A hybrid genetic algorithm for flowshop lot streaming with setups and variable sublots

Lot streaming is the process of splitting a given lot or job to allow the overlapping of successive operations in flowshops or multi-stage manufacturing systems to reduce manufacturing lead time. Recent literature shows that significant lead time improvement is possible if variable sublots, instead of equal or consistent sublots, are used when production setup time is considered. However, lot streaming problems with variable sublots are difficult to solve to optimality using off-shelf optimisation packages even for problems of small and experimental sizes. Thus, efficient solution procedures are needed for solving such problems for practical applications. In this paper, we develop a mathematical programming model and a hybrid genetic algorithm for solving n-job m-machine lot streaming problems with variable sublots considering setup times. The preliminary computational results are encouraging.     

Lot Streaming Flow Shop with a Heterogeneous Machine

Abstract

It is possible to obtain greater productivity of a production system by overlapping the operations required to process a manufacturing order. This methodology, known as lot streaming, requires dividing the production order (lot) into smaller sublots. In this article, we study production systems that include machines that operate in batch mode (processing a group of units at the same time) and single processing machines (processing one unit at a time) arranged in a flow shop configuration, that is all jobs must go through the same production stages in the same order. The obtained results show that addressing the problem with consistent sublots (a common sublot size used for the whole process) is inefficient. On the other hand, addressing the problem considering the sizing of sublots for each machine (variable sublots) greatly improves the quality of the solution but is computationally intensive (limiting the size of the problem that can be solved). Therefore, a decomposition procedure is proposed on the decision of sublots sizing. This procedure greatly improves the solution obtained using consistent sublots and does so with lower computational requirements than the variable sublots approach.     

Lot streaming in the presence of learning in sublot-attached setup times and processing times

Lot streaming is the process of splitting a production lot into sublots, and then processing the sublots on different machines in an overlapping manner. In this paper, we study the use of lot streaming for processing a lot in a two-machine flow shop when a sublot-attached setup time is incurred before the processing of each sublot. The objective is to determine number of sublots and sublot sizes and minimize makespan. We also consider the case when the effect of learning is observed in processing times, sublot-attached setup times, or, both. We present closed-form expressions for optimal sublot sizes and efficient search schemes to determine optimal number of sublots.     

Lot streaming multiple jobs with values exponentially deteriorating over time in a job-shop environment

The main issue in lot streaming (LS) is determining the means by which to split jobs into sub-jobs to improve the makespan (or some other criterion). However, LS has been overlooked in most studies dealing with scheduling problems associated with specific kinds of job shops, where the job value exponentially deteriorates over time. The current study attempts to determine whether the expected benefits of LS would be evident in the job-shop scheduling problem (JSP) with the objective of maximising the total value of jobs. This study comprised two stages. In the first stage, we studied the influence of a fixed number of sub-jobs on the performance of the LS by systematically varying this parameter using the fixed number job splitting (FNJS) approach. We considered a total of 12 dispatching rules for the analysis of relative performance. Simulation results suggest that dividing each job into several sub-jobs increases the total value of jobs. In addition, dispatching rules incorporating information related to job value perform better than those without this information. In the second stage of the study, we proposed a genetic algorithm-based job splitting (GAJS) approach. The simulation results led us to conclude that the GAJS approach is superior to the FNJS approach in terms of the total value of the jobs and the average number of sub-jobs generated.     

Lot streaming with attached setups in three-machine flow shops

Lot streaming is the process of splitting a job or lot to allow overlapping between successive operations in a multistage production system. This use of transfer lots usually results in a significantly shorter makespan for the schedule. We study the structural properties of schedules which minimize the makespan for a single job with attached setup times in a flow shop. The structure of the optimal schedules is more complex than in the case with no setups or detached setups, as it may follow a much larger variety of patterns. Using the structural insights obtained, however, it is possible to find the optimal solution with s sublots in O(s) time for the three-machine case.     

Two-stage hybrid flow shop batching and lot streaming with variable sublots and sequence-dependent setups

A paint manufacturing firm's customers typically place orders for two or more products simultaneously. Each product belongs to a family that denotes batching compatibility during manufacturing. Further, products can be split into several sublots to allow overlapping production in a two-stage hybrid flow shop wherein various identical, capacitated machines operate in parallel at each stage. We present a mixed-integer linear program (MILP) for this integrated batching and lot streaming problem with variable sublots, incompatible job families, and sequence-dependent setup times. The model determines the number and size of sublots for each product and the production sequencing for each sublot such that the total weighted completion time is minimised. To promote practical implementation, we develop and evaluate heuristics to efficiently solve this problem.     

Improving the applicability of workload control (WLC): the influence of sequence-dependent set-up times on workload controlled job shops

Simulation has demonstrated that the workload control (WLC) concept can improve performance in job shops, but positive empirical results are scarce. A key reason for this is that the concept has not been developed to handle a number of practical considerations, including sequence-dependent set-up times. This paper investigates the influence of sequence-dependent set-up times on the performance of a workload-controlled job shop. It introduces new set-up-oriented dispatching rules and assesses the performance impact of controlled order release. Simulation results demonstrate that combining an effective WLC order release rule with an appropriate dispatching rule improves performance over use of a dispatching rule in isolation when set-up times are sequence dependent. The findings improve our understanding of how this key implementation challenge can be overcome. Future research should investigate whether the results hold if set-up time parameters are dynamic and set-up times are not evenly distributed across resources.     

Lot splitting to minimize average flow-time in a two-machine flow-shop

Lot splitting is a technique for accelerating the flow of work by splitting job lots into sublots, In this paper we investigate the lot splitting scheduling problem in a two-machine flow-shop environment with detached setups and with batch availability. The performance measure considered is the average flow-time which is indicative of the increasingly important manufacturing lead-time. Our contribution is both theoretic and practical for the case of general (not necessarily equal) sublots. We identify properties of the optimal solution and develop a solution procedure to solve the problem. We then present a computational study which indicates that our solution technique is very efficient.     

Analysis of gap times in a two-stage stochastic flowshop with overlapping operations

The impact of transfer batching (also referred to as lot splitting) on the performance of flowshops has received widespread attention in the literature. Most papers have emphasized the usefulness of lot splitting in cutting down average flow times, as it enables the overlapping of operations at different stages of the flowshop. However, while most analytical papers have studied deterministic flowshops, an important downside of lot splitting has been overlooked; i.e., the occurrence of idle time between the processing of consecutive sublots belonging to the same process batch (referred to as gap times). Gap times add no value to the product; they merely increase the process batch makespan at the different stages. In deterministic systems, these gap times may be avoided by balancing the processing rates of the different machines in the shop; in stochastic settings, however, they may occur even when the system is perfectly balanced, due to the inherent variability in the setup and processing times. Studying a two-stage flowshop with a single product type, this paper provides insight into the behavior of the gap times, and develops an approximation for the process batch makespan at the second stage in terms of the system characteristics and the lot splitting policy.     

A due date-based dispatching rule for flexible manufacturing systems

In the paper a new dispatching rule is proposed, which extends the CEXSPT rule for dispatching jobs in a general cell's environment, i.e., a multiple-machine cell, where each machine type is assigned to a priority value. Each job is represented as a finite sequence of operations, ordered according to the type priorities of the cell's machines they are performed by. The algebraic background of the dispatching rule is described. The dispatching rule is implemented in the GOLDEN COMMON LISP programming language for IBM PC AT and compatible computers. A computer study of the performance of the proposed dispatching rule is conducted based on a four-machine cell, and the results are reported and analysed. The conclusions obtained are that the proposed dispatching rule produces cell's makespans, better than the CEXSPT dispatching rule, because it reduces idle time on cell's machines.     

Flexible job shop scheduling with lot streaming and sublot size optimisation

Models and optimisation approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimisation procedure is proposed. First, the makespan value is minimised with the smallest sublots defined for the problem instance. This makes it possible to shorten the makespan significantly, because each sublot is transferred separately to the next operation of a job. In the second stage, the sizes of the sublots are maximised without increasing the obtained makespan value. In this way, the quantity of sublots and transport activities is limited together with the related manufacturing cost. Two objectives are defined for the second stage. The first one is the maximisation of the sum of the sublot sizes of all operations, the second one is the maximisation of the number of the operations which do not need to be split at all. Mixed-integer linear programming, constraint programming and graph-based models are implemented for the problem. Two optimisation approaches are developed and compared in computational experiments for each stage and objective, one approach is based on a third-party solver, and the second one on an independent own implementation, namely a tabu search and a greedy constructive heuristic.     

Lot streaming in a multiple product permutation flow shop with intermingling

In this paper we study the multi-product lot streaming problem in a permutation flow shop. The problem involves splitting given order quantities of different products into sublots and determining their optimal sequence. Each sublot has to be processed successively on all machines. The sublots of the particular products are allowed to intermingle, that is sublots of different jobs may be interleaved. A mixed integer programming formulation is presented which enables us to find optimal sublot sizes as well as the optimal sequence simultaneously. With this formulation, small- and medium-sized instances can be solved in a reasonable time. The model is further extended to deal with different settings and objectives. As no lot streaming instances are available in the literature, LSGen, a problem generator, is presented, facilitating valid and reproducible instances. First results concerning the average benefit of lot streaming with multiple products are presented, and are based on a computational study with 160 small- and medium-sized instances.     

A methodology for planning and controlling workload in a job-shop: a four-way decision-making problem

There has been extensive research on workload and input–output control with the objective of improving manufacturing operations in job-shops. In this paper, a multiple decision-making scheme is proposed to plan and control operations in a general job-shop, and to improve delivery and workload related performance measures. The job-shop characteristics reinforce the need for designing a global system that controls both the jobs entering (order acceptance, due date setting and job release) and the work-in-process (dispatching), leading to an improvement of operational measures. Previous research has concentrated on scheduling a set of orders through the shop floor, according to some decision mechanism, in order to optimise some measure of performance (usually total lead time). This means that, since only a part of the decision-making system is being optimised, the resulting decision may be sub-optimal. In this paper it is shown that the performance of the different decision rules changes when they are considered simultaneously. Hence, a higher level approach, where the four decisions (order acceptance, due date setting, job release and dispatching) are considered at the same time, should be adopted to improve job-shop operational performance.     

An application of genetic algorithms to lot-streaming flow shop scheduling

A Hybrid Genetic Algorithm (HGA) approach is proposed for a lot-streaming flow shop scheduling problem, in which a job (lot) is split into a number of smaller sublots so that successive operations can be overlapped. The objective is the minimization of the mean weighted absolute deviation of job completion times from due dates. This performance criterion has been shown to be non-regular and requires a search among schedules with intermittent idle times to find an optimal solution. For a given job sequence, a Linear Programming (LP) formulation is presented to obtain optimal sublot completion times. Objective function values of LP solutions are used to guide the HGA's search toward the best sequence. The performance of the HGA approach is compared with that of a pairwise interchange method.     

The performance of Due Date setting rules in assembly and multi-stage job shops: an assessment by simulation

Setting short yet reliable Due Dates (DDs) is an important early production planning and control task. The majority of job-shop research on DD setting assumes simple product structures without assembly operations. However, in practice, product structures are often complex, and multiple final assembly operations may be required. This paper evaluates the performance of DD setting rules in the context of complex product structures, considering two scenarios: two-level assembly job shops, where orders converge on one final assembly operation; and two-level multi-stage job shops, where a series of assembly operations are undertaken. New rules are proposed which are substantially simpler and more suitable for practical use than those in the literature. These rules are only outperformed by a more sophisticated rule from the wider literature, newly introduced into the context of assembly and multi-stage job shops. Which rule to apply in practice depends on whether a manager considers the improvement in performance more important than the loss of simplicity. Future research should investigate how jobs can be planned and controlled effectively when some or all DDs are set externally by customers rather than internally using a DD setting rule.     

A multi-attribute dispatching rule for automated guided vehicle systems

This paper considers the dispatching problem associated with operations of automated guided vehicles (AGVs). A multi-attribute dispatching rule for dispatching of an AGV is developed and evaluated. The multi-attribute rule, using the additive weighting method, considers three system attributes concurrently: the remaining space in the outgoing buffer of a workstation, the distance between an idle AGV and a workstation with a job waiting for the vehicle to be serviced, and the remaining space in the input buffer of the destination workstation of a job. A neural network approach is used to obtain dynamically adjusting attribute weights based on the current status of the manufacturing system. Simulation analysis of a job shop is used to compare the multi-attribute dispatching rule with dynamically adjusting attribute weights to the same dispatching rule with fixed attribute weights and to several single attribute rules. Results show that the multi-attribute dispatching rule with the ability to adapt attribute weights to job shop operational conditions provides a better balance among the performance measures used in the study.     

New dispatching rules for shop scheduling: A step forward

This paper provides a set of new dispatching rules for the minimization of various performance measures such as mean, maximum and variance of flow time and tardiness in dynamic shops. A static rule which minimizes the number of tardy jobs is also proposed. To evaluate these proposed rules, their relative performance is analysed in open job shops and reported in comparison with the standard benchmark rules such as the SPT (shortest process time) and EDD (earliest due-date), popular rules like ATC (apparent tardiness cost) and MOD (modified operational due-date), and the best performing rules in current literature such as RR, PT + WINQ, PT + WINQ + SL and AT-RPT. Thereafter, a comparative analysis of the relative performance of these rules is carried out in job shops (with no machine revisitation of jobs) and flow shops (with missing operations on jobs) in dynamic environments. Based on the simulation study and analysis of results in different manufacturing environments viz. job shops and flow shops, observations and conclusions are made, highlighting some interesting aspects about the effect of routeing on the individual performance of rules.     

Scheduling in dynamic assembly job-shops with jobs having different holding and tardiness costs

Most studies on scheduling in dynamic job-shops assume that the holding cost of a job is given by the flowtime of the job and that the tardiness cost of a job is given by the tardiness of the job. In other words, unit holding and unit tardiness costs of a job are assumed. However, in reality, such an assumption need not hold, and it is quite possible that there are different costs for holding and tardiness for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (manufacturing multilevel jobs) with the consideration of different holding and tardiness costs for different jobs. An attempt is made to develop efficient dispatching rules by incorporating the relative costs of holding and tardiness of jobs in the form of scalar weights. The primary objective of scheduling considered here is the minimization of the total scheduling cost consisting of the sum of holding and tardiness costs. The performance of the scheduling rules in minimizing the individual components of total scheduling cost is also observed. The results of an extensive simulation study on the performance of different dispatching rules show that the proposed rules are effective in minimizing the means and maximums of the primary measure, and are quite robust with respect to different job structures and experimental settings.     

On discrete lot streaming in no-wait flow shops

Lot streaming is the process of splitting a job or lot to allow overlapping between successive operations in a multistage production system. This use of transfer lots usually results in a substantially shorter makespan for the corresponding schedule. In this paper, we study the discrete lot streaming problem for a single job in no-wait flow shops. We present a new linear programming formulation for the problem. We show that the optimal solutions are the same for the m ×2 case with or without no-wait constraints. We also present a fast, polynomial-time solution method for this case. For the general case, we prove that any solution which is 'close' to the continuous optimal solution will be a good approximation for the discrete problem. This property allows us to present two quickly obtainable approximations of very good quality.     

An extension of modified-operational-due-date priority rule incorporating job waiting times and application to assembly job shop

The well-known priority dispatching rule MOD (Modified Operational Due Date) in job shop scheduling considers job urgency through ODD (Operational Due Date) and also incorporates SPT (Shortest Processing Time)-effect in prioritising operationally late jobs; leading to robust behaviour in Mean Tardiness (MT) with respect to tightness/looseness of due dates. In the present paper, we study an extension of the MOD rule using job-waiting-time based discrimination among operationally late jobs to protect long jobs from excessive delays by incorporating an ‘acceleration property’ into the scheduling rule. Formally, we employ a weighted-SPT dispatching priority index of the form: (Processing time)/(Waiting time)^α for operationally late jobs, while the priority index is ODD for operationally non-late jobs; and the latter class of jobs has a lower priority than the former class. In the context of Assembly Job Shop scheduling, some existing literature includes considerable focus around the concept of ‘Staging Delay’, i.e., waiting of components or sub-assemblies for their counterparts for assembly. Some existing approaches attempt dynamic anticipation of staging delay problems and re-prioritisation of operations along converging branches. In the present paper, rather than depending on such a centralised and largely backward scheduling approach, we consider a partially decentralised approach, endowing jobs with a priority index yielding an ‘acceleration property’ based on a ‘look-back’ in terms of waiting time, rather than ‘look-ahead’. For the particular case, in our proposed rule, whenα is set at zero and when all jobs at a machine are operationally late, our rule agrees with MOD as both exhibit the SPT effect. In simulation tests of our priority scheme for assembly job shops, in comparison with leading heuristics in literature, we found our rule to be particularly effective in: (1) minimising conditional mean tardiness, (2) minimising 99-percentile-point of the tardiness distribution, through proper choice ofα. We also exploit an interesting duality between the scheduling and queueing control versions of the problem. Based on this, some exact and heuristic analysis is given to guide the choice ofα, which is also supported by numerical evidence.