A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes

This paper investigates the scheduling problem of parallel identical batch processing machines in which each machine can process a group of jobs simultaneously as a batch. Each job is characterized by its size and processing time. The processing time of a batch is given by the longest processing time among all jobs in the batch. Based on developing heuristic approaches, we proposed a hybrid genetic heuristic (HGH) to minimize makespan objective. To verify the performance of our algorithm, comparisons are made through using a simulated annealing (SA) approach addressed in the literature as a comparator algorithm. Computational experiments reveal that affording the knowledge of problem through using heuristic procedures, gives HGH the ability of finding optimal or near optimal solutions in a reasonable time.     

Decomposition heuristics for minimizing earliness–tardiness on parallel burn-in ovens with a common due date

This paper considers a scheduling problem for parallel burn-in ovens in the semiconductor manufacturing industry. An 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. We suggest three decomposition heuristics. The first heuristic applies the exact algorithm due to Emmons and Hall (for the nonbatching problem) in order to assign the jobs to separate early and tardy job sets for each of the parallel burn-in ovens. Then, we use job sequencing rules and dynamic programming in order to form batches for the early and tardy job sets and sequence them optimally. The second proposed heuristic is based on genetic algorithms. We use a genetic algorithm in order to assign jobs to each single burn-in oven. Then, after forming early and tardy job sets for each oven we apply again sequencing rules and dynamic programming techniques to the early and tardy jobs sets on each single machine in order to form batches. The third heuristic assigns jobs to the m early job sets and m tardy jobs sets in case of m burn-in ovens in parallel via a genetic algorithm and applies again dynamic programming and sequencing rules. We report on computational experiments based on generated test data and compare the results of the heuristics with known exact solution for small size test instances obtained from a branch and bound scheme.     

Tabu search heuristic for two-machine flowshop with batch processing machines

Batch processing machines are frequently encountered in many industrial environments. A batch processing machine is one which can process several jobs simultaneously as a batch. The processing time of a batch is equal to the largest processing time of any job in the batch. This study deals with the problem of scheduling jobs in a flowshop with two batch processing machines such that the makespan is minimized. A heuristic based on Tabu search (TS) technique is proposed. The proposed heuristic is compared with a heuristic based on mixed integer linear programming (MILP). Because the complexity of the MILP-based heuristic is depended on the number of job batches, the comparison is under up-to-eight batches problem. In order to measure the proposed TS-based heuristic in larger batch problem, the relative error percentage with the lower bound (REP_LB) is used. The results show that the proposed heuristic is efficient and effective for the problems with relative large job sizes.     

A branch and price algorithm to minimize makespan on a single batch processing machine with non-identical job sizes

In this paper, we consider the scheduling problem on a single batch processing machine with non-identical job sizes; in which the machine has a limited capacity and can process a group of jobs simultaneously as a batch. The processing time of a batch is the longest processing time of all jobs in the batch. The objective is to minimize the makespan. We formulate the problem using Dantzig–Wolfe decomposition as a set partitioning problem. Based on the set partitioning formulation, we present a tight lower bound using column generation method. A heuristic algorithm is also developed to generate the basic solution in the column generation method. A branch and price algorithm which combines the column generation technique with branch and bound method is then presented to obtain the optimal solution of the problem. The efficiency of the proposed branch and price algorithm is ultimately compared to the branch and bound algorithm from the literature, based on the generated sample problems.     

Two-machine flowshop scheduling with intermediate transportation under job physical space consideration

In this paper, we study a coordinated production–transportation scheduling problem in a two-machine flowshop environment where a single transporter may carry several jobs simultaneously as a batch between the machines. Each job has its own physical-space requirement while being loaded into the transporter. The goal is to minimize the makespan. For the jobs with the same size of physical space during transportation, we present a heuristic algorithm with an absolute worst-case ratio of 2 and a polynomial-time optimal algorithm for a special case with given job sequence. For the jobs having different size of physical storage space, a heuristic algorithm is constructed with an absolute worst-case ratio of 7/3 and asymptotic worst-case ratio of 20/9. Computational experiments demonstrate that the two heuristic algorithms developed are capable of generating near-optimal solutions quickly.     

Minimizing the makespan on a batch machine with non-identical job sizes: an exact procedure

A batch processing machine can simultaneously process several jobs forming a batch. This paper considers the problem of scheduling jobs with non-identical capacity requirements, on a single-batch processing machine of a given capacity, to minimize the makespan. The processing time of a batch is equal to the largest processing time of any job in the batch. We present some dominance properties for a general enumeration scheme and for the makespan criterion, and provide a branch and bound method. For large-scale problems, we use this enumeration scheme as a heuristic method.Scope and purposeUsually in classical scheduling problems, a machine can perform only one job at a time. Although, one can find machines that can process several jobs simultaneously as a batch. All jobs of a same batch have common starting and ending times. Batch processing machines are encountered in many different environments, such as burn-in operations in semiconductor industries or heat treatment operations in metalworking industries. In the first case, the capacity of the machine is defined by the number of jobs it can hold. In the second case, each job has a certain capacity requirement and the total size of a batch cannot exceed the capacity of the machine. Hence, the number of jobs contained in each batch may be different. In this paper, we consider this second case (which is more difficult) and we provide an exact method for the makespan criterion (minimizing the last ending time).     

Genetic tabu search for the fuzzy flexible job shop problem

This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances.     

Scheduling of parallel machines with sequence-dependent batches and product incompatibilities in an automotive glass facility

This application is motivated by a complex real-world scheduling problem found in the bottleneck workstation of the production line of an automotive safety glass manufacturing facility. The scheduling problem consists of scheduling jobs (glass parts) on a number of parallel batch processing machines (furnaces), assigning each job to a batch, and sequencing the batches on each machine. The two main objectives are to maximize the utilization of the parallel machines and to minimize the delay in the completion date of each job in relation to a required due date (specific for each job). Aside from the main objectives, the output batches should also produce a balanced workload on the parallel machines, balanced job due dates within each batch, and minimal capacity loss in the batches. The scheduling problem also considers a batch capacity constraint, sequence-dependent processing times, incompatible product families, additional resources, and machine capability. We propose a two-phase heuristic approach that combines exact methods with search heuristics. The first phase comprises a four-stage mixed-integer linear program for building the batches; the second phase is based on a Greedy Randomized Adaptive Search Procedure for sequencing the batches assigned to each machine. We conducted experiments on instances with up to 100 jobs built with real data from the manufacturing facility. The results are encouraging both in terms of computing time—5 min in average—and quality of the solutions—less than 10 % relative gap from the optimal solution in the first phase and less than 5 % in the second phase. Additional experiments were conducted on randomly generated instances of small, medium, and large size.     

Heuristic scheduling of jobs on parallel batch machines with incompatible job families and unequal ready times

This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication, where the machines can be modeled as parallel batch processors. We attempt to minimize total weighted tardiness on parallel batch machines with incompatible job families and unequal ready times of the jobs. Given that the problem is NP-hard, we propose two different decomposition approaches. The first approach forms fixed batches, then assigns these batches to the machines using a genetic algorithm (GA), and finally sequences the batches on individual machines. The second approach first assigns jobs to machines using a GA, then forms batches on each machine for the jobs assigned to it, and finally sequences these batches. Dispatching and scheduling rules are used for the batching phase and the sequencing phase of the two approaches. In addition, as part of the second decomposition approach, we develop variations of a time window heuristic based on a decision theory approach for forming and sequencing the batches on a single machine.     

Earliness–tardiness minimization on scheduling a batch processing machine with non-identical job sizes

This paper considers the scheduling problem of minimizing earliness–tardiness (E/T) on a single batch processing machine with a common due date. The problem is extended to the environment of non-identical job sizes. First, a mathematical model is formulated, which is tested effectively under IBM ILOG CPLEX using the constraint programming solver. Then several optimal properties are given to schedule batches effectively, and by introducing the concept of ARB (Attribute Ratio of Batch), it is proven that the ARB of each batch should be made as small as possible in order to minimize the objective, designed as the heuristic information for assigning jobs into batches. Based on these properties, a heuristic algorithm MARB (Minimum Attribute Ratio of Batch) for batch forming is proposed, and a hybrid genetic algorithm is developed for the problem under study by combining GA (genetic algorithm) with MARB. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in the literature, both for small and large problem instances.     

Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.     

Machine scheduling with job class setup and delivery considerations

We study machine scheduling problems in which the jobs belong to different job classes and they need to be delivered to customers after processing. A setup time is required for a job if it is the first job to be processed on a machine or its processing on a machine follows a job that belongs to another class. Processed jobs are delivered in batches to their respective customers. The batch size is limited by the capacity of the delivery vehicles and each shipment incurs a transport cost and takes a fixed amount of time. The objective is to minimize the weighted sum of the last arrival time of jobs to customers and the delivery (transportation) cost. For the problem of processing jobs on a single machine and delivering them to multiple customers, we develop a dynamic programming algorithm to solve the problem optimally. For the problem of processing jobs on parallel machines and delivering them to a single customer, we propose a heuristic and analyze its performance bound.     

Order acceptance using genetic algorithms

This paper uses a genetic algorithm to solve the order-acceptance problem with tardiness penalties. We compare the performance of a myopic heuristic and a genetic algorithm, both of which do job acceptance and sequencing, using an upper bound based on an assignment relaxation. We conduct a pilot study, in which we determine the best settings for diversity operators (clone removal, mutation, immigration, population size) in connection with different types of local search. Using a probabilistic local search provides results that are almost as good as exhaustive local search, with much shorter processing times. Our main computational study shows that the genetic algorithm always dominates the myopic heuristic in terms of objective function, at the cost of increased processing time. We expect that our results will provide insights for the future application of genetic algorithms to scheduling problems.     

A memetic algorithm for minimizing total weighted tardiness on parallel batch machines with incompatible job families and dynamic job arrival

This paper addresses a scheduling problem motivated by scheduling of diffusion operations in the wafer fabrication facility. In the target problem, jobs arrive at the batch machines at different time instants, and only jobs belonging to the same family can be processed together. Parallel batch machine scheduling typically consists of three types of decisions—batch forming, machine assignment, and batch sequencing. We propose a memetic algorithm with a new genome encoding scheme to search for the optimal or near-optimal batch formation and batch sequence simultaneously. Machine assignment is resolved in the proposed decoding scheme. Crossover and mutation operators suitable for the proposed encoding scheme are also devised. Through the experiment with 4860 problem instances of various characteristics including the number of machines, the number of jobs, and so on, the proposed algorithm demonstrates its advantages over a recently proposed benchmark algorithm in terms of both solution quality and computational efficiency.     

A genetic algorithm for a bicriteria supplier selection problem

In this paper, we discuss the problem of selecting suppliers for an organisation, where a number of suppliers have made price offers for supply of items, but have limited capacity. Selecting the cheapest combination of suppliers is a straightforward matter, but purchasers often have a dual goal of lowering the number of suppliers they deal with. This second goal makes this issue a bicriteria problem – minimisation of cost and minimisation of the number of suppliers. We present a mixed integer programming (MIP) model for this scenario. Quality and delivery performance are modelled as constraints. Smaller instances of this model may be solved using an MIP solver, but large instances will require a heuristic. We present a multi-population genetic algorithm for generating Pareto-optimal solutions of the problem. The performance of this algorithm is compared against MIP solutions and Monte Carlo solutions.     

Local search algorithm with path relinking for single batch-processing machine scheduling problem

The single batch-processing machine problem is to minimize makespan, which has broad applications, including engineering fundamentals and theoretical background. The machine can process several jobs as a batch simultaneously, and every job has three different attributes: job size, processing time, and job arrival. In this paper, a hybrid local search algorithm with path relinking (LP) is devised to solve the problem. We not only generate an optimal initial solution firstly but also pay more attention to improving the solution quality. Three kinds of local searches are applied to enhance the diversity of solutions; the path relinking is adopted to explore better solutions through local tracks connecting the current solution and the best in the elite set. With these approaches, it can keep a balanced rate between exploratory and exploitative capacity. Computational experiments on 40 benchmark instances indicate that LP has the superior convergence and robust performance and it surpasses the current state-of-the-art methods such as genetic algorithm and ant colony optimization, especially for large instances.

     

Dynamic and heuristic fuzzy connectives-based crossover operators for controlling the diversity and convergence of real-coded genetic algorithms

Genetic algorithms are adaptive methods which may be used as approximation heuristic for search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover, and mutation. A great problem in the use of genetic algorithms is the premature convergence, a premature stagnation of the search caused by the lack of diversity in the population and a disproportionate relationship between exploitation and exploration. The crossover operator is considered one of the most determinant elements for solving this problem. In this article we present two types of crossover operators based on fuzzy connectives for real-coded genetic algorithms. The first type is designed to keep a suitable sequence between the exploration and the exploitation along the genetic algorithm's run, the dynamic fuzzy connectives-based crossover operators, the second, for generating offspring near to the best parents in order to offer diversity or convergence in a profitable way, the heuristic fuzzy connectives-based crossover operators. We combine both crossover operators for designing dynamic heuristic fuzzy connectives-based crossover operators that show a robust behavior. © 1996 John Wiley & Sons, Inc.     

Minimizing total earliness and tardiness on a single machine using a hybrid heuristic

This paper focuses on scheduling jobs with different processing times and distinct due dates on a single machine with no inserted idle time as to minimize the sum of total earliness and tardiness. This scheduling problem is a very important and frequent industrial problem that is common to most just-in-time production environments. This NP hard scheduling problem is herein solved using a hybrid heuristic which combines local search heuristics (dispatching rules, hill climbing and simulated annealing) and an evolutionary algorithm based on genetic algorithms. The heuristic involves low and high, relay and teamwork hybridization. Computational results reflect the sizeable solution quality improvement induced by hybridization, and assess the impact of each type of hybridization on the efficiency of the hybrid heuristic.     

Heuristics for minimizing total completion time and maximum lateness on identical parallel machines with setup times

This paper aims at minimizing the total completion time together with the maximum lateness. Jobs are processed by parallel machines in batches. A setup is required before processing a batch, which is common for all jobs in the batch. Jobs are continuously processed after the setup time. The processing length of a batch is the sum of the setup time and processing times of the jobs it contains. Due to the availability constraint, the completion time of a job is the time when a batch is totally processed. Considering due dates, the jobs need to be processed in a way that the total completion time and the maximum lateness are minimized. This problem is a kind of NP-hard so first we present a constructive heuristic to solve the problem. Then we propose a genetic algorithm whose initial population is formed by using the heuristic approach. Computational experiments are carried out to evaluate the performance of the proposed algorithms.     

Scheduling a capacitated batch-processing machine to minimize makespan

This paper aims at improving the utilization of a single batch-processing machine. The batch-processing machine can process a batch of jobs, as long as the number of jobs and the total size of all the jobs in a batch do not violate the machine's capacity. The processing time of the job and its size is known. The processing time of a batch is the longest processing time among all the jobs in the batch. The objective is to minimize the makespan. Since the problem under study is NP-hard, a Simulated Annealing (SA) approach is proposed. The effectiveness of our solution procedure in terms of solution quality and run time is evaluated through experiments. The results obtained from the SA approach were compared with a commercial solver called CPLEX. Our computational study demonstrates the effectiveness of our approach in solving problem instances with 20 or more jobs in a shorter run time with better solutions.