An energy-efficient scheduling and rescheduling method for production and logistics systems†

Scheduling can be defined as the allocation of available resources over time while optimising a set of criteria like early completion time of task, holding inventory, etc. The complexity of the scheduling problem, already known to be high, increases if dynamic events and disruptions are considered. In addition, in production and logistics, designers of scheduling systems must consider sustainability-related expectations. This paper presents an energy-efficient scheduling and rescheduling method (named Green Rescheduling Method, GRM). GRM aims at the solving of the dynamic scheduling problem under the condition of a certain level of routing flexibility enabling the reassignment of tasks to new resources. The key performance indicators integrated into the proposed GRM are effectiveness and efficiency-oriented. Applications concern the domains of production and logistics. In order to assess the proposed approach, experimentations have been made and results illustrate the applicability of GRM to build efficient and effective scheduling and rescheduling both for flexible manufacturing systems and inventory distribution systems in a physical internet network. A mathematical formulation for flexible job shop problem with energy consumption is also proposed using mixed Integer programming to evaluate the performance of the predictive part of GRM.     

Studying the impact of sequence-dependent set-up times in integrated process planning and scheduling with E-ACO heuristic

In job-shop scheduling, the importance of set-up issues is well known and has been considered in many solution approaches. However, in integrated process planning and scheduling (IPPS) involving flexible process plans, the set-up times are often ignored, or absorbed into processing times in IPPS domain, with the purpose to reduce the complexity. This is based on the assumption that set-up times are sequence-independent, or short enough to be ignored compared to processing times. However, it is not uncommon to encounter sequence-dependent set-up times (SDSTs) in practical production. This paper conducts a detailed investigation on the impact of SDSTs on the practical performance of the schedule: a comparative study is made for different cases where set-up times are (1) separately considered, (2) absorbed into processing times, or (3) totally ignored. An enhanced version of ant colony optimisation (E-ACO) algorithm is used to solve the IPPS problem, with the objective to minimise the total makespan. The following four types of set-up issues are considered: part loading/unloading, fixture preparation, tool switching and material transportation. Situations with various set-up time lengths have been studied and compared. A special case of IPPS problem involving a large number of identical jobs has been specifically studied and discussed. The results have shown that, set-up times should be carefully dealt with under different circumstances.     

A neural network decision-making model for job-shop scheduling

Scheduling in a job-shop system is a challenging task. Simulation modelling is a well-known approach for evaluating the scheduling plans of a job-shop system; however, it is costly and time-consuming, and developing a model and interpreting the results requires expertise. As an alternative, we have developed a neural network (NN) model focused on detailed scheduling that provides a versatile job-shop scheduling analysis framework for management to easily evaluate different possible scheduling scenarios based on internal or external constraints. A new approach is also proposed to enhance the quality of training data for better performance. Previous NN models in scheduling focus mainly on job sequencing and simple operations flow, and may not consider the complexities of real-world operations. The proposed model’s output proved statistically equivalent to the results of the simulation model. The study was accomplished using sensitivity analysis to measure the effectiveness of the input variables of the NN model and their impact on the output, revealing that the batch size variable had a significant impact on the scheduling results in comparison with other variables.     

Flow shop rescheduling under different types of disruption

Almost all manufacturing facilities need to use production planning and scheduling systems to increase productivity and to reduce production costs. Real-life production operations are subject to a large number of unexpected disruptions that may invalidate the original schedules. In these cases, rescheduling is essential to minimise the impact on the performance of the system. In this work we consider flow shop layouts that have seldom been studied in the rescheduling literature. We generate and employ three types of disruption that interrupt the original schedules simultaneously. We develop rescheduling algorithms to finally accomplish the twofold objective of establishing a standard framework on the one hand, and proposing rescheduling methods that seek a good trade-off between schedule quality and stability on the other.     

A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem

Scheduling for the flexible job-shop is a very important issue in both fields of combinatorial optimization and production operations. However, due to combination of the routing and sequencing problems, flexible job-shop scheduling problem (FJSP) presents additional difficulty than the classical job-shop scheduling problem and requires more effective algorithms. This paper developed a filtered-beam-search-based heuristic algorithm (named as HFBS) to find sub-optimal schedules within a reasonable computational time for the FJSP with multiple objectives of minimising makespan, the total workload of machines and the workload of the most loaded machine. The proposed algorithm incorporates dispatching rules based heuristics and explores intelligently the search space to avoid useless paths, which makes it possible to improve the search speed. Through computational experiments, the performance of the presented algorithm is evaluated and compared with those of existing literature and those of commonly used dispatching rules, and the results demonstrate that the proposed algorithm is an effective and practical approach for the FJSP.     

Auction-based approach for a flexible job-shop scheduling problem with multiple process plans

This study addresses the flexible job-shop scheduling problem with multiple process plans with the objective of minimizing the overall makespan. A nonlinear programming model is formulated to allocate machines and schedule jobs. An auction-based approach is proposed to address the integrated production route selection and resource allocation problem and focus on improving resource utilization and productive efficiency to reduce the makespan. The approach consists of an auction for process plans and an auction for machines. The auctions are evaluated to select a more suitable route for production and allocate resources to a more desirable job. Numerical experiments are conducted by testing new large benchmark instances. A comparison of Lingo and other existing algorithms demonstrates the effectiveness and stability of the proposed auction-based approach. Furthermore, SPSS is used to prove that the proposed method exhibits an absolute advantage, particularly for medium-scale or large-scale instances.     

Distributed supply‐chain project rescheduling: Part I—impacts of information‐sharing strategies

A supply‐chain project normally involves a number of independent and autonomous enterprises that share information to varying levels. The initial project schedule (preschedule) established at the time of forming the supply‐chain often requires a series of amendments due to unexpected or abrupt disturbances such as temporary resource outage (e.g. machine break), arrival or cancellation of orders from customers, and change in an operation's processing time (e.g. rework). Rescheduling or adaptive scheduling is a process of updating/repairing the preschedule to adapt to the disturbances. Appropriate rescheduling methods must be chosen and applied depending on the specific protocol of sharing information agreed between the enterprises in the supply chain. This paper is concerned with the impacts of different levels of information sharing on the performance of supply‐chain project rescheduling problems. Three rescheduling methods are examined in the research. They are distributed AOR (Affected Operations Rescheduling), negotiation‐based rescheduling (NEG), and centralized total rescheduling (TR). These three rescheduling algorithms represent three typical information‐sharing scenarios: little information sharing, limited information sharing and complete information sharing, respectively. A comprehensive computational study is conducted under different experimental settings. The results show that NEG and distAOR outperforms the TR rescheduling in terms of total cost minimization and stability of schedule and contractual relationship. NEG is superior in both rescheduling efficiency and effectiveness due to the effect of a moderate level of information sharing.     

Flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints

The purpose of this research is to solve flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints in the operations. We first formulate the problem as a Mixed-Integer Linear Program (MILP). The MILP can be used to compute optimal solutions for small-sized problems. We also developed a heuristic algorithm that can obtain a good solution for the problem regardless of its size. Moreover, we have developed a representation and schedule builder that always produces a legal and feasible solution for the problem, and developed genetic and tabu search algorithms based on the proposed schedule builder. The results of the computational experiments show that the developed meta-heuristics are very effective.     

Flexible job-shop scheduling problem under resource constraints

A flexible job-shop-scheduling problem is an extension of classical job-shop problems that permit an operation of each job to be processed by more than one machine. The research methodology is to assign operations to machines (assignment) and determine the processing order of jobs on machines (sequencing) such that the system objectives can be optimized. This problem can explore very well the common nature of many real manufacturing environments under resource constraints. A genetic algorithm-based approach is developed to solve the problem. Using the proposed approach, a resource-constrained operations–machines assignment problem and flexible job-shop scheduling problem can be solved iteratively. In this connection, the flexibility embedded in the flexible shop floor, which is important to today's manufacturers, can be quantified under different levels of resource availability.     

A generic deadlock-free reactive scheduling approach

In this paper, a generic deadlock-free reactive scheduling (GDRS) approach is proposed. The approach can react to the occurrence of a variety of disruptions in flexible job shops, in real time. Internal and external disruptions such as machine breakdown, process time variation, urgent job, arrival of a new job order, and order cancellation are considered. Performance comparisons of the proposed approach with that of Total Rescheduling (TR), and with the modified Affected Operations Rescheduling (mAOR) heuristic proposed earlier in the literature are presented by considering scheduling efficiency and stability. The results show that, for most of the disruptions considered, GDRS retains the rescheduling efficiency of TR while providing superior system stability over the other two approaches.     

Proposal of a multi-agent model for the sustainable truck scheduling and containers grouping problem in a Road-Rail physical internet hub

Physical Internet (PI) was introduced as a global standardised and interconnected logistics system based on PI-nodes, PI-movers and PI-containers as a mean toward global logistics sustainability. One important issue regarding PI-nodes concerns the planning and scheduling of operations and the management of PI-containers, both in a deterministic and a perturbed environment. This research considers the Road-Rail PI-hub sustainable truck scheduling and PI-containers grouping problem. In our research we consider the weighted sum of the number of used wagons, the internal distance travelled by PI-containers from PI-docks to wagons as well as the trucks’ tardiness, which translate the search for sustainable logistics. In this paper, an effective and reactive multi-agent system based model (MAS) is developed for the resolution of the trucks scheduling and PI-containers grouping. To ensure the efficiency of the MAS and improve the quality of each of its solutions, three concurrent hybrid meta-heuristics are embedded within three parallel scheduling agents. Then, a mixed integer linear programming model (MILP) is proposed to evaluate the performance of the MAS. Finally, the MAS is also evaluated under internal perturbations. The obtained results show the ability of the MAS to provide alternative sustainable solutions by rescheduling trucks in case of disruptions.     

Integrated process planning and scheduling – multi-agent system with two-stage ant colony optimisation algorithm

In this paper, a two-stage ant colony optimisation (ACO) algorithm is implemented in a multi-agent system (MAS) to accomplish integrated process planning and scheduling (IPPS) in the job shop type flexible manufacturing environments. Traditionally, process planning and scheduling functions are performed sequentially and the actual status of the production facilities is not considered in either process planning or scheduling. IPPS is to combine both the process planning and scheduling problems in the consideration, that is, the actual process plan and the schedule are determined dynamically in accordance with the order details and the status of the manufacturing system. The ACO algorithm can be applied to solve IPPS problems. An innovative two-stage ACO algorithm is introduced in this paper. In the first stage of the algorithm, instead of depositing pheromones on graph edges as in common ant algorithms, ants are directed to deposit pheromones at the nodes to select a set of more favourable processes. In the second stage, the set of nodes not selected in the first stage will be ignored, and pheromones will be deposited along the graph edges while the ants traverse the paths connecting the selected set of nodes.     

An improved Intelligent Water Drops algorithm for achieving optimal job-shop scheduling solutions

Job-shop scheduling is a typical NP-hard problem which has drawn continuous attention from researchers. In this paper, the Intelligent Water Drops (IWD) algorithm, which is a new meta-heuristics, is customised for solving job-shop scheduling problems. Five schemes are proposed to improve the original IWD algorithm, and the improved algorithm is named the Enhanced IWD algorithm (EIWD) algorithm. The optimisation objective is the makespan of the schedule. Experimental results show that the EIWD algorithm is able to find better solutions for the standard benchmark instances than the existing algorithms. This paper has made a contribution in two aspects. First, to the best of the authors’ knowledge, this research is the first to apply the IWD algorithm to the job-shop scheduling problem. This work can inspire further studies of applying IWD algorithm to other scheduling problems, such as open-shop scheduling and flow-shop scheduling. Second, this research further improves the original IWD algorithm by employing five schemes to increase the diversity of the solution space as well as the solution quality.     

A hybrid genetic algorithm and tabu search for a multi-objective dynamic job shop scheduling problem

In most real manufacturing environments, schedules are usually inevitable with the presence of various unexpected disruptions. In this paper, a rescheduling method based on the hybrid genetic algorithm and tabu search is introduced to address the dynamic job shop scheduling problem with random job arrivals and machine breakdowns. Because the real-time events are difficult to express and take into account in the mathematical model, a simulator is proposed to tackle the complexity of the problem. A hybrid policy is selected to deal with the dynamic feature of the problem. Two objectives, which are the schedule efficiency and the schedule stability, are considered simultaneously to improve the robustness and the performance of the schedule system. Numerical experiments have been designed to test and evaluate the performance of the proposed method. This proposed method has been compared with some common dispatching rules and meta-heuristic algorithms that have been widely used in the literature. The experimental results illustrate that the proposed method is very effective in various shop-floor conditions.     

A variable neighbourhood search algorithm for the flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a generalisation of the classical job-shop scheduling problem which allows an operation of each job to be executed by any machine out of a set of available machines. FJSP consists of two sub-problems which are assigning each operation to a machine out of a set of capable machines (routing sub-problem) and sequencing the assigned operations on the machines (sequencing sub-problem). This paper proposes a variable neighbourhood search (VNS) algorithm that solves the FJSP to minimise makespan. In the process of the presented algorithm, various neighbourhood structures related to assignment and sequencing problems are used for generating neighbouring solutions. To compare our algorithm with previous ones, an extensive computational study on 181 benchmark problems has been conducted. The results obtained from the presented algorithm are quite comparable to those obtained by the best-known algorithms for FJSP.     

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.     

Predictable scheduling of a single machine with breakdowns and sensitive jobs

Production schedules released to the shop floor have two important functions: allocating shop resources to different jobs to optimize some measure of shop performance and serving as a basis for planning external activities such as material procurement, preventive maintenance and delivery of orders to customers. Schedule modification may delay or render infeasible the execution of external activities planned on the basis of the predictive schedule. Thus it is of interest to develop predictive schedules that can absorb disruptions without affecting planned external activities while maintaining high shop performance. We present a predictable scheduling approach, that inserts additional idle time into the schedule to absorb the impacts of breakdowns. The effects of disruptions on planned support activities are measured by the deviations of job completion times in the realized schedule from those in the predictive schedule. We apply our approach to minimizing total tardiness on a single machine with stochastic machine failures. We then extend the procedure to consider the case where job processing times are affected by machine breakdowns, and provide specialized rescheduling heuristics. Extensive computational experiments show that this approach provides high predictability with minor sacrifices in shop performance.     

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.     

An effective estimation of distribution algorithm for the flexible job-shop scheduling problem with fuzzy processing time

Considering the fuzzy nature of the data in real-world scheduling, an effective estimation of distribution algorithm (EDA) is proposed to solve the flexible job-shop scheduling problem with fuzzy processing time. A probability model is presented to describe the probability distribution of the solution space. A mechanism is provided to update the probability model with the elite individuals. By sampling the probability model, new individuals can be generated among the search region with promising solutions. Moreover, a left-shift scheme is employed for improving schedule solution when idle time exists on the machine. In addition, some fuzzy number operations are used to calculate scheduling objective value. The influence of parameter setting is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Numerical testing results and comparisons with some existing algorithms are provided, which demonstrate the effectiveness of the proposed EDA.     

Flexible job-shop scheduling with flexible workdays,preemption, overlapping in operations and satisfaction criteria: an industrial application

This paper addresses a real scheduling problem, namely, a complex flexible job-shop scheduling problem (FJSP) with special characteristics (flexible workdays, preemption and overlapping in operations), where the objective is to maximise a satisfaction criterion defined through goal programming. To allow for flexible workdays, the solution representation of the classical FJSP is extended to consider overtime decisions and a sequence of time-cell states, which is used to model resource capability. A new temporal-constraint-handling method is proposed to solve the problem of overlapping in operations in a flexible-workday environment. Three solution methods are proposed to solve this scheduling problem: a heuristic method based on priority rules, a goal-guided tabu search (GGTS) and an extended genetic algorithm (EGA). In the GGTS, the neighbourhood functions are defined based on elimination approaches, and five possible neighbourhood functions (N0???N1???N2???N3???N4) are presented. The effectiveness and efficiency of the three solution methods are verified using dedicated benchmark instances. Computational simulations and comparisons indicate that the proposed N4-based GGTS demonstrates performance competitive with that of the EGA and the GGTSs based on the other neighbourhood functions (N0, N1, N2 and N3) for solving the scheduling problem.