Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment

This paper proposes a scenario-based two-stage stochastic programming model with recourse for master production scheduling under demand uncertainty. We integrate the model into a hierarchical production planning and control system that is common in industrial practice. To reduce the problem of the disaggregation of the master production schedule, we use a relatively low aggregation level (compared to other work on stochastic programming for production planning). Consequently, we must consider many more scenarios to model demand uncertainty. Additionally, we modify standard modelling approaches for stochastic programming because they lead to the occurrence of many infeasible problems due to rolling planning horizons and interdependencies between master production scheduling and successive planning levels. To evaluate the performance of the proposed models, we generate a customer order arrival process, execute production planning in a rolling horizon environment and simulate the realisation of the planning results. In our experiments, the tardiness of customer orders can be nearly eliminated by the use of the proposed stochastic programming model at the cost of increasing inventory levels and using additional capacity.     

An immune algorithm for scheduling a hybrid flow shop with sequence-dependent setup times and machines with random breakdowns

Much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. Furthermore, most scheduling problems that have been discussed in the literature are under the assumption that machines are continuously available. Nevertheless, in most real-life industries a machine can be unavailable for many reasons, such as unanticipated breakdowns (stochastic unavailability), or due to scheduled preventive maintenance where the periods of unavailability are known in advance (deterministic unavailability). This paper deals with hybrid flow shop scheduling problems in which there are sequence-dependent setup times (SDSTs), and machines suffer stochastic breakdowns, to optimise objectives based on the expected makespan. With the increase in manufacturing complexity, conventional scheduling techniques for generating a reasonable manufacturing schedule have become ineffective. An immune algorithm (IA) can be used to tackle complex problems and produce a reasonable manufacturing schedule within an acceptable time. In this research, a computational method based on a clonal selection principle and an affinity maturation mechanism of the immune response is used. This paper describes how we can incorporate simulation into an immune algorithm for the scheduling of a SDST hybrid flow shop with machines that suffer stochastic breakdowns. The results obtained are analysed using a Taguchi experimental design.     

A hybrid computer simulation-artificial neural network algorithm for optimisation of dispatching rule selection in stochastic job shop scheduling problems

Industrial systems are constantly subject to random events with inevitable uncertainties in production factors, especially in processing times. Due to this stochastic nature, selecting appropriate dispatching rules has become a major issue in practical problems. However, previous research implies that using one dispatching rule does not necessarily yield an optimal schedule. Therefore, a new algorithm is proposed based on computer simulation and artificial neural networks (ANNs) to select the optimal dispatching rule for each machine from a set of rules in order to minimise the makespan in stochastic job shop scheduling problems (SJSSPs). The algorithm contributes to the previous work on job shop scheduling in three significant ways: (1) to the best of our knowledge it is the first time that an approach based on computer simulation and ANNs is proposed to select dispatching rules; (2) non-identical dispatching rules are considered for machines under stochastic environment; and (3) the algorithm is capable of finding the optimal solution of SJSSPs since it evaluates all possible solutions. The performance of the proposed algorithm is compared with computer simulation methods by replicating comprehensive simulation experiments. Extensive computational results for job shops with five and six machines indicate the superiority of the new algorithm compared to previous studies in the literature.     

Flexible job-shop scheduling/rescheduling in dynamic environment: a hybrid MAS/ACO approach

In real-world manufacturing, disruptions are often encountered during the execution of a predetermined schedule, leading to the degradation of its optimality and feasibility. This study presents a hybrid approach for flexible job-shop scheduling/rescheduling problems under dynamic environment. The approach, coined as ‘HMA’ is a combination of multi-agent system (MAS) negotiation and ant colony optimisation (ACO). A fully distributed MAS structure has been constructed to support the solution-finding process by negotiation among the agents. The features of ACO are introduced into the negotiation mechanism in order to improve the performance of the schedule. Experimental studies have been carried out to evaluate the performance of the approach for scheduling and rescheduling under different types of disruptions. Different rescheduling policies are compared and discussed. The results have shown that the proposed approach is a competitive method for flexible job-shop scheduling/rescheduling for both schedule optimality and computation efficiency.     

Mitigating supply and production uncertainties with dynamic scheduling using real-time transport information

Supply and production uncertainties can affect the scheduling and inventory performance of final production systems. Facing such uncertainties, production managers normally choose to maintain the original production schedule, or follow the first-in-first-out policy. This paper develops a new, dynamic algorithm policy that considers scheduling and inventory problems, by taking advantage of real-time shipping information enabled by today’s advanced technology. Simulation models based on the industrial example of a chemical company and the Taguchi’s method are used to test these three policies under 81 experiments with varying supply and production lead times and uncertainties. Simulation results show that the proposed dynamic algorithm outperforms the other two policies for supply chain cost. Results from Taguchi’s method show that companies should focus their long-term effort on the reduction of supply lead times, which positively affects the mitigation of supply uncertainty.     

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.     

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.     

Novel slack-based robust scheduling rule for a semiconductor manufacturing system with uncertain processing time

The NP-hard scheduling problems of semiconductor manufacturing systems (SMSs) are further complicated by stochastic uncertainties. Reactive scheduling is a common dynamic scheduling approach where the scheduling scheme is refreshed in response to real-time uncertainties. The scheduling scheme is overly sensitive to the emergence of uncertainties because the optimization of performance (such as minimum make-span) and the system robustness cannot be achieved simultaneously by conventional reactive scheduling methods. To improve the robustness of the scheduling scheme, we propose a novel slack-based robust scheduling rule (SR) based on the analysis of robustness measurement for SMS with uncertain processing time. The decision in the SR is made in real time given the robustness. The proposed SR is verified under different scenarios, and the results are compared with the existing heuristic rules. Simulation results show that the proposed SR can effectively improve the robustness of the scheduling scheme with a slight performance loss.     

Distributed policy search reinforcement learning for job-shop scheduling tasks

We interpret job-shop scheduling problems as sequential decision problems that are handled by independent learning agents. These agents act completely decoupled from one another and employ probabilistic dispatching policies for which we propose a compact representation using a small set of real-valued parameters. During ongoing learning, the agents adapt these parameters using policy gradient reinforcement learning, with the aim of improving the performance of the joint policy measured in terms of a standard scheduling objective function. Moreover, we suggest a lightweight communication mechanism that enhances the agents' capabilities beyond purely reactive job dispatching. We evaluate the effectiveness of our learning approach using various deterministic as well as stochastic job-shop scheduling benchmark problems, demonstrating that the utilisation of policy gradient methods can be effective and beneficial for scheduling problems.     

Scheduling and order acceptance for the customised stochastic lot scheduling problem

This paper develops and analyses several customer order acceptance policies to achieve high bottleneck utilisation for the customised stochastic lot scheduling problem (CSLSP) with large setups and strict order due dates. To compare the policies, simulation is used as the main tool, due to the complicated nature of the problem. Also, approximate upper and lower bounds for the utilisation are provided. It is shown that a greedy approach to accept orders performs poorly in that it achieves low utilisation for high customer order arrival rates. Rather, good acceptance and scheduling policies for the CSLSP should sometimes reject orders to create slack even when there is room in the schedule to start new production runs. We show that intelligently introducing slack enables the achievement of high utilisation. One particularly simple policy is to restrict the number of families present.     

A lever concept integrated with simple rules for flow shop scheduling

The development of more efficient and better performing priority dispatching rules (PDRs) for production scheduling is relevant to modern flow shop scheduling practice because they are simple, easy to apply and have low computational complexity, especially for large-scale problems. While the current research trend in scheduling is towards finding superior solutions through meta-heuristics, they are computationally expensive and many meta-heuristics also use PDRs to generate starting points. In this paper, we analyse the properties of flow shop scheduling problems to minimise maximum completion time, and generate a new dominance rule that is complementary to Szwarc’s rule. These dominance rules indicate that a weighting factor should be included in sequencing to account for the possibility that a single job’s processing time can generate idle time repeatedly within a flow line. Two new PDRs with a leveraged weighting factor are proposed to minimise makespan and average completion time. Computational results on Taillard’s benchmark problems and on historical operating room data show that the proposed PDRs perform much better than established PDRs without an increase in computational complexity.     

考虑急件到达的单机鲁棒调度方法

实际生产过程中经常会有急件到达。由于急件的优先级最高,其到达容易扰乱初始调度,使实际调度性能恶化,影响调度目标的实现。针对以总拖期为目标且带有释放时间的单机调度问题,研究了在有急件到达情况下的鲁棒调度方法,以降低急件对实际调度性能的影响。鉴于该调度问题是NP hard问题,根据工件释放时间和交货期的关系构造“金字塔”结构,获得该调度问题的占优性质。根据这些占优性质和急件到达特点,研究急件到达情景下的占优规则,据此求解急件到达情景下的占优调度集合,作为鲁棒调度的备选调度方案集合。提出了应对急件到达的鲁棒调度算法。给出仿真算例验证了算法的有效性,算例表明本文给出的鲁棒调度方法能有效避免急件到达造成实际调度性能的恶化。      

Multi-criteria optimisation-based dynamic scheduling for controlling FMS

This study deals with controlling flexible manufacturing systems (FMS) operating in volatile production environments. Most studies that address this issue use some sort of adaptive scheduling that enables the FMS to cope with the randomness and variability efficiently. The methods presented in the literature are usually based on heuristics and use simple dispatching rules. They do not consider changing the decision criteria dynamically as the system conditions change. In contrast to previous studies, the present study focuses on developing a control mechanism for dynamic scheduling that is based on incremental optimisation. This means that each time a scheduling decision is made, the local optimisation problem is solved such that the next jobs to be processed on machines are selected. The objective function (dominant decision criterion) for this optimisation problem is selected dynamically based on production order requirements, actual shop-floor status and system priorities. The proposed multi-criteria optimisation-based dynamic scheduling methodology was evaluated and compared with some known scheduling rules/policies. The results obtained demonstrate the superiority of the suggested methodology as well as its capability to cope with a multi-criteria environment.     

Chemical process dynamic optimization based on the differential evolution algorithm with an adaptive scheduling mutation strategy

To solve chemical process dynamic optimization problems, a differential evolution algorithm integrated with adaptive scheduling mutation strategy (ASDE) is proposed. According to the evolution feedback information, ASDE, with adaptive control parameters, adopts the round-robin scheduling algorithm to adaptively schedule different mutation strategies. By employing an adaptive mutation strategy and control parameters, the real-time optimal control parameters and mutation strategy are obtained to improve the optimization performance. The performance of ASDE is evaluated using a suite of 14 benchmark functions. The results demonstrate that ASDE performs better than four conventional differential evolution (DE) algorithm variants with different mutation strategies, and that the whole performance of ASDE is equivalent to a self-adaptive DE algorithm variant and better than five conventional DE algorithm variants. Furthermore, ASDE was applied to solve a typical dynamic optimization problem of a chemical process. The obtained results indicate that ASDE is a feasible and competitive optimizer for this kind of problem.     

Quay crane scheduling in container terminals

The problem of scheduling identical quay cranes moving along a common linear rail to handle containers for a ship is studied. The ship has a number of container-stacking compartments called bays, and only one quay crane can work on a bay at the same time. The objective of the scheduling problem is to find the work schedule for each quay crane which minimizes the ship’s stay time in port. Finding the optimal solution of the scheduling problem is computationally intractable and a heuristic is proposed to solve it. The heuristic first decomposes the difficult multi-crane scheduling problem into easier subproblems by partitioning the ship into a set of non-overlapping zones. The resulting subproblems for each possible partition are solved optimally by a simple rule. An effective algorithm for finding tight lower bounds is developed by modifying and enhancing an effective lower-bounding procedure proposed in the literature. Computational experiments were carried out to evaluate the performance of the heuristic on a set of test problems randomly generated based on typical terminal operations data. The computational results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 4.8% above their lower bounds.     

Workshop scheduling using practical (inaccurate) data Part 2: An investigation of the robustness of scheduling rules in a dynamic and stochastic environment

In research on generating a predictive schedule, the scheduling problem is often viewed as a deterministic problem. However, the real-life job shop environment is stochastic in that information on job attributes and shop floor status is not precisely known in advance. In this situation, in order to increase the effectiveness of a predictive schedule in practice, the focus should be on creating a robust schedule. The purpose of this paper is to investigate the robustness of a number of scheduling rules in a dynamic and stochastic environment using the rolling time horizon approach. A cost-based performance measure is used to evaluate the scheduling rules. The simulation results, under various conditions in a balanced and unbalanced shop, are presented and the effects of the rescheduling interval and operational factors including shop load conditions and a bottleneck on the robustness of the schedule are studied. From the results the key factors that influence the robustness of a scheduling system are identified and, consequently, general guidelines for creating robust schedules are proposed.     

Assessing scheduling policies in a permutation flowshop with common due dates

This paper focuses onto a situation arising in most real-life manufacturing environments when scheduling has to be performed periodically. In such a scenario, different scheduling policies can be adopted, being perhaps the most common to assume that, once a set of jobs has been scheduled, their schedule cannot be modified (‘frozen’ schedule). This implies that, when the next set of jobs is to be scheduled, the resources may not be fully available. Another option is assuming that the schedule of the previously scheduled jobs can be modified as long as it does not violate their due date, which has been already possibly committed to the customer. This policy leads to a so-called multi-agent scheduling problem. The goal of this paper is to discern when each policy is more suitable for the case of a permutation flowshop with common due dates. To do so, we carry out an extensive computational study in a test bed specifically designed to control the main factors affecting the policies, so we analyse the solution space of the underlying scheduling problems. The results indicate that, when the due date of the committed jobs is tight, the multi-agent approach does not pay off in view of the difficulty of finding feasible solutions. Moreover, in such cases, the policy of ‘freezing’ the schedule of the jobs leads to a very simple scheduling problem with many good/acceptable solutions. In contrast, when the due date has a medium/high slack, the multi-agent approach is substantially better. Nevertheless, in this latter case, in order to perceive the full advantage of this policy, powerful solution procedures have to be designed, as the structure of the solution space of the latter problem makes extremely hard to find optimal/good solutions.     

Applying a hybrid simulated annealing and tabu search approach to non-permutation flowshop scheduling problems

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.     

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.     

The single-day surgery scheduling problem: sequential decision-making and threshold-based heuristics

Scheduling elective surgeries is a dynamic, sequential decision-making process that must balance the costs of deferring waiting cases and blocking higher-priority cases. Although other surgery scheduling problems have received extensive treatment in the literature, this paper presents the first single-day scheduling problem formulation to capture this aspect of the scheduling process while also incorporating surgical block schedules, block release policies, and waiting lists. Theoretical results for the special case in which all cases have the same duration motivate a range of threshold-based heuristics for the general problem with multiple case durations. Our computational results demonstrate the effectiveness of the proposed heuristics and show how block release dates affect the quality of the scheduling decisions. Based on these results, we propose a new approach to surgery scheduling. In particular, to make more equitable waiting list decisions, operating room (OR) managers should gradually release unused OR time over the course of several days leading up to the day of surgery.