β-Robust scheduling for single-machine systems with uncertain processing times

In scheduling environments with processing time uncertainty, system performance is determined by both the sequence in which jobs are ordered and the actual processing times of jobs. For these situations, the risk of achieving substandard system performance can be an important measure of scheduling effectiveness. To hedge this risk requires an explicit consideration of both the mean and the variance of system performance associated with alternative schedules, and motivates a β-robustness objective to capture the likelihood that a schedule yields actual performance no worse than a given target level. In this paper we focus on β-robust scheduling issues in single-stage production environments with uncertain processing times. We define a general β-robust scheduling objective, formulate the β-robust scheduling problem that results when job processing times are independent random variables and the performance measure of interest is the total flow time across all jobs, establish problem complexity, and develop exact and heuristic solution approaches. We then extend the 0-robust scheduling model to consider situations where the uncertainty associated with individual job processing times can be selectively controlled through resource allocation. Computational results are reported to demonstrate the efficiency and effectiveness of the solution procedures.     

Modelling and scheduling analysis of multi-cluster tools with residency constraints based on time constraint sets

This paper is dedicated to the scheduling problem of multi-cluster tools with process module residency constraints and multiple wafer product types. The problem is formulated as a non-linear programming model based on a set of time constraint sets. An effective algorithm called the time constraint sets based (TCSB) algorithm is presented as a new method to schedule the transport modules to minimise the makespan of a number of wafers. In approach, time constraint sets are maintained for all the resources and necessary operations to exploit the remaining production capacities during the scheduling process. To validate the proposed algorithm on a broader basis, a series of simulation experiments are designed to compare our TCSB algorithm with the benchmark with regard to cluster factor, configuration flexibilities and the variation of the processing times and residency constraint times. The results indicate that the proposed TCSB algorithm gives optimal or near optimal scheduling solutions in most cases.     

原油处理过程短期生产计划优化

在原油处理过程短期生产计划的递阶求解方法中,原油处理短期生产计划问题分为上下两层,上层根据市场需求产生一个目标炼油计划;在此基础上,下层得到一个详细生产计划以实现目标炼油计划。研究了在上层目标炼油计划已知的情况下,下层详细生产计划的求解问题。为该问题建立了基于离散时间表示的混合整数线性规划模型,分析了问题的特点并将其进行转化,给出了基于启发式的求解方法,在保证目标炼油计划实现的前提下,对原油转运过程中油品切换及不同油品的罐底混合进行了优化,取得了一定的成果。用一个工业实例验证了启发式规则的可行性和有效性。     

Economics of sugar production: a case study

The manufacture of sugar from crushed sugar-cane involves processing through a number of stages. The yield of crystalline sugar per unit of processed juice depends on a variety of process parameters. Increased yield is also related to the determination of a suitable mix of in-process ingredients. In this paper a case study is presented where the use of product mix has been made. The product mix in this case is arrived at by considering the profit motive of the entrepreneur and keeping in view the constraints imposed by the processing times at various stages and the capacities of the equipment at each stage. The problems of implementation of the proposed product mix were then explored and a suitable production schedule has been suggested taking into consideration certain important constraints imposed by the Indian environment.     

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance     

Simultaneous versus sequential loading and scheduling of flexible assembly systems

A monolithic and a hierarchical approach is presented for loading and scheduling in a general flexible assembly system and a flexible assembly line. The system is made up of a set of assembly stations of various types each with limited working space and is capable of simultaneously producing a mix of product types. The objective is to determine an assignment of assembly tasks to stations and an assembly schedule for all products so as to complete the products in a minimum time. In the monolithic approach loading and scheduling decisions are made simultaneously. In the hierarchical approach, however, first the station workloads are balanced by solving the loading problem, and then detailed assembly schedule is determined for prefixed task assignments and assembly routes by solving a standard job-shop problem. Mixed integer programming formulations are presented for simultaneous and for sequential loading and scheduling. Loading and scheduling with alternative or with single task assignments are considered. Numerical examples are included to illustrate and compare the two approaches proposed.     

Makespan estimation and order acceptance in batch process industries when processing times are uncertain

Batch process industries are characterized by complex precedence relationships between operations, which renders the estimation of an acceptable workload very difficult. A detailed schedule based model can be used for this purpose, but for large problems this may require a prohibitive large amount of computation time. We propose a regression based model to estimate the makespan of a set of jobs. We extend earlier work based on deterministic processing times by considering Erlang-distributed processing times in our model. This regression-based model is used to support customer order acceptance. Three order acceptance policies are compared by means of simulation experiments: a scheduling policy, a workload policy and a regression policy. The results indicate that the performance of the regression policy can compete with the performance of the scheduling policy in situations with high variety in the job mix and high uncertainty in the processing times. Correspondence to: C.V. Ivanescu     

Capacity-constrained scheduling for a logic IC final test facility

A capacity-constrained scheduling using the concept of the theory of constraints for a semiconductor Logic IC final test operation is presented. The scheduling of the IC final test considers unrelated parallel machines with multiple constraint problems. A broad product mix, variable lot sizes and yields, long and variable set-up times, as well as limited test equipment capacity characterize the operations in this test facility. Discrete event simulation models based on e-M-Plant? are developed to implement the capacity-constrained scheduling algorithm. A comparison is also made with other rules, which are combinations of the rules such as first come first serve and earliest due date for the order scheduling, and the rules such as minimum set-up time, shortest processing time and shortest set-up time plus processing time for the dispatching test equipment. The simulation results show that the proposed capacity-constrained scheduling outperforms other rules for the committed volume performance in many different operational conditions. Directions for future research are also presented.     

Mixed integer programming for scheduling surface mount technology lines

This paper presents new mixed integer programming formulations for blocking scheduling of SMT (Surface Mount Technology) lines for printed wiring board assembly. The SMT line consists of several processing stages in series, separated by finite intermediate buffers, where each stage has one or more identical parallel machines. A board that has completed processing on a machine may remain there and block the machine until a downstream machine becomes available for processing. The objective is to determine an assembly schedule for a mix of board types so as to complete the boards in a minimum time. Scheduling with continuous or with limited machine availability is considered. Numerical examples and some computational results are presented to illustrate applications of the models proposed.     

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.     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

Solving multi-objective rescheduling problems in dynamic permutation flow shop environments with disruptions

In multi-objective optimisation problems, optimal decisions need to be made in the presence of trade-offs among conflicting objectives which may sometimes be expressed in different units of measure. This makes it difficult to reduce the problem to a single-objective optimisation. Furthermore, when disruptive changes emerge in manufacturing environments, such as the arrival of new jobs or machine breakdowns, the scheduling system should be adapted by responding quickly. In this paper, we propose a rescheduling architecture for solving the problem based on a predictive-reactive strategy and a new method to calculate the reactive schedule in each rescheduling period. Additionally, we developed a methodology that allows the use of multi-objective performance metrics to evaluate dispatching rules. These rules are applied at a benchmark specifically designed for this paper considering three objective functions: makespan, total weighted tardiness and stability. Three types of disruptions are also considered: arrivals of new jobs, machine breakdowns and variations in job processing times. Results showed that the RANDOM rule provides a better behaviour compared to other evaluated rules and a lower ratio of non-dominated solutions compared to ATC (apparent tardiness cost) and FIFO (first-in-first-out) rules. Moreover, the behaviour of the hypervolume metric depends on the problem dimensions.     

A scatter search approach to sequence-dependent setup times job shop scheduling

Scheduling jobs on multiple machines is a difficult problem when real-world constraints such as the sequence setup time, setup times for jobs and multiple criteria are used for solution goodness. It is usually sufficient to obtain a near-optimal solution quickly when an optimal solution would require days or weeks of computation. Common scheduling heuristics such as Shortest Processing Time can be used to obtain a feasible schedule quickly, but are not designed for multiple simultaneous objectives. We use a new meta-heuristic known as a scatter search (SS) to solve these types of job shop scheduling problems. The results are compared with solutions obtained by common heuristics, a tabu search, simulated annealing, and a genetic algorithm. We show that by combining the mechanism of diversification and intensification, SS produces excellent results in a very reasonable computation time. The study presents an efficient alternative for companies with a complicated scheduling and production situation.     

Dynamic scheduling for complex engineer-to-order products

The current paper considers dynamic production scheduling for manufacturing systems producing products with deep and complex product structures and complicated process routings. It is assumed that manufacturing and assembly processing times are deterministic. Dynamic scheduling problems may be either incremental (where the schedule for incoming orders does not affect the schedule for existing orders) or regenerative (where a new schedule is produced for both new and existing orders). In both situations, a common objective is to minimize total costs (the sum of work-in-progress holding costs, product earliness and tardiness costs). In this research, heuristic and evolutionary-strategy-based methods have been developed to solve incremental and regenerative scheduling problems. Case studies using industrial data from a company that produces complex products in low volume demonstrate the effectiveness of the methods. Evolution strategy (ES) provides better results than the heuristic method, but this is at the expense of significantly longer computation times. It was found that performing regenerative planning is better than incremental planning when there is high interaction between the new orders and the existing orders.     

A dynamic scheduling algorithm for singe-arm two-cluster tools with flexible processing times

This article presents a dynamic algorithm for job scheduling in two-cluster tools producing multi-type wafers with flexible processing times. Flexible processing times mean that the actual times for processing wafers should be within given time intervals. The objective of the work is to minimize the completion time of the newly inserted wafer. To deal with this issue, a two-cluster tool is decomposed into three reduced single-cluster tools (RCTs) in a series based on a decomposition approach proposed in this article. For each single-cluster tool, a dynamic scheduling algorithm based on temporal constraints is developed to schedule the newly inserted wafer. Three experiments have been carried out to test the dynamic scheduling algorithm proposed, comparing with the results the ‘earliest starting time’ heuristic (EST) adopted in previous literature. The results show that the dynamic algorithm proposed in this article is effective and practical.     

Centralized Scheduling and Priority Implementation Heuristics for a Dynamic Job Shop Model

The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. A multi-pass heuristic program, which has proven effective in earlier research, is applied to the up-dated static scheduling problem at each review time. A procedure is proposed for implementing priorities on the shop floor between review times. The procedure is expressly designed to integrate the scheduling of newly arriving jobs to modify the schedule. In simulation experiments using tardiness statistics for evaluation, centralized scheduling and the proposed implementation procedure proved to be an extremely effective combination. Comparison with another procedure that gives the centralized schedule precedence over new arrivals indicates the importance of the implementation procedure when periodic centralized scheduling is used in a dynamic situation.     

The burn-in test scheduling problem with batch dependent processing time and sequence dependent setup time

The burn-in test scheduling problem (BTSP) is a variation of the complex batch processing machine scheduling problem, which is also a generalisation of the liquid crystal injection scheduling problem with incompatible product families and classical identical parallel machine problem. In the case we investigated on the BTSP, the jobs are clustered by their product families. The product families can be clustered by different product groups. In the same product group, jobs with different product families can be processed as a batch. The batch processing time is dependent on the longest processing time of those jobs in that batch. Setup times between two consecutive batches of different product groups on the same batch machine are sequentially dependent. In addition, the unequal ready times are considered in the BTSP which involves the decisions of batch formation and batch scheduling in order to minimise the total machine workload without violating due dates and the limited machine capacity restrictions. Since the BTSP involves constraints on unequal ready time, batch dependent processing time, and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with compatible product families or incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Consequently, this paper proposes a mixed integer programming model to solve the BTSP exactly. In addition, two efficient solution procedures which solve the BTSP are also presented.     

Cyclic scheduling heuristics for a re-entrant job shop manufacturing environment

Two efficient cyclic scheduling heuristics for re-entrant job shop environments were developed. Each heuristic generated an efficient and feasible cyclic production schedule for a job shop in which a single product was produced repetitively on a set of machines was to determine an efficient and feasible cyclic schedule which simultaneously minimized flow time and cycle time. The first heuristic considered a repetitive production re-entrant job shop with a predetermined sequence of operations on a single product with known processing times, set-up and material handling times. The second heuristic was a specialization of the first heuristic where the set-up for an operation could commence even while the preceding operation was in progress. These heuristics have been extensively tested and computational results are provided. Also, extensive analysis of worst-case and trade-offs between cycle time and flow time are provided. The results indicate that the proposed heuristics are robust and yield efficient and superior cyclic schedules with modest computational effort.     

Sensitivity analysis of a fuzzy multiobjective scheduling problem

This paper concerns sensitivity analysis of a class of complex job shop scheduling problems which are characterized by: (1) a large number of jobs and machines, (2) uncertain jobs processing times, and (3) multiple measures of schedule performance including average weighted tardiness, the number of tardy jobs, the total setup times, the total idle time of machines, and the total flow times of jobs. The base schedule is generated by applying a new fuzzy multiobjective genetic algorithm which takes into consideration batching of the jobs of a similar type, jobs’ lots sizing and load balancing of the machines. The aim of the proposed sensitivity analysis of a generated schedule is to investigate the consequences of prolongations of job processing times on the measures of schedule performance. The processing times are described by triangular fuzzy numbers and their prolongation is done by expanding the supports of fuzzy numbers. The sensitivity analysis is performed through a series of numerical experiments. The effects of prolongations of job processing times on the measures of performance of a generated schedule are recorded and analysed. It is shown that the sensitivity analysis is among the primaries in evaluating the quality of a generated schedule. The sensitivity analysis is used in identifying the critical jobs and the critical machines which have the properties that the prolongations of their processing times produce the largest deteriorations of the performance measures and the overall quality of a generated schedule.     

Multitasking scheduling problems with a rate-modifying activity

Motivated by the behavioral phenomena that occur while human operators are carrying out tasks, we study multitasking scheduling problems with a rate-modifying activity. In the problems, the processing of a selected task suffers from interruptions by other tasks that are available but unfinished, and the human operators regularly engage rest breaks during work shifts allowing them to recover or mitigate some of the negative effects of fatigue. The objectives are to respectively minimize: makespan, total completion time, maximum lateness, and due-date assignment related cost by determining when to schedule the rate modifying activity and the optimal task sequence in the presence of multitasking. Scheduling models and algorithms are proposed to solve the problems. The numerical examples are presented to illustrate the theorems and algorithms.