Heuristic methods for the single machine scheduling problem with different ready times and a common due date

The single machine scheduling problem with a common due date and non-identical ready times for the jobs is examined in this work. Performance is measured by the minimization of the weighted sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, the application of constructive heuristics that exploit specific characteristics of the problem to improve their performance is investigated. The proposed approaches are examined through a computational comparative study on a set of 280 benchmark test problems with up to 1000 jobs.     

Integrated process planning and scheduling using an imperialist competitive algorithm

Effective performance of modern manufacturing systems requires integrating process planning and scheduling more tightly, which is consistently challenged by the intrinsic interrelation and intractability of these two problems. Traditionally, these two problems are treated sequentially or separately. Integration of process planning and scheduling (IPPS) provides a valuable approach to improve system performance. However, IPPS is more complex than job shop scheduling or process planning. IPPS is strongly NP-hard in that, compared to an NP-hard job shop scheduling problem with a determined process plan, the process plan for each job in IPPS is also to be optimised. So, an imperialist competitive algorithm (ICA) is proposed to address the IPPS problem with an objective of makespan minimisation. An extended operation-based representation scheme is presented to include information on various flexibilities of process planning with respect to determined job shop scheduling. The main steps of the proposed ICA, including empires construction, assimilation, imperialistic competition, revolution and elimination, are elaborated using an illustrative example. Performance of the proposed ICA was evaluated on four sets of experiments taken from the literature. Computational results of the ICA were compared with that of some existing algorithms developed for IPPS, which validates the efficiency and effectiveness of the ICA in solving the IPPS problem.     

Minimising total weighted earliness and tardiness penalties on identical parallel machines using a fast ruin-and-recreate algorithm

This paper studies the scheduling problem of minimising total weighted earliness and tardiness penalties on identical parallel machines against a restrictive common due date. This problem is NP-hard in the strong sense and arises in many just-in-time production environments. A fast ruin-and-recreate (FR&R) algorithm is proposed to obtain high-quality solutions to this complex problem. The proposed FR&R algorithm is tested on a well-known set of benchmark test problems that are taken from the literature. Computational results provide evidence of the efficiency of FR&R, which consistently outperform existing algorithms when applied to benchmark instances. This work provides a viable alternative approach for efficiently solving this practical but complex scheduling problem.     

Permutation flow shop scheduling with earliness and tardiness penalties

We consider the permutation flow shop scheduling problem with earliness and tardiness penalties (E/T) and common due date for jobs. We show that the problem can be sub-divided into three cases: (i) the due date is such that all jobs are necessarily tardy; (ii) the due date is unrestricted; and (iii) the due date is between the two. Based on analytical results we provide partial characterisation of the optimal solution and develop a comprehensive approach for solving the problem over the entire range of due dates. Our approach, which draws upon the existing literature and results for the single machine problem, successfully exploits the properties of the optimal solution. Limited computational results indicate that the performance of the heuristic is reasonable and has the potential to significantly improve performance. This approach has been incorporated as part of the scheduling module of the production planning and scheduling system we developed for a medium-sized bulk drug manufacturer.     

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.     

A branch-and-bound algorithm for minimizing the sum of maximum earliness and tardiness with unequal release times

This article addresses the problem of minimizing the sum of maximum earliness and tardiness on a single machine with unequal release times. It is proven that this problem is NP-hard in the strong sense and a branch-and-bound algorithm is developed as an exact method. In the proposed algorithm, modified dispatching rules based on different release times are proposed as the upper bound, while a procedure considering preemption assumption is used to obtain a good lower bound. Also, dominance rules based on no unforced idle time, adjacent pairwise interchanges in the base problem, and job blocks are used to fathom the nodes. In order to evaluate the efficiency of the proposed algorithm, 4,860 instances were randomly generated, varying from 7 to 1,000 jobs. It is shown that the branch-and-bound algorithm was capable of optimally solving 94.1% of the instances, showing its efficiency in solving all problem sizes.     

A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem

This paper deals with the two-stage assembly flowshop scheduling problem with minimisation of weighted sum of makespan and mean completion time as the objective. The problem is NP-hard, hence we proposed a meta-heuristic named imperialist competitive algorithm (ICA) to solve it. Since appropriate design of the parameters has a significant impact on the algorithm efficiency, we calibrate the parameters of this algorithm using the Taguchi method. In comparison with the best algorithm proposed previously, the ICA indicates an improvement. The results have been confirmed statistically.     

Group scheduling in flexible flow shops: a hybridised approach of imperialist competitive algorithm and electromagnetic-like mechanism

This paper applied a novel evolutionary algorithm, imperialist competitive algorithm (ICA), for a group scheduling problem in a hybrid flexible flow shop with sequence-dependent setup times by minimising maximum completion time. This algorithm simulates a social-economical procedure, imperialistic competition. Initial population is generated randomly and evolution is carried out during the algorithm. Firstly individuals, countries, are divided into two categories: imperialists and colonies. Imperialist competition will occur among these empires. This competition will increase some empires authority by ruining a weak empire and dividing its colonies among others. Electromagnetic-like mechanism concepts are employed here to model the influence of the imperialist on their colonies. The algorithm will continue until one imperialist exists and possesses all countries. In order to prevent carrying out extensive experiments to find optimum parameters of the algorithm, we apply the Taguchi approach. The computational results are compared with the outstanding benchmark on the flow shop scheduling problem, random key genetic algorithms (RKGA), and it shows superiority of the ICA.     

Minimizing earliness–tardiness on a single burn-in oven with a common due date and maximum allowable tardiness constraint

This paper considers a scheduling problem for a single burn-in oven in the semiconductor manufacturing industry where the oven is a batch processing machine with restricted capacity. The batch processing time is set by the longest processing time among those of all the jobs contained in the batch. All jobs are assumed to have the same due date. The objective is to minimize the sum of the absolute deviations of completion times from the due date (earliness–tardiness) of all jobs under the constraint that the maximum tardiness should be less than or equal to the maximum allowable time value. We suggest several two-phase heuristic algorithms for this problem. In the first phase, some heuristic algorithms are developed without maximum allowable tardiness constraint. If the schedule from the first phase violates the maximum tardiness constraint, then the schedule is changed to satisfy maximum allowable tardiness constraint in the second phase. The suggested heuristics are based on genetic algorithms and dominance properties of optimal schedules. We present the results of computational experiments that clearly show the solution quality obtained by the suggested heuristics.     

A two-layer dynamic scheduling method for minimising the earliness and tardiness of a re-entrant production line

This study focuses on the dynamic scheduling problem of a re-entrant production line, in which all of the parts are assumed to have the same processing routes and be processed on every machine. A two-layer dynamic scheduling method is proposed for the dynamic scheduling of the re-entrant line with the objective of minimising total earliness and tardiness. This method consists of two layers. The top layer is to select the appropriate scheduling policy, and the bottom layer is to generate the scheduling by using the policy selected in the top layer. In the top layer, three different rules are constructed for selecting scheduling policies, namely the lateness comparison rule, the lateness variation comparison rule, and the equal interval switching rule. In the bottom layer, three different scheduling policies are proposed to generate the real-time scheduling for manufacturing, namely the FCFS (first come first service) scheduling policy, the PI (proportional-integral) scheduling policy, and the fuzzy PI scheduling policy. Considering that the real-time status of manufacturing changes constantly, it is necessary to switch among different scheduling policies to adapt to this change. Numerical experiments are performed in the situations with and without urgent jobs. The results show that the proposed two-layer dynamic scheduling method outperforms any single scheduling policy (e.g., the FCFS policy, the PI policy and the fuzzy PI policy) for the dynamic scheduling of a re-entrant production line.     

A discrete artificial bee colony algorithm for single machine scheduling problems

This paper presents a discrete artificial bee colony algorithm for a single machine earliness–tardiness scheduling problem. The objective of single machine earliness–tardiness scheduling problems is to find a job sequence that minimises the total sum of earliness–tardiness penalties. Artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic, which mimics the foraging behaviour of honey bee swarms. In this study, several modifications to the original ABC algorithm are proposed for adapting the algorithm to efficiently solve combinatorial optimisation problems like single machine scheduling. In proposed study, instead of using a single search operator to generate neighbour solutions, random selection from an operator pool is employed. Moreover, novel crossover operators are presented and employed with several parent sets with different characteristics to enhance both exploration and exploitation behaviour of the proposed algorithm. The performance of the presented meta-heuristic is evaluated on several benchmark problems in detail and compared with the state-of-the-art algorithms. Computational results indicate that the algorithm can produce better solutions in terms of solution quality, robustness and computational time when compared to other algorithms.     

A hybrid particle swarm optimisation for scheduling just-in-time single machine with preemption,machine idle time and unequal release times

This paper addresses preemption in just-in-time (JIT) single–machine-scheduling problem with unequal release times and allowable unforced machine idle time as realistic assumptions occur in the manufacturing environments aiming to minimise the total weighted earliness and tardiness costs. Delay in production systems is a vital item to be focussed to counteract lost sale and back order. Thus, JIT concept is targeted including the elements required such as machine preemption, machine idle time and unequal release times. We proposed a new mathematical model and as the problem is proven to be NP-hard, three meta-heuristic approaches namely hybrid particle swarm optimisation (HPSO), genetic algorithm and imperialist competitive algorithm are employed to solve the problem in larger sizes. In HPSO, cloud theory-based simulated annealing is employed with a certain probability to avoid being trapped in a local optimum. Taguchi method is applied to calibrate the parameters of the proposed algorithms. A number of numerical examples are solved to demonstrate the effectiveness of the proposed approach. The performance of the proposed algorithms is evaluated in terms of relative percent deviation and computational time where the computational results clarify better performance of HPSO than other algorithms in quality of solutions and computational time.     

An efficient imperialist competitive algorithm for scheduling in the two-stage assembly flow shop problem

This paper considers a two-stage assembly flow shop problem where m parallel machines are in the first stage and an assembly machine is in the second stage. The objective is to minimise a weighted sum of makespan and mean completion time for n available jobs. As this problem is proven to be NP-hard, therefore, we employed an imperialist competitive algorithm (ICA) as solution approach. In the past literature, Torabzadeh and Zandieh (2010 Torabzadeh, E., and M. Zandieh. 2010. “Cloud theory-based Simulated Annealing Approach for Scheduling in the Two-stage Assembly Flow Shop.” Advances in Engineering Software 41: 1238–1243.[Crossref], [Web of Science ®] , [Google Scholar]) showed that cloud theory-based simulated annealing algorithm (CSA) is an appropriate meta-heuristic to solve the problem. Thus, to justify the claim for ICA capability, we compare our proposed ICA with the reported CSA. A new parameters tuning tool, neural network, for ICA is also introduced. The computational results clarify that ICA performs better than CSA in quality of solutions.     

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.     

Due date assignment in single machine with stochastic processing times

This paper considers two different due date assignment and sequencing problems in single machine where the processing times of jobs are random variables. The first problem is to minimise the maximum due date so that all jobs are stochastically on time. It is shown that sequencing the jobs in decreasing service level (DSL) order optimally solves the problem. The results are then extended for two special cases of flow shop problem. The other problem is to minimise a total cost function which is a linear combination of three penalties: penalty on job earliness, penalty on job tardiness, and penalty associated with long due date assignment. The assignment of a common due date and distinct due dates are investigated for this problem. It is shown that the optimal sequence for the case of common due date is V-shaped.     

Stochastic single machine scheduling with random common due date

This paper studies the single machine scheduling problem for minimising the expected total weighted deviations of completion times from random common due date. Jobs have exponentially distributed processing times and the common due date is a generalised Erlang distribution. The optimal schedules are shown to be ∧-shaped. Moreover, we give the optimal schedules when the machine is subject to stochastic breakdowns with independent and exponentially distributed uptimes and downtimes.     

An electromagnetism-like mechanism for the single machine total stepwise tardiness problem with release dates

In recent years, a new type of tardiness cost, called stepwise tardiness, has received attention. To the authors’ knowledge, only a few studies have investigated this type of tardiness in the scheduling problem. This study considered the single machine total stepwise tardiness problem with release dates, which is strongly NP hard. Because of the essential complexity of the problem, heuristics were first developed to quickly generate initial solutions. Subsequently, a new electromagnetism-like mechanism (EM), which is a novel metaheuristic, was proposed to improve the solution quality. The new EM includes a natural encoding scheme, a new distance measure between solutions, and effective attraction and repulsion operators. Comparisons with a current EM and other metaheuristics were performed to verify the proposed EM. The computational results show that the proposed EM exhibits good performance for the considered problem.     

Minimising total tardiness for the identical parallel machine scheduling problem with splitting jobs and sequence-dependent setup times

This paper focuses on an identical parallel machine scheduling problem with minimising total tardiness of jobs. There are two major issues involved in this scheduling problem; (1) jobs which can be split into multiple sub-jobs for being processed on parallel machines independently and (2) sequence-dependent setup times between the jobs with different part types. We present a novel mathematical model with meta-heuristic approaches to solve the problem. We propose two encoding schemes for meta-heuristic solutions and three decoding methods for obtaining a schedule from the meta-heuristic solutions. Six different simulated annealing algorithms and genetic algorithms, respectively, are developed with six combinations of two encoding schemes and three decoding methods. Computational experiments are performed to find the best combination from those encoding schemes and decoding methods. Our findings show that the suggested algorithm provides not only better solution quality, but also less computation time required than the commercial optimisation solvers.     

A note on single machine scheduling and due date assignment with general position-dependent processing times

This note considers single machine scheduling and due date assignment in which a job’s processing time depends on its position in a sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and the total earliness of the scheduled jobs. We analyse these problems with three different due date assignment methods. We provide a generic polynomial-time dynamic programming algorithm to solve the problems.     

A comparison of metaheuristic procedures to schedule jobs in a permutation flow shop to minimise total earliness and tardiness

This paper considers the problem of scheduling jobs in a permutation flow shop with the objective of minimising total earliness and tardiness. A genetic algorithm is proposed for the problem. This procedure and five other procedures were tested on problem sets that varied in terms of number of jobs, machines and the tightness and range of due dates. It was found that the genetic algorithm procedure was consistently effective in generating good solutions relative to the other procedures.