Two-stage heuristic procedure for scheduling job shops

We present a jointly optimal selection and scheduling scheme for the lossy transmission of frames governed by a dependency relation and a delay constraint over a link with limited capacity. A main application for this is scalable video streaming. Our objective is to select a subset of frames and decide their transmission schedule such that the overall video quality at the receiver is maximized. The problem is solved for two of the most common classes of dependency structures for video encoding, which include as a special case the popular hierarchical dyadic structure. We formally characterize the structural properties of an optimal transmission schedule in terms of frame dependency. It is shown that regardless of the subset of frames selected for transmission, any optimal schedule has an equivalent canonical form that is a subsequence of a unique universal sequence containing all frames. The canonical form can be computed efficiently through the construction of a dependency tree. This leads to separable but jointly optimal frame selection and scheduling algorithms that have quadratic computational complexity in the number of frames. Simulation with video traces demonstrates that the optimal scheme can substantially outperform existing suboptimal alternatives.

In the Digital Age, many new tools have emerged through the use of advanced monitoring systems and relatively low cost, powerful computation. In particular, system Reliability increases have been achieved through various applications of remote monitoring. Mathematical optimization applied to scheduling has been used in many industries to lower costs successfully, generally as a planning tool. More recently, it has found application in day-to-day operational planning for the heavy industries of power generation and oil and gas, since computation time has decreased down to minutes instead of days. Combining this with the powerful improvements in statistical and machine learning forecasting, the intersection of these domains has resulted in operational optimization. Combining maintenance planning models into the operational optimization framework provides operators with the opportunity to extend maintenance intervals purely based on optimized scheduling, which costs nearly nothing compared with having to purchase new parts to achieve extended time between maintenance. When the application involves drivers utilizing carbon based fuels, it is often true that the optimized schedule results in reduced emissions compared with typical base-case operation, which in many locations can result in further cost reductions. In this paper we propose a framework for scheduling machines at a particular location such that no machine exceeds a certain threshold, t¯, in running time. In particular, the solution attempts to push the facility-wide time between maintenance sessions to some operator defined limit higher than any individual unit’s required time between maintenance. The framework utilizes Mixed Integer Programming with partially stochastic demand forecasts to solve for optimal running schedules through Monte Carlo simulation. Optimality of a running schedule is based on multiple factors including ability to meet the demand forecast, number of starts required, start-reliability and possible over-fire of engines. The resulting set of solutions provide a likelihood of success in reaching a given site level extended time between maintenance. Operators can use this framework to determine how far the time between maintenance can be extended and determine the probability that a given extension can actually be realized at the physical site. This framework can also be used at managerial levels that consider personnel planning and future capital expenditures.

We consider a reader-writer system consisting of a single server and a fixed number of jobs (or customers) belonging to two classes. Class one jobs are called readers and any number of them can be processed simultaneously. Class two jobs are called writers and they have to be processed one at a time. When a writer is being processed no other writer or readers can be processed. A fixed number of readers and writers are ready for processing at time 0. Their processing times are independent random variables. Each reader and writer has a fixed waiting cost rate. We find optimal scheduling rules that minimize the expected total waiting cost (expected total weighted flowtime). We consider both nonpreemptive and preemptive scheduling. The optimal nonpreemptive schedule is derived by a variation of the usual interchange argument, while the optimal schedule in the preemptive case is given by a Gittins index policy. These index policies continue to be optimal for systems in which new writers enter the system in a Poisson fashion.

SummaryModern power systems are being shifted its attention towards distributed generations (DGs). DGs have allured more concern as an auspicious opportunity with considerable economic profits. To minimize the power generation costs of DGs, day‐to‐day operation scheduling is essential. The role of this study is to offer an optimal operation schedule for DG with several energy sources including renewable energy sources (RES), considering economic facets. In order to achieve the cost minimization along with optimal scheduling, an objection function has been formulated and solved using the optimization algorithms. This study aims to present the applications of differential evolution (DE) algorithm and its variants such as opposition‐based differential evolution (ODE), self‐adaptive differential evolution (SaDE), improved differential evolution (IDE), and cultivated differential evolution (CuDE) for scheduling DG optimally. A scheme for optimal scheduling of thermal, wind power, and solar PV generators has been evaluated. The simulations have been carried out on IEEE 14 bus system, IEEE 30 bus system, IEEE 57 bus system, and Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO), as a real part of 62 bus Indian utility system (IUS). The novelty of this study lies in simulating a real‐time system for solving optimal scheduling problem, in that way helping decision makers to choose the optimal operation points. The results indicate that the SaDE outperformed other DE variants by giving the best fitness value and convergence rate.

In this paper, we consider a cellular/infostation integrated network that supports on-demand data service delivery over a wireless link to users in a high-speed train. For the requests with different lifetimes and prices that they are willing to pay, we develop the optimal packet schedule that aims at earning the maximum revenue. To this end, we formulate the problem as an integer linear program (ILP). The problem cannot be solved efficiently by existing ILP solvers with guaranteed polynomial-time complexity in the worst case. By exploring the special structure of the formulated ILP, we propose a novel Checker algorithm and prove that this algorithm is guaranteed to find the offline optimal schedule in polynomial time. Based on the relevant insights, we further develop a class of online Checker algorithms that require only causal knowledge of service demands and wireless channel capacities. It is established that these online algorithms have a worst-case competitive ratio of 1/2, i.e., total revenue earned by them is at least half as much as the revenue earned by an offline optimal schedule that knows the complete a priori knowledge of future requests and channel conditions. Simulation results are provided to demonstrate the merit of the proposed algorithms.

It is a great challenge to find an optimal one-wafer cyclic schedule for a single-arm multicluster tool that is widely adopted in semiconductor fabrication. Aiming to tackle this significant problem, an optimal scheduling strategy is determined first for each individual tool under the condition that the bottleneck individual tool is transport-bound. Then, by developing a Petri net model with robot waiting being explicitly described to reveal the properties of the entire system, this paper shows that to schedule such a tool optimally is to allocate the robot waiting time properly. Then, this paper presents the necessary and sufficient conditions for the existence of an optimal one-wafer cyclic schedule. Thereafter, an efficient algorithm is developed to check the given conditions and find such a schedule efficiently if existing. Finally, two industrial examples are used to verify that the proposed method is applicable and effective.

A set of tasks {T1, T2, ..., Tr] are to be scheduled on a two-processor computing system. The execution time of each of the tasks is given. Moreover, a partial ordering ≪ over the set of tasks is specified. If Ti ≪ Tj, it is required that the execution of Tj will not begin until the completion of the execution of Ti. Let ω denote the total elapsed time for the execution of all the tasks in the set when an optimal non-preemptive schedule is used. Let ω′ denote the total elapsed time for the execution of all the tasks in the set when an optimal preemptive schedule is used. Trivially, we know that ω ≥ ω′ However, it can be shown that ω′ ≥ 3/4 ω This result can be extended to an n-processor computing system. In this case, ω′ ≥ n+1/2n ω Moreover, these are best possible bounds. A possible interpretation of the results is: The installation of a high speed drum in a two-processor computing system will increase the operation speed of the system by at most 25%. For an n-processor system, the increment is at most 50%. (The installation of a high speed drum enables us to interrupt the execution of tasks at will.)

Approximate optimal periodic scheduling of multiple sensors with constraints

We analyze a human and multi-robot collaboration system and propose a method to optimally schedule the human attention when a human operator receives collaboration requests from multiple robots at the same time. We formulate the human attention scheduling problem as a binary optimization problem which aims to maximize the overall performance among all the robots, under the constraint that a human has limited attention capacity. We first present the optimal schedule for the human to determine when to collaborate with a robot if there is no contention occurring among robots' collaboration requests. For the moments when contentions occur, we present a contention-resolving Model Predictive Control (MPC) method to dynamically schedule the human attention and determine which robot the human should collaborate with first. The optimal schedule can then be determined using a sampling based approach. The effectiveness of the proposed method is validated through simulation that shows improvements.

We consider two-machine flow shop scheduling problems with storage to minimize the makespan. Under a storage constraint, each job has its own size, and the total size of the job(s) being processed on the machine(s) and the job(s) waiting for the second operation cannot exceed the given capacity. It is known that the computational complexity is strongly NP-hard and in general an optimal schedule does not exist in the set of schedules with the same job sequences on two machines, referred to as a permutation set. Thus, we consider two cases such that an optimal schedule exists in the permutation set. These two cases have the special structure of processing times. In the first case, the processing times of two machines for each job are identical, while in the second case, machine 2 dominates machine 1, that is, the smallest processing time of the second group of operations is larger than or equal to the largest one of the first group of operations. We show that the first case is strongly NP-hard and admits a polynomial-time approximation scheme (PTAS), while the second case is solved in polynomial time.

We present a new approach to decrease task preemptions and migrations in optimal global real-time schedules on symmetric multiprocessors. Contrary to classical approaches, our method proceeds in two steps, one off-line to place jobs on intervals and one on-line to schedule them dynamically inside each interval. We propose a new linear programming formulation and a local scheduler which exhibits low complexity and produces few task preemptions and migrations. We compare our approach with other optimal scheduling algorithms, using the implicit-deadline periodic task model. Simulation results illustrate the competitiveness of our approach with respect to task preemptions and migrations.

With increased uncertainties and depressed security margins of distribution networks, the risk of violating load or voltage constraints has increased. The usual risk-prevention method is to set an appropriate optimal schedule of active distribution networks to reserve enough margin without incurring extra operating costs. In this study, an optimal scheduling method for an active distribution network is proposed that allows for a low level of violation risk to minimize operating costs while maintaining good system security. Overload violation risk cost is a financial cost due to the cost of countermeasures needed to avoid overload violation. In this study, the N-0 security regions of overload are set as the constraint that provides the definition and calculation of the bidirectional violation distance of overloading for active distribution networks based on the N-0 security region. The relationship between the violation distance of overloading and the countermeasures against overload violation have been established based on the power flow equations, enabling the calculation of the countermeasures cost. The assessment model for the overload violation risk cost is derived from the cost of countermeasures and probability distributions of nodal power. The point estimation algorithm is introduced to simplify the calculation. The calculation of risk cost is fixed through the conditional value-at-risk. On this basis, a novel optimization scheduling model of active distribution networks that considers risk cost is constructed. Examples of the optimal schedule are designed and the validity of the proposed method is verified.

This paper proposes an optimal day-ahead optimization schedule for gas-electric integrated energy system (IES) considering the bi-directional energy flow. The hourly topology of electric power system (EPS), natural gas system (NGS), energy hubs (EH) integrated power to gas (P2G) unit, are modeled to minimize the day-ahead operation cost of IES. Then, a second-order cone programming (SOCP) method is utilized to solve the optimization problem, which is actually a mixed integer nonconvex and nonlinear programming issue. Besides, cutting planes are added to ensure the exactness of the global optimal solution. Finally, simulation results demonstrate that the proposed optimization schedule can provide a safe, effective and economical day-ahead scheduling scheme for gas-electric IES.

The importance of preventive maintenance management has been gradually recognized specially with the great attention to the role of health technology management. Finding the optimal schedule to perform preventive maintenance for medical equipment is rarely considered in the literature. This research suggests using ant colony optimization method to solve the problem of finding the optimal preventive maintenance schedule. We developed 2 versions of the algorithm, both starting from a prioritized medical equipment list and differing in the heuristic function. The experimental results indicate the effectiveness of the ant colony optimization algorithm for this kind of problems.

Many work zones exist in the urban road network and have a great negative impact on city traffic. Finding the optimal work zone schedule can minimize the negative impact of work zones on traffic. This paper focuses on the day-based work zone scheduling problem in the urban network. Existing studies on the day-based work zone scheduling problem do not consider the progression of day-to-day traffic from a non-equilibrium state to an equilibrium state during the construction period. For the first time, this paper proposes a model for day-based work zone scheduling by introducing a day-to-day traffic assignment model, in which the target of the optimization problem is minimizing the increase in travel cost caused by work zones. Numerical examples are presented to explore the variations of the optimal construction sequence for different work durations, crew numbers, and model parameter values. Some new findings are obtained in the paper. When the construction duration of each work zone is relatively short (for example, less than 20 days), the optimal scheduling will obviously change with the work duration; when all of the construction durations increase to a threshold (for example, 60 days), the optimal construction sequence will no longer change. An optimal crew number exists that can minimize the increment of travel cost caused by work zones. During the construction period, the total travel cost in the network can be decreased by guiding travelers to change their original travel habits.