Mixed-integer linear programming method for multi-degree and multi-hoist cyclic scheduling with time windows

Multi-degree cyclic hoist scheduling and multi-hoist cyclic scheduling are both capable of improving the throughput in an automatic electroplating line. However, previous research on integrated multi-degree and multi-hoist cyclic scheduling is rather limited. This article develops an optimal mixed-integer linear programming model for the integrated multi-degree and multi-hoist cyclic scheduling with time window constraints. This model permits overlap on hoist coverage ranges, and it proposes new formulations to avoid hoist collisions, by which time window constraints and tank capacity constraints are also formulated. A set of available benchmark instances and newly generated instances are solved using the CPLEX solver to test the performance of the proposed method. Computational results demonstrate that the proposed method outperforms the zone partition heuristic without overlapping, and the throughputs are improved by a significant margin using the proposed method, especially for large-size instances.     

Minimising the makespan in the two-machine job shop problem under availability constraints

Classical scheduling problem assumes that machines are available during the scheduling horizon. This assumption may be justified in some situations but it does not apply if maintenance requirements, machine breakdowns or other availability constraints have to be considered. In this paper, we treat a two-machine job shop scheduling problem with one availability constraint on each machine to minimise the maximum completion time (makespan). The unavailability periods are known in advance and the processing of an operation cannot be interrupted by an unavailability period (non-preemptive case). We present in our approach properties dealing with permutation dominance and the optimality of Jackson's rule under availability constraints. In order to evaluate the effectiveness of the proposed approach, we develop two mixed integer linear programming models and two schemes for a branch and bound method to solve the tackled problem. Computational results validate the proposed approach and prove the efficiency of the developed methods.     

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.     

Scheduling Multi-Mode Resource-Constrained Projects Using Heuristic Rules Under Uncertainty Environment

Project scheduling is a key objective of many models and is the proposed method for project planning and management. Project scheduling problems depend on precedence relationships and resource constraints, in addition to some other limitations for achieving a subset of goals. Project scheduling problems are dependent on many limitations, including limitations of precedence relationships, resource constraints, and some other limitations for achieving a subset of goals. Deterministic project scheduling models consider all information about the scheduling problem such as activity durations and precedence relationships information resources available and required, which are known and stable during the implementation process. The concept of deterministic project scheduling conflicts with real situations, in which in many cases, some data on the activity' s durations of the project and the degree of availability of resources change or may have different modes and strategies during the process of project implementation for dealing with multi-mode conditions surrounded by projects and their activity durations. Scheduling the multi-mode resource-constrained project problem is an optimization problem whose minimum project duration subject to the availability of resources is of particular interest to us. We use the multi-mode resource allocation and scheduling model that takes into account the dynamicity features of all parameters, that is, the scheduling process must be flexible to dynamic environment features. In this paper, we propose five priority heuristic rules for scheduling multi-mode resource-constrained projects under dynamicity features for more realistic situations, in which we apply the proposed heuristic rules (PHR) for scheduling multi-mode resource-constrained projects. Five projects are considered test problems for the PHR. The obtained results rendered by these priority rules for the test problems are compared by the results obtained from 10 well-known heuristics rules rendered for the same test problems. The results in many cases of the proposed priority rules are very promising, where they achieve better scheduling dates in many test case problems and the same results for the others. The proposed model is based on the dynamic features for project topography.     

A multi-objective scatter search for the ladle scheduling problem

We consider the ladle scheduling problem, which can be regarded as a vehicle routing problem with semi-soft time windows and adjustment times. The problem concerns allocating ladles to serve molten steel based on a given steelmaking scheduling plan, and determining the modification operations for the empty ladles after the service process. In addition, combining the controllable processing time of molten steel, the other aspect of the problem is to determine the service start times taking into consideration the technological constraints imposed in practice. We present a non-linear mathematical programming model with the conflicting objectives of minimising the occupation ratio of the ladles and maximising the degree of satisfaction with meeting the soft windows. To solve the multi-objective model, we develop a new scatter search (SS) approach by re-designing the common components of SS and incorporating a diversification generator, a combination method and a diversification criterion to conduct a wide exploration of the search space. We analyse and compare the performance of the proposed approach with a multi-objective genetic algorithm and with manual scheduling adopted in practical production using three real-life instances from a well-known iron–steel production plant in China. The computational results demonstrate the effectiveness of the proposed SS approach for solving the ladle scheduling problem.     

Modelling and scheduling analysis of multi-cluster tools with residency constraints based on time constraint sets

This paper is dedicated to the scheduling problem of multi-cluster tools with process module residency constraints and multiple wafer product types. The problem is formulated as a non-linear programming model based on a set of time constraint sets. An effective algorithm called the time constraint sets based (TCSB) algorithm is presented as a new method to schedule the transport modules to minimise the makespan of a number of wafers. In approach, time constraint sets are maintained for all the resources and necessary operations to exploit the remaining production capacities during the scheduling process. To validate the proposed algorithm on a broader basis, a series of simulation experiments are designed to compare our TCSB algorithm with the benchmark with regard to cluster factor, configuration flexibilities and the variation of the processing times and residency constraint times. The results indicate that the proposed TCSB algorithm gives optimal or near optimal scheduling solutions in most cases.     

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.     

A study on the performance of scheduling rules in buffer-constrained dynamic flowshops

Most studies on scheduling in manufacturing systems using dispatching rules deal with jobshops, while there are only few reports dealing with dynamic flowshops. It is known that the performance of many dispatching rules in dynamic jobshops is different from that in dynamic flowshops. Moreover, many research reports assume that there are no buffer constraints in the shop, and even those reports dealing with buffer-constrained shops present the evaluation of existing dispatching rules for unconstrained shops in the context of buffer constraints with the consideration of a limited number of objectives of scheduling. In this study, we deal with the problem of scheduling in dynamic flowshops with buffer constraints. With respect to different time-based objectives, the best dispatching rules for scheduling in unconstrained shops have been identified from the existing literature. In addition, two new dispatching rules specially designed for flowshops with buffer constraints are proposed. All dispatching rules under consideration are evaluated in dynamic flowshops with buffer constraints on the basis of an extensive simulation study covering different levels of buffer constraints, shop load or utilization, and missing operations in flowshops. The proposed rules are found to perform better than the existing dispatching rules in buffer-constrained flowshops with respect to many measures of performance.     

Scheduling optimization of design stream line for production research and development projects

In a development project, efficient design stream line scheduling is difficult and important owing to large design imprecision and the differences in the skills and skill levels of employees. The relative skill levels of employees are denoted as fuzzy numbers. Multiple execution modes are generated by scheduling different employees for design tasks. An optimization model of a design stream line scheduling problem is proposed with the constraints of multiple executive modes, multi-skilled employees and precedence. The model considers the parallel design of multiple projects, different skills of employees, flexible multi-skilled employees and resource constraints. The objective function is to minimize the duration and tardiness of the project. Moreover, a two-dimensional particle swarm algorithm is used to find the optimal solution. To illustrate the validity of the proposed method, a case is examined in this article, and the results support the feasibility and effectiveness of the proposed model and algorithm.     

A real option-based supply chain project evaluation and scheduling method

Supply chain departments spend their time managing numerous projects that will improve and maintain their supply chains. Recent literature has most frequently described the content of these projects and their scheduling but neglected to include risk and uncertainty in the expected cost, profits and time durations of these projects. In this article, we have introduced real option valuation (ROV) to supply chain project scheduling as a flexible method to quantify those risks. Our proposed two-step framework links ROV to all relevant constraints of a multi-project set-up by binary fuzzy goal programming. We applied the framework to a real-life case study data of 21 projects that were facing numerous risks and resource constraints. The results show how scheduling performance improved in comparison to methods ignoring risk and uncertainty (e.g. net present value-based scheduling). For validation we conducted hypothesis tests and sensitivity analysis, and provide an in-depth discussion. The findings contribute to research and practice by capturing project-related risks and managerial flexibilities in general and in supply chains in particular.     

Adaptive scheduling and tool flow control in flexible job shops

The recent manufacturing environment is characterized as having diverse products due to mass customization, short production lead-time, and ever-changing customer demand. Today, the need for flexibility, quick responsiveness, and robustness to system uncertainties in production scheduling decisions has dramatically increased. In traditional job shops, tooling is usually assumed as a fixed resource. However, when a tooling resource is shared among different machines, a greater product variety, routing flexibility with a smaller tool inventory can be realized. Such a strategy is usually enabled by an automatic tool changing mechanism and tool delivery system to reduce the time for tooling set-up, hence it allows parts to be processed in small batches. In this paper, a dynamic scheduling problem under flexible tooling resource constraints is studied and presented. An integrated approach is proposed to allow two levels of hierarchical, dynamic decision making for job scheduling and tool flow control in flexible job shops. It decomposes the overall problem into a series of static sub-problems for each scheduling horizon, handles random disruptions by updating job ready time, completion time, and machine status on a rolling horizon basis, and considers the machine availability explicitly in generating schedules. The effectiveness of the proposed dynamic scheduling approach is tested in simulation studies under a flexible job shop environment, where parts have alternative routings. The study results show that the proposed scheduling approach significantly outperforms other dispatching heuristics, including cost over time (COVERT), apparent tardiness cost (ATC), and bottleneck dynamics (BD), on due-date related performance measures. It is also found that the performance difference between the proposed scheduling approach and other heuristics tend to become more significant when the number of machines is increased. The more operation steps a system has, the better the proposed method performs, relative to the other heuristics.     

An improved imperialist competitive algorithm based photolithography machines scheduling

Abstract: Photolithography machine is one of the most expensive equipment in semiconductor manufacturing system, and as such is often the bottleneck for processing wafers. This paper focuses on photolithography machines scheduling with the objective of total completion time minimisation. In contrast to classic parallel machines scheduling, it is characterised by dynamical arrival wafers, re-entrant process flows, dedicated machine constraints and auxiliary resources constraints. We propose an improved imperialist competitive algorithm (ICA) within the framework of a rolling horizon strategy for the problem. We develop a variable time interval-based rolling horizon strategy to decide the scheduling point. We address the global optimisation in every local scheduling by proposing a mixed cost function. Moreover, an adaptive assimilation operator and a sociopolitical competition operator are used to prevent premature convergence of ICA to local optima. A chaotic sequence-based local search method is presented to accelerate the rate of convergence. Computational experiments are carried out comparing the proposed algorithm with ILOG CPLEX, dispatching rules and meta-heuristic algorithms in the literature. It is observed that the algorithm proposed shows an excellent behaviour on cycle time minimisation while with a good on time delivery rate and machine utilisation rate.     

混合工作日历下批量生产柔性作业车间多目标调度方法

提出了一种混合工作日历下批量生产柔性作业车间多目标调度方法。考虑设备的混合工作日历约束,构建了以生产周期最短、制造成本最低为优化目标的批量生产柔性作业车间多目标调度模型。设计了一种带精英策略的非支配排序遗传算法(NSGA II)求解该模型。算法中,采用“基于工序和设备的分段编码”方式分别对工序和设备进行编码;采用“基于工序和设备的分段交叉和变异方式”进行交叉和变异操作,采用“遗传算子改进策略”保证交叉、变异后子代个体的可行性;解码操作采用“基于平顺移动的原理”和“基于工作日历的时间推算技术”推算工序的调整开始、调整结束、加工开始和加工结束时刻。最后,通过案例分析验证了所提方法的有效性。     

Solving comprehensive dynamic job shop scheduling problem by using a GRASP-based approach

There are many dynamic events like new order arrivals, machine breakdowns, changes in due dates, order cancellations, arrival of urgent orders etc. that makes static scheduling approaches very difficult. A dynamic scheduling strategy should be adopted under such production circumstances. In the present study an event driven dynamic job shop scheduling mechanism under machine capacity constraints is proposed. The proposed method makes use of the greedy randomised adaptive search procedure (GRASP) by also taking into account orders due dates and sequence-dependent set-up times. Moreover, order acceptance/rejection decision and Order Review Release mechanism are integrated with scheduling decision in order to meet customer due date requirements while attempting to execute capacity adjustments. We employed a goal programming-based logic which is used to evaluate four objectives: mean tardiness, schedule unstability, makespan and mean flow time. Benchmark problems including number of orders, number of machines and different dynamic events are generated. In addition to event-driven rescheduling strategy, a periodic rescheduling strategy is also devised and both strategies are compared for different problems. Experimental studies are performed to evaluate effectiveness of the proposed method. Obtained results have proved that the proposed method is a feasible approach for rescheduling problems under dynamic environments.     

Critical chain project buffer sizing based on resource constraints

Project scheduling is a complex process involving many types of resources and activities that require optimisation. The resource-constrained project scheduling problem is one of the well-known problematic issues when project activities have to be scheduled to minimise the project duration. Consequently, several methods have been proposed for adjusting the buffer size but none of these traditional methods consider buffer sizing accuracy based on resource constraints. The purpose of this paper is to develop a buffer sizing method based on a fuzzy resource-constrained project scheduling problem in order to obtain an appropriate proportionality between the activity duration and the buffer size. Specifically, a comprehensive resource-constrained method that considers both the general average resource constraints (GARC) and the highest peak of resource constraints (HPRC) is proposed in order to obtain a new buffer sizing method. This paper contributes to the research by considering several different aspects. First, this paper adopts a fuzzy method to calculate and obtain the threshold amount. Second, this paper discusses the resource levelling problem and proposes the HPRC method. Third, the proposed method uses a fuzzy quantitative model to calculate the resource requirement. The findings indicate that the project achieved higher efficiency, providing effective protection and an appropriate buffer size.     

Two-machine flow shop problem with unit-time operations and conflict graph

This paper addresses the problem of scheduling, on a two-machine flow shop, a set of unit-time operations subject to the constraints that some conflicting jobs cannot be scheduled simultaneously on different machines. In the context of our study, these conflicts are modelled by general graphs. The problem of minimising the maximum completion time (makespan) is known to be NP-hard in the strong sense. We propose a mixed-integer linear programming (MILP) model. Then, we develop a branch and bound algorithm based on new lower and upper bound procedures. We further provide a computer simulation to measure the performance of the proposed approaches. The computational results show that the branch and bound algorithm outperforms the MILP model and can solve instances of size up to 20,000 jobs.     

Biogeography-based optimisation for flexible manufacturing system scheduling problem

Biogeography-based optimisation (BBO) algorithm is a new evolutionary optimisation algorithm based on geographic distribution of biological organisms. With probabilistic operators, this algorithm is able to share more information from good solutions to poor ones. BBO prevents the good solutions to be demolished during the evolution. This feature leads to find the better solutions in a short time rather than other metaheuristics. This paper provides a mathematical model which integrates machine loading, part routing, sequencing and scheduling decision in flexible manufacturing systems (FMS). Moreover, it tackles the scheduling problem when various constraints are imposed on the system. Since this problem is considered to be NP-hard, BBO algorithm is developed to find the optimum /near optimum solution based on various constraints. In the proposed algorithm, different types of mutation operators are employed to enhance the diversity among the population. The proposed BBO has been applied to the instances with different size and degrees of complexity of problem adopted from the FMS literature. The experimental results demonstrate the effectiveness of the proposed algorithm to find optimum /near optimum solutions within reasonable time. Therefore, BBO algorithm can be used as a useful solution for optimisation in various industrial applications within a reasonable computation time.     

On scheduling models for the frequency interval assignment problem with cumulative interferences

In this article, models and methods for solving a real-life frequency assignment problem based on scheduling theory are investigated. A realistic frequency assignment problem involving cumulative interference constraints in which the aim is to maximize the number of assigned users is considered. If interferences are assumed to be binary, a multiple carrier frequency assignment problem can be treated as a disjunctive scheduling problem since a user requesting a number of contiguous frequencies can be considered as a non-preemptive task with a processing time, and two interfering users can be modelled through a disjunctive constraint on the corresponding tasks. A binary interference version of the problem is constructed and a disjunctive scheduling model is derived. Based on the binary representation, two models are proposed. The first one relies on an interference matrix and the second one considers maximal cliques. A third, cumulative, model that yields a new class of scheduling problems is also proposed. Computational experiments show that the case-study frequency assignment problem can be solved efficiently with disjunctive scheduling techniques.     

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.