Dispatching rules in scheduling Dispatching rules in scheduling: a fuzzy approach

Job-shop scheduling through simulation uses various kinds of dispatching rules such as SPT or the slack time rule. Each of these rules aims at satisfying a single criterion although workshop management is a multi-criteria problem. This paper proposes a way to use fuzzy logic in order to build aggregated rules allowing to obtain a compromise between the satisfaction of several criteria. When the criteria of performance change with the evolution of the production environment, these aggregated rules can be parametrized in order to modify the respective influence of the elementary rules they are composed of.     

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.     

A GRASP for scheduling printed wiring board assembly

The assembly of printed wiring boards (PWBs) typically involves the coordination of thousands of components and hundreds of part numbers in a job shop environment with up to 50 different processes and workstations. In this paper we present a greedy randomized adaptive search procedureor GRASP, for solving the daily scheduling problem that is found in such environments. The advantages of the proposed methodology are its ability to respond quickly to changing organizational goals, revised customer requests, and a multitude of shop-floor contingencies. A flexible lot-sizing heuristic with user overrides allows the scheduling algorithm to alter the production strategy in the face of random disturbances, such as machine failures, component stockouts, and demand perturbations.

The algorithms, embedded in a decision support system, have been implemented at Texas Instruments' (TI) Austin facility. This facility assembles boards for internal use and for a growing number of external customers. Before implementation it was necessary to convince management that the new approach would significantly outperform the scheduling methods that were currently in use. We were able to do this by running a series of experiments using real data that compared TI's rule set for scheduling starts and WIP with our methodology. The results indicated that over 10% increase in net revenues could be achieved with the GRASP and that comparable improvements in cycle time, flowline balance, and throughput could also be realized. Operational experience over the last two years has borne this out.     

PCB assembly scheduling for collect-and-place machines using genetic algorithms

In printed circuit board (PCB) assembly, collect-and-place machines, which use a revolver-type placement head to mount electronic components onto the board, represent one of the most popular types of assembly machinery. The assignment of feeders to slots in the component magazine and the sequencing of the placement operations are the main optimisation problems for scheduling the operations of an automated placement machine. In this paper, we present different genetic algorithms (GAs) for simultaneously solving these highly interrelated problems for collect-and-place machines in PCB assembly. First we consider single-gantry machines as the basic type of machinery. In the conventional GA approach all placement operations and the feeder-slot assignment are represented by a single chromosome. In order to increase the efficiency of the genetic operators, we present a novel GA approach, which integrates a clustering algorithm for generating sub-sections of the PCB and grouping the corresponding placement operations. It is shown that the proposed GAs can be extended to schedule dual-gantry placement machines, which are equipped with two independent placement heads and two dedicated component magazines. Hence, component feeders have to be allocated between the two magazines. To solve this allocation problem, two different heuristic strategies are proposed. Finally, detailed numerical experiments are carried out to evaluate the performances of the proposed GAs.     

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.     

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.     

Production scheduling decision rules in changing and non-linear environments

Holt at al. (1960) modollod the production scheduling problem with quadratic costs and derived an optimal set of scheduling rules. Our experiment found those rules may not be effective if costs are non-quadratic. This may explain the relative lack of use of these rules in industry.     

Fabrication and assembly scheduling in a two-machine flowshop

This paper considers a fabrication scheduling problem to minimize the makespan in a two-machine flowshop. Each job has a unique component and a common component to be processed on the first machine. On machine 1, the common components of the jobs are grouped into batches for processing with a setup cost incurred whenever a batch is formed. A job is ready for its assembly operation on the second machine if both its unique and common components are finished on machine 1. The problems with batch availability and item availability are known as NP-hard. In this paper, we give proofs for the strong NP-hardness of the two problems. The results suggest that it is very unlikely to develop polynomial- or pseudo-polynomial-time algorithm for finding exact solutions for the two problems.     

Regression-based due date assignment rules for improved assembly shop performance

Many simulation studies have evaluated sequencing rules and due date assignment methods for scheduling job shops. More recently researchers have studied multistage, or assembly, shops. Typically, due dates have been set by using a fixed multiple of the critical path length. This paper evaluates the effects on shop performance due to using a regression-based approach for setting due dates. The findings show that marked improvement in the performance of dispatching rules can occur when the proposed due date setting procedure is used.     

A parametric procedure for multicriterion sequence scheduling for JustIn-Time mixed-model assembly lines

The sequencing of products for final assembly in JIT mixed-model manufacturing systems is sometimes based on multiple criteria. The two main criteria that have been discussed in the literature are: the smoothing of parts utilization and the smoothing of the product load. Product rate variation smoothing and sub-assembly load variation smoothing may also be considered. One procedure for treating these multiple criteria is by the use of a weighted multi-attribute cost function, which is an aggregation of the respective objective functions. However, one difficulty which may be associated with this approach is in obtaining proper estimates for the weights. In this paper, we propose an alternative approach (a parametric procedure), which utilizes only the relative preference information for the criteria. A numerical example is presented to illustrate the procedure.     

Two-stage assembly flow-shop scheduling problem with non-identical assembly machines considering setup times

In this paper, we address the two stage assembly flow-shop problem with multiple non-identical assembly machines in stage two to minimise weighted sum of makespan and mean completion time. Also, sequence dependent setup times are considered for the first stage. This problem is a generalisation of previously proposed two stage assembly flow-shop problems (TSAFSP). In many real world industrial and production systems, there is more than one assembly machine to assemble job components. After extending a mathematical mixed-integer linear programming model to solve the problem, we use GAMS software. The TSAFSP has been known as NP-hard. Therefore, our more general problem is NP-hard too and so for large sized problems the right way to proceed is with the use of heuristic algorithms. So in this paper a hybrid VNS heuristic, which is a combination of the variable neighbourhood search (VNS) algorithm and a novel heuristic is developed and its solutions compared with solutions obtained by GAMS. Computational experiments reveal that the hybrid VNS heuristic performs much better than GAMS with respect to the percentage errors and run times.     

Dispatching rules and flexible environments: the influence on buffer behaviour

Frequent production requirements are linked to effective and profitable strategies for the management of queues, e.g. input buffers of machining centres and selection of rough workpieces from central storage. As a matter of fact, management policy performances must be evaluated by focusing not only on induced queue lengths or customer waiting times, but also on the future composition of the queues themselves, this being a consequence of the dispatching rule adopted. The question acquires further importance when flexible environments and buffer capacity constraints are considered. The aim of the present study is to illustrate an analytical procedure, based on the Markov chains theory, able to forecast the composition of buffers starting from any initial configuration. Attention is given to the buffer behaviour during the transient period and the steady state: results are offered for sequential and prioritized dispatching of items, together with application examples derived from common industrial situations. In the final sections, the possible extension of the procedure is considered and outlined with regard to particular management rules, thus introducing a further development of the present research.     

New formulations for the setup assembly line balancing and scheduling problem

We present three new formulations for the setup assembly line balancing and scheduling problem (SUALBSP). Unlike the simple assembly line balancing problem, sequence-dependent setup times are considered between the tasks in the SUALBSP. These setup times may significantly influence the station times. Thus, there is a need for scheduling the list of tasks within each station so as to optimize the overall performance of the assembly line. In this study, we first scrutinize the previous formulation of the problem, which is a station-based model. Then, three new formulations are developed by the use of new sets of decision variables. In one of these formulations, the schedule-based formulation, SUALBSP is completely formulated as a scheduling problem. That is, no decision variable in the model directly denotes a station. All the proposed formulations will be improved by the use of several enhancement techniques such as preprocessing and valid inequalities. These improved formulations can be applied to establishing lower bounds on the problem. To assess the performance of new formulations, results of an extensive computational study on the benchmark data sets are also reported.     

Rolling horizon production scheduling of multi-model PCBs for several assembly lines

The joint task of allocating several PCB assembly jobs to a set of production lines, load balancing of the line machines and job scheduling is considered. The production facility includes a number of assembly lines of different kinds, the PCB jobs are of different types and they should be allocated to suitable (i.e. feasible) lines. Scheduling of the production should respect the predefined release and due dates, and the objective is to minimise the sum of job tardy times. The scheduling is of the rolling-horizon-type where at the beginning of each planning period new jobs are inserted in the current non-preemptive production programme of unfinished jobs from the past planning periods. A mathematical formulation and a two-phase heuristic (including initial job-to-line allocation and schedule improving steps) are given for the problem. Experimental tests with jobs from practice were convincing.     

A simulation analysis of sequencing rules for ASRS in a pull-based assembly facility

Just-in-time (JIT) systems operate on a pull-based production control. The material needed is expected to be at its production site when and only when it is needed. When an automated storage retrieval system (ASRS) is used as a valve warehouse to support JIT manufacturing, the delivery time becomes critical. This paper presents an investigation on the effect of job sequencing rule on delivery performance of an ASRS, which is used as a valve warehouse to support a pull-based Kanban-driven assembly line. The analysis was based on computer simulation. The interaction of the sequencing rules with other control variables was also examined     

Determination of the number of containers,production kanbans and withdrawal kanbans; and scheduling in kanban flowshops - Part 2

We consider the problem of determination of the number of containers or container size, production kanbans and withdrawal kanbans, and scheduling of containers in presence of material handling between workstations, and dual blocking mechanisms operative on both workstations and material handling. A heuristic is proposed to address the problem of determining the number of containers, and production and withdrawal kanbans, and also determining the sequence of containers to minimize the sum of weighted flowtime, weighted earliness and weighted tardiness of containers. Recursive equations, developed in part 1 of this paper, are used for time-tabling of the sequence of containers. An extensive performance evaluation of the heuristic and a benchmark procedure, based on random search, has been carried out by generating a number of problems of various sizes.     

Experimental investigation of flexible manufacturing system scheduling decision rules

This paper reports the results of an experimental investigation of scheduling decision rules for a dedicated flexible manufacturing system. A simulation model of an existing flexible manufacturing system (FMS) comprised of 16 computer numerical controlled machines (CNC) was constructed using actual operation routings and machining times to evaluate the performance of various part loading and routing procedures. The results indicate that FMS performance is significantly affected by the choice of heuristic parts scheduling rules.     

Workshop scheduling using practical (inaccurate) data Part 1: The performance of heuristic scheduling rules in a dynamic job shop environment using a rolling time horizon approach

This paper is a report on a simulation study to investigate the performance of a number of scheduling rules on the basis of a rolling time horizon approach for a dynamic job shop environment. The performance measure considered is an economic objective which includes the main costs involved in a scheduling decision. The first purpose of the study was to find the best scheduling rule and the second to investigate the effects of the rescheduling interval on performance and examine whether there is a policy that can always improve performance. The simulation study, which is part of a larger project on practical workshop scheduling, has been carried out under widely varying conditions in terms of due date tightness, shop load level, and shop load balance level. The results show that a recently developed scheduling rule, SPT-C/R, is the most appropriate scheduling rule in minimizing overall cost and that the relationship between performance and rescheduling interval can be shown.     

A competitive memetic algorithm for the distributed two-stage assembly flow-shop scheduling problem

This article addresses the distributed two-stage assembly flow-shop scheduling problem (DTSAFSP) with makespan minimisation criterion. A mixed integer linear programming model is presented, and a competitive memetic algorithm (CMA) is proposed. When designing the CMA, a simple encoding scheme is proposed to represent the factory assignment and the job processing sequence; and a ring-based neighbourhood structure is designed for competition and information sharing. Moreover, some knowledge-based local search operators are developed to enhance the exploitation ability. The influence of parameter setting on the CMA is investigated using the analysis of variance method. Extensive computational tests and comparisons are carried out, which demonstrate the effectiveness of the proposed CMA in solving the DTSAFSP.