Maintenance schedule optimisation for a railway power supply system

High reliability is the crucial requirement in railway operation and a power supply system is one of the key components of electrified railways. The cost-effectiveness of the maintenance works is also the concern of the railway operators while the time window on trackside maintenance is often limited. Maintenance scheduling is thus essential to uphold reliability and to reduce operation cost. It is however difficult to formulate the optimal schedule to meet both reliability and maintenance cost for a railway power supply system as a whole because of its functional complexity and demanding operation conditions. Maintenance scheduling models to achieve reliability and maintenance cost are proposed in this study. Optimisation algorithms are then developed to attain the solutions of the model. The applicability of the models and efficiency of the solution algorithms are demonstrated in an example. The proposed methods are vitally important for the railway engineers and operators to assure the service quality in the increasing demands of the modern electrified railways.     

物料需求计划不稳定性的模拟研究

介绍物料需求计划不稳定性的基本概念和模拟研究方法。在不确定性需求的流动式计划环境下,研究冻结参数和计划算法在不同生产条件下对物料需求计划不稳定性的影响。通过设计模拟实验和大量模拟计算及统计分析表现：费用结构、预测模式、冻结比例、计划周期和计划算法对物料需求计划不稳定性有较大影响,且交互作用显著。研究结果对减小物料需求计划的不稳定性有一定指导意义。     

A scheduling model for systems with task and health dependent remaining useful life prognostics

When we schedule a system to perform a task, a factor that should be taken into account is the remaining useful life prognostics of the system. This prognostics of the system may depend not only on the health state of the system, but also on the characteristics of the task to be performed. Assuming such prognostics is available at the time of system scheduling, the problem is to find a method to schedule the system, which can improve the expected profit rate. Two system life models were proposed for the case considered in this paper. Due to the dynamic nature of the problem, a global optimal policy is hard to find, we proposed an approach based on the approximated expected profit rate to schedule the systems. The approach is validated through simulations compared with a number of other task scheduling rules to show the advantage of the proposed approach. We also find the optimal global stationary result by exhaustive search of small scheduling problems of few systems and tasks to compare with the proposed approximate one. Further numerical analyses are presented to demonstrate the process of determining a decision variable and the sensitivity analysis in terms of a cost parameter.     

Group production scheduling for minimum total tardiness Part(I)

This paper considers the problem of group scheduling on a single stage to minimize total tardiness. It is assumed that jobs are classified into several groups on the basis of group technology. Optimal decision as to scheduling sequences will be made as to product group and specific job. This paper proves basic theorems that establish the relative order in which pairs of groups are processed in an optimal schedule. In general, scheduling problems of moderate size may be at least partially ordered so that very few schedules remain to be searched. Two practical algorithms for determining the optimal group schedule and the near optimal group schedule are proposed. Numerical examples are presented in detail.     

Determination methodology for optimising the energy storage size for power system

A methodology for determining the optimal size of energy storage system (ESS) integrated with thermal power system is presented in this study. The optimal size is characterised by the rated stored energy and the maximum power rating of installed ESS for which the power system can achieve maximum revenue. Therefore the ESS cost formulation is conducted by analysing economic cost benefit measures considering life cycle of ESS. Since unit commitment (UC) scheduling is an important and integral part of power system cost optimisation, this study considers the operating schedule of thermal units (TU) while resolving ESS schedule. This proposed method uses tabu search (TS)-based evolutionary technique for solving this optimisation problem. TS is included in this algorithm to avoid re-evaluation of already evaluated ESS size which is powered by max priority heap and hash table data structure. The weekly schedule period is considered instead of daily to achieve more precise results. The proposed method is applied in two different power systems to determine the appropriate size of to be installed ESS. Experimental results reported that establishing the proposed method is an effective one to compute the optimal size of ESS for different sized power systems.     

Reliability‐based Optimal Maintenance Scheduling by Considering Maintenance Effect to Reduce Cost

A new reliability‐based optimal maintenance scheduling method is presented that considers the effect of maintenance in reducing costs. An ordering list of element maintenance effects with various maintenance‐interval types is constructed. By means of this ordering list, reliability‐based optimal maintenance scheduling for simple reliability structures and composite reliability systems is then carried out. The properties of the proposed method, such as the evaluation of maintenance cost reduction, the simplicity of the proposed method by sacrificing system availability within the allowance method, the operation decision based on the optimal maintenance schedule, etc., are discussed. With simulations, the effectiveness of the proposed method is verified. Copyright © 2005 John Wiley & Sons, Ltd.     

Adaptive production scheduling of virtual production systems using object-oriented Petri nets with changeable structure

Virtual Production Systems (VPSs) are logically constructed by organizing production resources belonging to one or more physical manufacturing systems. VPSs can enhance the agility of manufacturing systems. However, an effective scheduling approach is required to cope with disturbance and changes to these systems. An adaptive production scheduling method is proposed. Object-oriented Petri nets with changeable structure (OPNs-CS) formulate the scheduling problem of VPSs. To resolve resource constraints in a VPS, the OPNs-CS is modified by introducing limited token available time and by revising the enabling and firing rules. The artificial intelligent heuristic search (A*) algorithm is modified and applied to generate the optimal or near optimal schedule. When a VPS encounters any disturbance, an estimate of the effects of the disturbance can be estimated by simulation on the OPNs-CS model. If the scheduling target (completion time) is not affected, rescheduling is not required. Whenever there is a change to the VPS, the TOPNs-CS model is updated to refresh VPS schedule. A case study is presented to demonstrate the procedures for applying the proposed scheduling approach. The given case study shows that the proposed approach is capable of scheduling a VPS dynamically in response to disturbances and changes are involved.     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

Robust makespan minimisation in identical parallel machine scheduling problem with interval data

Parallel machine scheduling problems are commonly encountered in a wide variety of manufacturing environments and have been extensively studied. This paper addresses a makespan minimisation scheduling problem on identical parallel machines, in which the specific processing time of each job is uncertain, and its probability distribution is unknown because of limited information. In this case, the deterministic or stochastic scheduling model may be unsuitable. We propose a robust (min–max regret) scheduling model for identifying a robust schedule with minimal maximal deviation from the corresponding optimal schedule across all possible job-processing times (called scenarios). These scenarios are specified as closed intervals. To solve the robust scheduling problem, which is NP-hard, we first prove that a regret-maximising scenario for any schedule belongs to a finite set of extreme point scenarios. We then derive two exact algorithms to optimise this problem using a general iterative relaxation procedure. Moreover, a good initial solution (optimal schedule under a mid-point scenario) for the aforementioned algorithms is discussed. Several heuristics are developed to solve large-scale problems. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.     

Real-time scheduling in manufacturing system with machining and assembly operations: a state of art

Manufacturing systems producing multiple products are common in many industries, where products are made from several parts and/or sub-assemblies that require machining operations in first stage and assembly operations at later stage. Several scheduling techniques are proposed in the literature for such manufacturing system to develop near optimal schedule. A disruption in the manufacturing necessitates adjusting previously planned schedule which is known as real-time scheduling. This paper presents a comparative evaluation of different scheduling methods proposed by different investigators for dealing such situations. The literature indicates that real-time scheduling of manufacturing system with machining and assembly operations is hardly attempted. The paper offers a framework for developing rescheduling methodologies for such manufacturing situations.     

Rescheduling parallel machines with stepwise increasing tardiness and machine assignment stability objectives

Nervousness in machine assignments during rescheduling can cause problems for the implementation of a scheduling system. This paper examines rescheduling due to the arrival of new jobs to the system. Parallel machine scheduling problems with stepwise increasing tardiness cost objectives, non-zero machine ready times, constraints that limit machine reassignments, and machine reassignment costs are considered. Simulation experiments and individual scheduling problems indicate that nervousness can be controlled at a low cost in some parallel machine scheduling environments. The rescheduling problems in the simulation are solved with a branch-and-price algorithm. Significant gains in schedule stability can be achieved by selecting the alternative optimal solution with the fewest machine reassignments.     

Integrated Project Scheduling and Material Planning with Variable Activity Duration and Rewards

Integrating project scheduling and material ordering adds more realism to project scheduling and considers additional trade-offs that could lead to reductions in the overall project cost. In this paper we review the evolution of the integrated problem, and investigate the impact of treating the activity duration as a decision variable on the activities schedule and materials plan. The effects of introducing rewards (penalties) for early (late) completion as well as materials quantity discounts on the project schedule and cost are also considered- These additions provide scheduling flexibility that might lead to further reduction in the project's total cost or makespan. Considering the various project costs, we found that there exists an optimal schedule that either starts as early as possible (ai time zero) or completes as late as possible. We also show that if the project starts at time zero, then its duration cannot be longer than that for the case where the schedule ends as late as possible. Ft is also shown that the material ordering policy does not follow the Wagner and Whitin model when activity duration is variable or in the presence of quantity discounts. These results have led to modeling and solving the problem in a more efficient manner. Extensive computational work shows the validity of the model and the solution approach.     

An algorithm for scheduling parallel processors

This paper deals with optimal scheduling of jobs on identical parallel processors. The paper develops an algorithm for determining the optimal schedule and gives a proof of the algorithm. The criterion used is that of minimizing the total cost for processing all jobs when the jobs are assigned non-decreasing waiting costs which are non-linear. Extension of the algorithm for jobs with due dates is also given. Computational results are given which indicate the effectiveness of the algorithm as compared to complete enumeration.     

Scheduling of recovery actions in the supply chain with resilience analysis considerations

Supply chain engineering models with resilience considerations have been mostly focused on disruption impact quantification within one analysis layer, such as supply chain design or planning. Performance impact of disruptions has been typically analysed without scheduling of recovery actions. Taking into account schedule recovery actions and their duration times, this study extends the existing literature to supply chain scheduling and resilience analysis by an explicit integration of the optimal schedule recovery policy and supply chain resilience. In particular, we compute a schedule optimal control policy and analyse the performance of this policy by varying the perturbation vector and representing the outcomes of variations in the form of an attainable set. We propose a scheduling model that considers the coordination of recovery actions in the supply chain. Further, we suggest a resilience index by using the notion of attainable sets. The attainable sets are known in control theory; their calculation is based on the schedule control model results and the minimax regret approach for continuous time parameters given by intervals. We show that the proposed indicator can be used to estimate the impact of disruption and recovery dynamics on the achievement of planned performance in the supply chain.     

Production scheduling of independent jobs on parallel identical processors

We study the scheduling of n independent jobs on m parallel identical processors. Using dynamic programming, the paper presents an algorithm to determine the optimal schedule for medium size problems with quite general cost functions. The application of the algorithm is illustrated by numerical examples.     

Minimising earliness and tardiness by integrating production scheduling with shipping information

Minimisation of earliness and tardiness is known to be critical to manufacturing companies because it may induce numerous tangible and intangible problems, i.e. extra storage cost, spacing, risk of damages, penalty, etc. In literature, earliness and tardiness is usually determined based on order due date, generally regarded as the time of delivering the finished products to the customers. In many papers, delivery time and cost required are usually simplified during the production scheduling. They usually assume that transportation is always available and unlimited. However, transportation usually constructs a critical portion of the total lead time and total cost in practice. Ignoring that will lead to an unreliable schedule. This is especially significant for electronic household appliances manufacturing companies as the studied company in this paper. In general, they usually rely on sea-freight transportation because of the economic reasons. As different sea-freight forwarders have different shipments to the same destination but with different shipping lead time, cost and available time. Adequately considering this shipping information with the production scheduling as an integrated model can minimise the costs induced by earliness and tardiness and the reliability of the schedule planned. In this paper, a two-level genetic algorithm (TLGA) is proposed, which is capable of simultaneously determining production schedule with shipping information. The optimisation reliability of the proposed TLGA is tested by comparing with a simple genetic algorithm. The results indicated that the proposed TLGA can obtain a better solution with lesser number of evolutions. In addition, a number of numerical experiments are carried out. The results demonstrate that the proposed integrated approach can reduce the tardiness, the storage cost, and shipping cost.     

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.     

Time-variant lot sizing models for the warehouse scheduling problem

We consider the problem of scheduling the delivery of n products into a warehouse with limited space under the assumptions of continuous demands at constant rates, infinite horizon, and no backorders. The delivery schedule is described by a cyclic schedule with time-varying lot sizes. The order frequencies and the order sequence are assumed to be given. We formulate a linear program that determines delivery times relative to the cycle length to minimize the relative maximum space used and show that the optimal solution is characterized by filling the warehouse at each order. We bound the optimal solution by using a worst-case analysis and give conditions under which the linear program has the same optimal solution as a quadratic program that minimizes the holding cost. Under general conditions, we derive a bound on the cost penalty that results when using the optimal solution of the linear program as a solution to the quadratic program. Finally, we complete a solution to the nonlinear lot-sizing model by determining the best cycle length corresponding to the solution to the linear program and present a bound on a quality of this solution.     

Dynamic co-ordinated scheduling in the supply chain under a process modernisation

A new dynamic model for co-ordinated scheduling of interlinked processes in a supply chain under a process modernisation is presented. Such a problem is vital in many of the supply chain management domains. This problem is represented as a special case of the scheduling problem with dynamically distributed jobs. The peculiarity of the proposed approach is the dynamic interpretation of scheduling based on a natural dynamic decomposition of the problem and its solution with the help of a modified form of continuous maximum principle blended with combinatorial optimisation. The special properties of the developed model allow using methods of discrete optimisation for the schedule calculation. Optimality and sufficiency conditions as well as structural properties of the model are investigated. Advantages and limitations of the proposed approach are discussed. With the developed approach, an explicit inclusion of a process modernisation in the SC co-ordinated decisions for a wide ranges of possible applications as well as a dynamic model and a tractable algorithm for optimal discrete time scheduling on the basis of continuous maximum principle have been obtained.     

Hedge against total flow time uncertainty of the uniform parallel machine scheduling problem with interval data

We consider a total flow time minimisation problem of uniform parallel machine scheduling when job processing times are only known to be bounded within certain given intervals. A minmax regret model is proposed to identify a robust schedule that minimises the maximum deviation from the optimal total flow time over all possible realisations of the job processing times. To solve this problem, we first prove that the maximal regret for any schedule can be obtained in polynomial time. Then, we derive a mixed-integer linear programming (MILP) formulation of our problem by exploiting its structural properties. To reduce the computational time, we further transform our problem into a robust single-machine scheduling problem and derive another MILP formulation with fewer variables and constraints. Moreover, we prove that the optimal schedule under the midpoint scenario is a 2-approximation for our minmax regret problem. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.