Open Scheduling Problem Research Articles

Many-objective optimization for scheduling of crude oil operations based on NSGA-Ⅲ with consideration of energy efficiency

Abstract Crude oil operations in refineries are characterized as a hybrid system since it contains both discrete-event and continuous processes, and it is extremely difficult to schedule such a system. For scheduling such a system, initially the discrete tasks to be performed during the scheduling horizon is unknown such that heuristics and meta-heuristics are not directly applicable, which further complicates its scheduling problem. Moreover, there are large number of objectives to be optimized, including the minimization of energy consumption due to that crude oil operations consume large amount of energy and therefore lead to large amount of emissions. Furthermore, the energy optimization problem is characterized as highly non-linearity. Hence, the scheduling problem of crude oil operations in refineries belongs to the many-objective optimization problems and it is extremely challenging. This paper addresses this challenging scheduling problem of crude oil operations. This scheduling problem is first converted to a discrete dynamic resource allocation problem such that meta-heuristics can be applicable. Then, with the results of large number of experiments, this work innovatively proposes an NSGA-Ⅲ-based optimization algorithm to efficiently solve the problem for Pareto-optimal solutions. By the proposed method, the genes in a chromosome are generated one by one and, when generating a gene, safeness check is done according to the derived safeness conditions such that each gene is feasible. In this way, the schedule feasibility can be ensured. An industrial case study is given to test its performance and comparison is made with the existing state-of-the-art algorithms for many-objective optimization problems. The results show its good performance in terms of convergence, solution diversity, time efficiency, and its applicability to real-life refinery scheduling problems.

Combining mixed integer programming and constraint programming to solve the integrated scheduling problem of container handling operations of a single vessel

In the container terminals of seaports, the container handling system consists of a variety of container handling machines such as quay cranes, internal yard trucks, and yard cranes. This study applies a holistic approach to the integrated scheduling of these machines for the container handling operations of a single vessel. We formulate this special hybrid flow shop scheduling problem through both mixed integer programming (MIP) and constraint programming (CP) techniques. Then we develop an easily-implemented approach that combines the strengths of MIP and CP. First, the MIP model, which only considers quay crane scheduling, is solved by an MIP solver, and a quay crane allocation plan is retrieved from the MIP solution. Then, this quay crane allocation plan is fed to the CP model, warm-starting the branch-and-prune algorithm built in a CP optimizer. Our numerical experiments reveal that this hybrid MIP/CP approach can solve the large-sized instances with up to 1000 containers, 6 quay cranes, 36 yard trucks, and 15 yard cranes to optimality with a gap of less than 3.31%, within a solution time of 2 minutes. If we increase the solution time to 5 minutes, this hybrid approach solves larger instances with up to 1400 containers to optimality with a gap of less than 1.41%. The state-of-the-art dedicated algorithms reported in the literature (which address an easier version of the same problem by ignoring non-crossing constraints and safety margins between quay cranes) are only able to find solutions for real-life instances with up to 500 containers within the solution time of 2930 or 5221 seconds, leaving a 4% or an unknown optimality gap. Thus, this study improves the solution of this integrated scheduling problem in terms of the instance size, solution efficiency, and solution optimality.

A New Method of Block Allocation Used in Two-Stage Operating Rooms Scheduling

This paper studies a weekly operation scheduling problem of elective surgery according to the block scheduling policy, to balance overtime (time used beyond the block) and undertime (time unused within the block) of each surgeon's blocks. The one week operation problem is divided into two stages: the first stage is to allocate patients to blocks and achieve the balance of the blocks to the same surgeon. Patients who can be scheduled on next week are determined according to the operating room (OR) capacity, surgeon's available time and patient priority. In the second stage, the operation date, operating room, and operation sequence are determined. When sequencing operations in blocks, we focus on surgical type and priority the two indicators. We present two integer programming (IP) models to solve the two stage problems, with the objects of 1) minimize the sum of all blocks' overtime and undertime penalty and 2) minimize the waiting cost for all patients. The two indicators are helpful to balance surgeons' workload among blocks and can improve patient's satisfaction. Directing at the first stage model, different from the previous studies, we will give a fast method to calculate the number of blocks for each surgeon, which can reduce the problem scale. The computational experiments are conducted illustrating its applicability to the problem in the operating theatre.

Consideration of reliability and economy to Capacity Configuration of energy storage system: Case Study of a large scale wind power plant in the Northwest China

Currently, a serious operation security problem of wind power plant has caused by the massive wind power integration, which has increased the difficulty of the operation in large scale wind power plant. Energy storage system (ESS) is thought the best choice to solve the operation scheduling problem of large-scale wind power plant, therefore, under the premise of ensuring the reliability of power supply and network constraints, it is particularly significant to select the proper capacity with both economy and feasibility, aiming at the problems above, this paper constructs capacity configuration of storage which is of statistical significance by studying the probability distribution characteristics, aiming at the deviation load during the operation of wind power plant, utilized Monte Carlo simulation, through whole lifetime NPV, payback period PBP and operation scheduling deviation OOD to verify the reliability and economy of the capacity. Finally, the actual operation data from a wind power plant installed 99MW in Northwest of China is utilized as a case study, simulation result shows that it could get the best storage capacity under the standard of the characteristics of economic and reliability criteria, which proves the validity and feasibility of the method in this paper.

Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs

Common operation scheduling (COS) problems arise in real-world applications, such as industrial processes of material cutting or component dismantling. In COS, distinct jobs may share operations, and when an operation is done, it is done for all the jobs that share it. We here propose a 0-1 LP formulation with exponentially many inequalities to minimize the weighted number of tardy jobs. Separation of inequalities is in NP, provided that an ordinary min Lmax scheduling problem is in P. We develop a branch-and-cut algorithm for two cases: one machine with precedence relation; identical parallel machines with unit operation times. In these cases separation is the constrained maximization of a submodular set function. A previous method is modified to tackle the two cases, and compared to our algorithm. We report on tests conducted on both industrial and artificial instances. For single machine and general processing times the new method definitely outperforms the other, extending in this way the range of COS applications.

Operation Scheduling Optimization of a Transfer Hub with Multiple Tank Farms Based on a New Continuous Time Representation

This study addresses the operation-scheduling problem of a transfer hub with multiple tank farms (M-TH) connected to a multiproduct pipeline network. As part of the pipeline network, the THs serve ...

Integrated scheduling of production and distribution operations in a global MTO supply chain

ABSTRACTThis paper addresses an integrated scheduling problem of production and distribution operations with the consideration of several important realistic features, such as multiple plants, multiple order sizes and multiple transportation modes in the commit-to-delivery business mode. This problem exists widely in many global make-to-order supply chain operations, which aims at minimizing the total cost of production and distribution by determining how to assign a large number of customer orders to multiple production plants, and how to transport the finished products to customer-specified global destinations. A memetic algorithm-based optimization approach, integrating a memetic optimization process and some heuristic procedures, is proposed to deal with this problem. The effectiveness of the proposed approach is demonstrated by extensive numerical experiments based on real industrial data. Experimental results demonstrate that (1) the proposed approach can effectively solve the problem investigated by generating good solutions for industrial-size instances, (2) the integrated scheduling generates better scheduling solutions than the sequential scheduling, and (3) the proposed memetic optimization process exhibits better optimum-seeking performance than a genetic algorithm-based optimization process.

Application and Comparison of Metaheuristic and New Metamodel Based Global Optimization Methods to the Optimal Operation of Active Distribution Networks

As an imperative part of smart grids (SG) technology, the optimal operation of active distribution networks (ADNs) is critical to the best utilization of renewable energy and minimization of network power losses. However, the increasing penetration of distributed renewable energy sources with uncertain power generation and growing demands for higher quality power distribution are turning the optimal operation scheduling of ADN into complex and global optimization problems with non-unimodal, discontinuous and computation intensive objective functions that are difficult to solve, constituting a critical obstacle to the further advance of SG and ADN technology. In this work, power generation from renewable energy sources and network load demands are estimated using probability distribution models to capture the variation trends of load fluctuation, solar radiation and wind speed, and probability scenario generation and reduction methods are introduced to capture uncertainties and to reduce computation. The Open Distribution System Simulator (OpenDSS) is used in modeling the ADNs to support quick changes to network designs and configurations. The optimal operation of the ADN, is achieved by minimizing both network voltage deviation and power loss under the probability-based varying power supplies and loads. In solving the computation intensive ADN operation scheduling optimization problem, several novel metamodel-based global optimization (MBGO) methods have been introduced and applied. A comparative study has been carried out to compare the conventional metaheuristic global optimization (GO) and MBGO methods to better understand their advantages, drawbacks and limitations, and to provide guidelines for subsequent ADN and smart grid scheduling optimizations. Simulation studies have been carried out on the modified IEEE 13, 33 and 123 node networks to represent ADN test cases. The MBGO methods were found to be more suitable for small- and medium-scale ADN optimal operation scheduling problems, while the metaheuristic GO algorithms are more effective in the optimal operation scheduling of large-scale ADNs with relatively straightforward objective functions that require limited computational time. This research provides solution for ADN optimal operations, and forms the foundation for ADN design optimization.

Monte Carlo simulation of district heating system short-term operation in electricity markets

Energy generation in district heating (DH) systems is usually done in combined heat and power (CHP) units which can efficiently produce both useful heat and electric power. There can also exist heat only boilers, electric heaters, heat pumps and heat storage tanks. The coupling of heat and power generation in the CHP units and the possibility to store heat for later use makes the short-term operation scheduling of such systems quite challenging. Furthermore, big DH systems produce power that is sold in the electricity markets. This makes the operation scheduling problem even more complex as the uncertainty of the electricity prices in the markets should be considered. To make optimal decisions under uncertainty, various mathematical optimization tools were developed, such as stochastic programming and robust optimization. In this paper, an approach based on a Monte Carlo simulation is followed. Initially, a model of DH system short-term operation and power trading is mathematically formulated. Then, this model is used to run a Monte Carlo simulation for a case study system where the values of stochastic parameters are simulated using autoregressive models. Results demonstrate that simulation is fast, taking 300–400 runs to converge. A comparison of two system configurations shows that the use of heat storage increases the daily expected profit by 11%. Finally, the electricity price volatility in this case study is such that mainly two CHP units are operating for most of the time.

Petri net-based approach to short-term scheduling of crude oil operations with less tank requirement

With the interaction of discrete-event and continuous processes, the short-term scheduling problem of crude oil operations is essentially combinatorial. Thus, it is preferred to develop computationally efficient techniques for a satisfactory solution other than an exactly optimal one. Based on this idea, such a scheduling issue is studied in the viewpoint of control theory. To do so, as charging tanks are a type of critical resources, it is crucial to determine how many charging tanks are required to obtain a feasible schedule. By using a hybrid Petri net to describe the behavior of crude oil operations, we show that a feasible schedule can be found for a system with two or more than two distillers if there are two charging tanks for each distiller, which is the least number of charging tanks for finding a feasible solution to reach the maximal productivity. Also, the requirements of the initial state for obtaining a feasible schedule are given and scheduling method is proposed. The scheduling method is simple and computationally efficient. An industrial case study is used to show how the proposed approach can be applied.

Joint Energy Replenishment and Operation Scheduling in Wireless Rechargeable Sensor Networks

Wireless charging is a promising way to solve the energy constraint problem in sensor networks. While extensive efforts have been made to improve the performance of charging and communication in wireless rechargeable sensor networks (WRSNs), little has been done to address the operation scheduling problem. To fill this void, we propose a joint energy replenishment and scheduling mechanism so as to maximize the network lifetime while making strict sensing guarantees in the WRSN. We first formulate the problem in a general 2-D space and prove its NP-completeness. We then devise an f-approximate scheduling mechanism by transforming the classical minimum set cover problem and develop an optimal energy-replenish strategy based on the energy consumption of nodes returned by the scheduling mechanism. Large-scale simulation results validate our design and show a 39.2% improvement of network lifetime over a baseline method.

Two-stage MINLP algorithm for the optimal synthesis and design of networks of CHP units

This paper proposes a Mixed Integer Non Linear Programming (MINLP) model and two-stage optimization algorithm for determining the most profitable synthesis and design of Combined Heat and Power units within a district heating network with heat storage while taking into account the optimal scheduling of the units over the year. A two-stage algorithm for tackling the challenging MINLP problem is devised: at the upper level the selection and sizing of the units is optimized by means of specifically selected evolutionary algorithms, while at the lower level the operational scheduling problem is linearized and optimized with a commercial Mixed Integer Linear Programing solver. Three different approaches, based on two different evolutionary algorithms and discrete variable relaxation, are devised and compared to tackle the upper level problem. Moreover a bounding technique is proposed to limit the computational time required to solve the lower-level problem. The overall algorithm is tested on an industrial scale problem to find the two system designs leading to the minimum energy consumption and the minimum total annual cost. Computational results indicate that the continuous relaxation of the plant sizes significantly helps to improve the convergence rate of the tested evolutionary algorithm and to find improved solutions. For the considered test case, the design optimized for the minimum energy consumption allows to save 64% of primary energy compared to the minimum total annual cost solution, but with a 28% higher total annual cost.

Optimal operation scheduling for microgrid with high penetrations of solar power and thermostatically controlled loads

Effective building/house energy management has been considered as an efficient way to mitigate the fluctuation of renewable energy in power distribution system. This article studies the operation scheduling problem for microgrid with high penetration of solar power and thermostatically controlled loads. Based on the established photovolaic model and thermostatically controlled load model, an optimal operation strategy for microgird is proposed. The scheme is based on the rolling horizon optimization strategy, where the control window continues to proceed with the update of real-time information, aiming to minimize the total operation costs over the current control window. Differential evolution algorithm is used to solve the proposed model, and the simulation results validate the efficiency of the proposed method.

Quantum circuit physical design flow for the multiplexed trap architecture

Physical design is the second process in the design flow of quantum circuits that receives a netlist as input and generates a layout at a target technology. Quantum physical design problem is intractable. This process tackles the operation scheduling, placement, and qubit routing problems. Some approaches have been proposed for the physical design in ion trap technology that is currently one of the most advanced quantum technologies. These methods do not use all capabilities of the technology. Focusing on this issue, in this paper, a physical design flow is proposed for the multiplexed trap architecture utilizing the capabilities provided by the technology not considered by other approaches to improve the latency and area metrics. Experimental results show that the proposed approach decreases the average latency of quantum circuits by about 39.5% for the attempted benchmarks.

Modelling and solving generalised operational surgery scheduling problems

The term ‘surgery scheduling’ is used to describe a variety of strategic, tactical and operational scheduling problems, many of which are critical to the quality of treatment and to the efficient use of hospital resources. We consider operational surgery scheduling problems. The exact problem formulation varies substantially between hospitals or, even, hospital departments. In addition, the level of detail varies between different planning situations, ranging from long term patient admission planning to the very detailed scheduling of a particular day׳s surgeries. This diversity makes it difficult to design general scheduling methods and software solutions that can be applied without extensive customisation for each application. We approach this challenge by proposing a new generalised model for surgery scheduling problems. We show how this model extends the multi-project, multi-mode resource constrained project scheduling problem with generalised time constraints, including some extensions that to our knowledge have not been previously studied. Furthermore, we present a search method for solving the proposed model. The algorithm uses on-line learning to balance computational loads between a construction and an improvement method, both working on high level solution representations. An adapted schedule generation scheme is used to map these to concrete schedules. We perform computational experiments using realistic problem instances from three surgery scheduling planning situations at a medium sized Norwegian hospital; day scheduling, week scheduling and admission planning. The results show that the algorithm performs well across these quite different problems without any off-line customisation or parameter tuning.

Short-Term Scheduling of Crude-Oil Operations: Enhancement of Crude-Oil Operations Scheduling Using a Petri Net-Based Control-Theoretic Approach

To effectively operate a refinery and make it competitive, efficient short-term scheduling techniques that utilize commercial software tools for practical applications need to be developed. However, cumbersome details make it difficult to solve the short-term scheduling problem (STSP) of crudeoil operations, and mathematical programming models fail to meet the industrial needs. This article proposes an innovative control-theoretic and formal model-based method to tackle this long-standing issue. This method first models the STSP as a hybrid Petri net (PN) and then derives critically important schedulability conditions. The conditions are used to decompose a complex problem into several tractable subproblems. In each subproblem, there are either continuous variables or discrete variables. For subproblems with continuous variables, this work proposes a linear programming-based method to solve them; while, for subproblems with discrete variables, this work adopts efficient heuristics. Consequently, the STSP is efficiently resolved,and the application of the proposed method is well illustrated via industrial case studies.

Integrated operations scheduling with delivery deadlines

An integrated scheduling problem of supply and distribution operations in a make-to-order supply chain is considered. The supply chain consists of contracted suppliers, capacitated processing centers, and many demand points. Processing centers customize and/or configure semi-finished products supplied by suppliers to finished products in terms of the requirements of demand points: order quantity and delivery deadline. The problem is to find the assignment of both suppliers and demand points to processing centers and the schedules for supply and distribution operations such that the total costs of shipping and penalty that unfulfilled customer orders incur are minimized, subject to network capacity and deadline constraints. In this paper, a heuristic algorithm is developed, based on partial relaxation and median threshold, which makes it possible to avoid dealing with the generalized assignment problem, a strongly NP-hard problem, in the solution process. Computational tests are performed over test cases randomly generated to assess the performance of the proposed algorithm. As compared to the use of commercial optimization package, CPLEX, computational results show that the proposed algorithm is able to find a good near-optimal solution to this problem with remarkably less computational time.

Sorting common operations to minimize the number of tardy jobs

We study an operation scheduling problem where a finite set of jobs with due dates must be completed by one machine: each job is completed as soon as a specific subset of unit operations is done. Distinct jobs may share operations, and when an operation is done, it is done for all the jobs that share it. The goal is to schedule operations so that the (weighted) number of tardy jobs is minimized. We reformulate the problem as maximum stable set problem on a special graph and study its structure. Valid inequalities and optimality cuts are derived, separated, and tested in a computational experience that identifies some features of hard instances and the potential contribution of the addition, at root, of various cut classes. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(4), 306–320 2014

Two Efficient Twin ELM Methods With Prediction Interval.

In the operational optimization and scheduling problems of actual industrial processes, such as iron and steel, and microelectronics, the operational indices and process parameters usually need to be predicted. However, for some input and output variables of these prediction models, there may exist a lot of uncertainties coming from themselves, the measurement error, the rough representation, and so on. In such cases, constructing a prediction interval (PI) for the output of the corresponding prediction model is very necessary. In this paper, two twin extreme learning machine (TELM) models for constructing PIs are proposed. First, we propose a regularized asymmetric least squares extreme learning machine (RALS-ELM) method, in which different weights of its squared error loss function are set according to whether the error of the model output is positive or negative in order that the above error can be differentiated in the parameter learning process, and Tikhonov regularization is introduced to reduce overfitting. Then, we propose an asymmetric Bayesian extreme learning machine (AB-ELM) method based on the Bayesian framework with the asymmetric Gaussian distribution (AB-ELM), in which the weights of its likelihood function are determined as the same method in RALS-ELM, and the type II maximum likelihood algorithm is derived to learn the parameters of AB-ELM. Based on RALS-ELM and AB-ELM, we use a pair of weights following the reciprocal relationship to obtain two nonparallel regressors, including a lower-bound regressor and an upper-bound regressor, respectively, which can be used for calculating the PIs. Finally, some discussions are given, about how to adjust the weights adaptively to meet the desired PI, how to use the proposed TELMs for nonlinear quantile regression, and so on. Results of numerical comparison on data from one synthetic regression problem, three University of California Irvine benchmark regression problems, and two actual industrial regression problems show the effectiveness of the proposed models.

Integrated batch production and distribution scheduling with limited vehicle capacity

We study a variation of the Integrated Production and Distribution Problem (IPDP) in which orders are processed and delivered in batches with limited vehicle capacity. We emphasize the no-wait condition between the production and distribution of each batch, and prove that the general version of this integrated operational scheduling problem is strongly NP-hard. Two special cases, with identical order processing time and identical delivery time respectively, are investigated to explore the optimal solution structures, such as how orders should be sequenced based on their processing and delivery time. These optimal solution structures not only help the design of polynomial time algorithms for the special cases, but also reveal insights that facilitate the development of the heuristic for the general problem. We also offer the analytical worst case error bound of this heuristic in solving the general problem by providing a performance ratio less than two, and numerically demonstrate the effectiveness of our heuristic in terms of accuracy and speed. Statistical tests are carried out to investigate the impacts of problem parameters, including order number, vehicle capacity, and variety of order processing time and delivery time, on the accuracy of the heuristic.