-time of a job is defined as the amount of time the job spends in the system before it completes; that is, $F_j = C_j - r_j$, where $C_j$ is the completion time of job. The objective is to minimize the total weighted flow-time of jobs. This NP-hard problem has been studied quite extensively for decades. In a recent breakthrough, Batra, Garg, and Kumar presented a {\em pseudo-polynomial} time algorithm that has an $O(1)$ approximation ratio. The design of a truly polynomial time algorithm, however, remained an open problem. In this paper, we show a transformation from pseudo-polynomial time algorithms to polynomial time algorithms in the context of min-WPFT. Our result combined with the result of Batra, Garg, and Kumar settles the long standing conjecture that there is a polynomial time algorithm with $O(1)$-approximation for min-WPFT.

In this book, we have concentrated on those optimization problems which allow efficient (that is, polynomial time) algorithms. In contrast, the final chapter deals with an archetypical NP-complete problem: the travelling salesman problem already introduced in Chap. 1. It is one of the most famous and important problems in all of combinatorial optimization—with manyfold applications in such diverse areas as logistics, genetics, telecommunications, and neuroscience—and has been the subject of extensive study for about 60 years. We saw in Chap. 2 that no efficient algorithms are known for NP-complete problems, and that it is actually quite likely that no such algorithms can exist. Now we address the question of how such hard problems—which regularly occur in practical applications—might be approached: one uses, for instance, approximation techniques, heuristics, relaxations, post-optimization, local search, and complete enumeration. We shall explain these methods only for the TSP, but they are typical for dealing with hard problems in general. We will also brie y explain the idea of a further extremely important approach—via polyhedra—to solving hard problems and present a list of notable large scale TSPs which were solved to optimality.KeywordsMinimal Span TreeTravel Salesman ProblemLarge InstanceLocal Search AlgorithmHamiltonian PathThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In order to enhance the production efficiency, scheduling problem of job-shop has used that thought of complex problem with complicated constraints and structure. This problem is characterized as NP-hard. In most cases, the excessive complexity of the problem makes it difficult to discover the best solution within affordable time. Hence, searching for estimated solutions in polynomial time rather than precise solutions at excessive cost is favored for challenging situations of the problem. In this paper, a parallel genetic algorithm with proposed adaptive genetic operators and migration operation is applied for job-shop scheduling problem. Through tests on numerous different experimental cases, the adaptive operator of genetic algorithm and the parallelism strategy are considerably improving the results effectively while decreasing the computation time. Also, the migration operation gives a greater effect on the performance of the algorithms.

We consider the problem of scheduling tasks on multiprocessor architectures in the presence of communication delays. Given a set of dependent tasks, the scheduling problem is to allocate the tasks to processors such that the pre-specified precedence constraints among the tasks are obeyed and certain cost-measures (such as the computation time) are minimized. Several cases of the scheduling problem have

The steelmaking-continuous casting production scheduling problem with uncertain processing time (UPT) is studied, especially for the case that the charges have complex technical routes. In order to compensate the temperature dropping of the charges and minimize the electric power cost under the time-of-use (TOU) electricity price, a left-right hybrid adjustment method based on a critical charge is proposesd to adjust the LF refining time. In addition, considering that the basic processing time of the charges and the start casting time of the first cast are uncertain, a cascade cross entropy algorithm (CCEA) is proposed to solve the steelmaking-continuous casting production scheduling problem. Two different simulation instances are designed to validate the good effect of the problem we considered in reducing the electric power cost.

Scheduling with uncertain processing times in mixed-criticality systems