Non-identical Capacities Research Articles

Fair scheduling on parallel batch machines with non-identical capacities

The fairness of jobs from agents is considered in an advanced manufacturing factory and the fair scheduling of jobs on parallel batch machines is studied for two competing agents. Each agent and the system aim to minimize the makespan of their own jobs and the weighted sum makespans of the two agents, respectively. A modified full-batch longest processing time (MFBLPT) algorithm is proposed to minimize the makespan, and a Kalai–Smorodinsky fairness (KSF) algorithm is proposed to obtain fair schedules. These algorithms are analysed based on worst-case ratios, and the results show that these ratios are related to the workloads and importance of agents. Computational experiments are conducted to compare the performance of algorithm KSF with that of machine-centric and agent-centric algorithms. The results show that the pursuance of fairness leads to interest losses of a system, and that a proper preference of an agent leads to good performance of algorithm KSF.

A matheuristic for flowshop scheduling with batch processing machines in textile manufacturing

Inspired by a real-world textile packing process, this paper investigates a novel hybrid flowshop scheduling problem with batch processing machines to minimize the makespan. Geometry sizes of textile products, non-identical capacities of packing machines, and the capacity of the needle detector are addressed in parallel-batching modes. To make batching and sequencing decisions simultaneously, a mixed integer linear programming model (MILP) is formulated. Then, a matheuristic method, Tabu Search with Fixing and Optimization (TSFO), is developed. Using tabu search to determine which variables to be fixed, the MILP is solved through a fix-and-optimize process. The results of extensive computational experiments show that the TSFO yields better solutions within much less computation time than solving the model directly in a commercial solver. Furthermore, the TSFO also outperforms an existing method in a special case from literature.

Parallel batch processing machines scheduling in cloud manufacturing for minimizing total service completion time

This paper considers the integrated scheduling problem of production and delivery on parallel batch processing machines with non-identical capacities in different locations in cloud manufacturing. It is assumed that the jobs have arbitrary release times, different job sizes, unequal processing times, and unique information of customers submitting jobs. The service completion time of a job is the sum of the production completion time and the delivery duration. The objective of the studied problem is to minimize the total service completion time. A mixed-integer programming (MIP) model is presented to solve this problem. Since the problem is NP-hard, an efficient heuristic algorithm and an improved particle swarm optimization algorithm are proposed. The two proposed algorithms are compared with several state-of-the-art algorithms and the commercial optimization solver (Gurobi) through extensive experiments, verifying the effectiveness of the proposed algorithms.

Efficient algorithms for scheduling equal-length jobs with processing set restrictions on uniform parallel batch machines.

We consider the problem of scheduling jobs with equal lengths on uniform parallel batch machines with non-identical capacities where each job can only be processed on a specified subset of machines called its processing set. For the case of equal release times, we give efficient exact algorithms for various objective functions. For the case of unequal release times, we give efficient exact algorithms for minimizing makespan.

An ant colony-based algorithm for integrated scheduling on batch machines with non-identical capacities

An ant colony-based algorithm for integrated scheduling on batch machines with non-identical capacities

Weak-restriction bi-objective optimization algorithm for scheduling with rejection on non-identical batch processing machines

We investigate the problem of scheduling a set of jobs with arbitrary sizes and unequal weights on a set of parallel batch machines with non-identical capacities. The objective is to minimize the makespan of the accepted jobs and the total rejection penalty of the rejected jobs, simultaneously. To address the studied problem, a Pareto-based ant colony optimization algorithm with the first job selection probability (FPACO) is proposed. A weak-restriction selection strategy is proposed to obtain the desirability of candidate jobs. Two objective-oriented heuristic information and pheromone matrices are designed, respectively, to record the experience in different search dimensions. Moreover, a local optimization algorithm is incorporated to improve the solution quality. Finally, the proposed algorithm is compared with four existing algorithms through extensive simulation experiments. The experimental results indicate that the proposed algorithm outperforms all of the compared algorithms within a reasonable time.

Integrated scheduling on parallel batch processing machines with non-identical capacities

ABSTRACTIn this article, the problem of scheduling a set of jobs on parallel batch machines with arbitrary capacities is considered. The jobs have identical processing time, non-identical sizes and unequal weights. After being processed, the jobs are delivered to the customers by the vehicles. The objective is to minimize the total weighted delivery time of the jobs. Two heuristic algorithms and an algorithm based on ant colony optimization (ACO) are presented to address the problem. Considering the relationship between the jobs and the batches, a three-level candidate list is designed for building the solutions effectively. Furthermore, based on the change of the normalized weight of the batch, the heuristic information is designed to control the search direction of the ants and improve the solution quality. The experimental results show that the performance of the proposed ACO algorithm is superior to the other algorithms compared.

An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic Algorithm

A major challenge faced by hospitals is to provide efficient medical services. The problem studied in this article is motivated by the hospital sterilization services where the washing step generally constitutes a bottleneck in the sterilization services. Therefore, an efficient scheduling of the washing operations to reduce flow time and work-in-process inventories is of great concern to management. In the washing step, different sets of reusable medical devices may be washed together as long as the washer capacity is not exceeded. Thus, the washing step is modeled as a batch scheduling problem where washers have nonidentical capacities and reusable medical device sets have different sizes and different ready times. The objective is to minimize the sum of completion times for washing operations. The problem is first formulated as a nonlinear integer programming model. Given that this problem is NP-hard, a genetic algorithm is then proposed to heuristically solve the problem. Computational experiments show that the proposed algorithm is capable of consistently obtaining high-quality solutions in short computation times.

An adaptive penalty guided genetic algorithm for scheduling parallel batch processing machines

We study the problem of scheduling a set of jobs with non-identical capacity requirements on parallel non-identical batch processing machines to minimise the makespan. We formulate the problem as a nonlinear integer programming model. Given that this problem is NP-hard, we propose a genetic algorithm to heuristically solve it. An adaptive penalty is combined to guide the search process to explore promising feasible and infeasible regions. Random problem instances were generated to test the approach with respect to solution quality and run time. Computational results demonstrate the effectiveness of the proposed algorithm.

An adaptive penalty guided genetic algorithm for scheduling parallel batch processing machines

We study the problem of scheduling a set of jobs with non-identical capacity requirements on parallel non-identical batch processing machines to minimise the makespan. We formulate the problem as a nonlinear integer programming model. Given that this problem is NP-hard, we propose a genetic algorithm to heuristically solve it. An adaptive penalty is combined to guide the search process to explore promising feasible and infeasible regions. Random problem instances were generated to test the approach with respect to solution quality and run time. Computational results demonstrate the effectiveness of the proposed algorithm.

Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities

We consider the problem of scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities to minimize makespan. A job can only be assigned to a machine whose capacity is not less than the size of the job. A machine can process a group of jobs as a batch simultaneously, as long as the total size of the jobs in this batch does not exceed the capacity of the machine. The processing time of a batch is equal to the longest processing time of all the jobs in the batch. For the case of equal release times, we obtain a fast 5-approximation algorithm, as well as an algorithm with approximation ratio arbitrarily close to 2. For the case of unequal release times and a fixed number of different batch capacities, we obtain an algorithm with approximation ratio arbitrarily close to 2. We also study the problem of scheduling jobs with equal release times, arbitrary sizes, inclusive processing set restrictions and incompatible families on batch machines with identical capacities to minimize makespan. We obtain a 8/3-approximation algorithm, as well as an algorithm with approximation ratio arbitrarily close to 2. If only a single family is considered, a 2-approximation algorithm is presented. It is likely that these results cannot be too substantially improved upon, since all of the problems studied cannot be approximated to within a ratio smaller than 2 unless P=NP.

An effective iterated greedy algorithm for scheduling unrelated parallel batch machines with non-identical capacities and unequal ready times

This study addresses the problem of scheduling a set of n jobs with arbitrary job sizes and non-zero ready times on a set of m unrelated parallel batch machines with different capacities so as to minimize the makespan. Unrelated parallel machines is the most general case of parallel machine environments where each machine processes each job at a different speed. In the studied problem, each machine can process several jobs simultaneously as a batch as long as the machine capacity is not exceeded. The batch processing time and the batch ready time are respectively equal to the largest processing time and the largest ready time among all the jobs in the batch.In this paper, we first provide a lower bound for the problem and a mixed integer programming (MIP) model. To solve the problem, a meta-heuristic based on the iterated greedy (IG) algorithm is proposed. IG is a simple meta-heuristic which generates a sequence of solutions by iterating over a greedy constructive heuristic using destruction and construction operations. In the recent literature this meta-heuristic has been employed to solve a considerable number of combinatorial optimization problems. This is because IG is easy to implement and it often exhibits an excellent performance. The effectiveness of the proposed IG algorithm is evaluated and compared by computational experiments on a large benchmark of randomly generated instances. The obtained results indicate that the proposed algorithm has a superior performance compared to some meta-heuristic algorithms proposed for similar problems.

Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan

We consider the problem of scheduling n jobs on m parallel batching machines with inclusive processing set restrictions and non-identical capacities. The machines differ in their functionality but have the same processing speed. The inclusive processing set restriction has the following property: the machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. Each job is characterized by a processing time that specifies the minimum time needed to process the job, a release date before which it cannot be processed, and a machine index which is the smallest index among the machines that can process it. Each batching machine has a limited capacity and can process a batch of jobs simultaneously as long as its capacity is not violated. The capacities of the machines are non-identical. The processing time of a batch is the maximum of the processing times of the jobs belonging to it. Jobs in the same batch have a common start time and a common completion time. The goal is to find a non-preemptive schedule so as to minimize makespan (the maximum completion time). When all jobs are released at the same time, we present two fast algorithms with approximation ratios 3 and 9/4, respectively. For the general case with unequal release dates, we develop a polynomial time approximation scheme (PTAS), which is also the first PTAS even for the case with equal release dates and without processing set restrictions.

Effective heuristics for makespan minimization in parallel batch machines with non-identical capacities and job release times

We consider the problem of scheduling a set of \begin{document} $n$ \end{document} jobs with arbitrary job sizes, processing times and release times on a set of \begin{document} $m$ \end{document} parallel batch machines with non-identical capacities; the objective is to minimize the makespan. We first present an algorithm to compute a lower bound for the optimal makespan. Based on different rules of batching the jobs and assigning the batches to the machines, several heuristics are proposed to solve the problem. The performance of the proposed heuristics is evaluated by computational experiments. The proposed heuristics are compared against the lower bound and against each other. Our results show that the one of the proposed algorithms outperforms all the other heuristics.

An effective discrete differential evolution algorithm for scheduling uniform parallel batch processing machines with non-identical capacities and arbitrary job sizes

Batch processing machines (BPMs) simultaneously process multiple jobs in a batch, which are commonly used in many industrial systems. This paper studies the scheduling problem of uniform parallel batch processing machines with arbitrary job sizes. These batch processing machines have non-identical capacities and different speeds. The objective is to minimize the makespan (or maximize the machine utilization). We formulate this problem as a mixed integer programming model. Since the problem is strongly NP-hard, an effective differential evolution-based hybrid algorithm is proposed for solving large-scale problems. Firstly, in this algorithm, individuals in the population are represented as discrete job sequences, and novel mutation and crossover operators are designed based on this representation. Next, a heuristic is developed to form batches and schedule the resulting batches on the uniform parallel machines. Then, the performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a random keys genetic algorithm (RKGA) and a particle swarm optimization (PSO) algorithm. Experimental results demonstrate the superiority of the proposed algorithm in terms of solution quality and robustness, especially for large-scale instances.

Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

We consider the problem of scheduling a set of n jobs with arbitrary job sizes on a set of m parallel batch machines with non-identical capacities; the objective is to minimize the makespan. The problem is known to be NP-hard. A heuristic based on the First-Fit-Decreasing (FFD) rule is presented as well as a meta-heuristic based on Max-Min Ant System (MMAS). The performances of the two heuristics are compared with a previously studied heuristic by computational experiments. The results show that both proposed algorithms outperform the previously studied heuristic. Moreover, the MMAS heuristic obtains better solutions compared with the FFD heuristic.

Automatic generation control of interconnected power system for robust decentralized random load disturbances using a novel quasi-oppositional harmony search algorithm

Abstract An effort is made in this paper to discuss the real-time problem of interconnected power system for resistance to random and rapid changes of small step load perturbation (SLP) in connection with automatic generation control (AGC). Rapid changes of loads, for a continuous period of time, always create problems in the benefits of optimum AGC performance. In view of this, a continuous nature of load profile is designed for its implementation in real-time application of AGC. In such case, the point of concern is to closely examine the frequency deviation and the behavior of tie-line power flow profiles within the control areas. To overcome these consequences, a novel quasi-oppositional harmony search (QOHS) algorithm based proportional–integral–derivative (PID) controller is proposed along with filtering technique. The test system under consideration is a three-area power system with two generating units (non-identical capacity) in each area having an appropriate generation rate constraint (GRC). Importance of considering the physical constraint (like GRC) is demonstrated by examining the closed loop performance of the studied power system model. The performance of the proposed QOHS algorithm is verified by comparing the obtained dynamic responses to those offered by the imperialist competitive algorithm for the same test system. In the final phase of investigation, the total load changes of all the three control areas are also considered for the purpose of analyzing the saturation and non-linearity effects of turbine. It may be apprehended from the simulation results that the proposed QOHS based PID controller is more efficient to minimize the effect of continuous SLP. The proposed QOHS algorithm shows the feasibility of the approach and is able to regain its steady-state operation for such load perturbation profiles.

Scheduling jobs with equal-processing-time on parallel machines with non-identical capacities to minimize makespan

We consider the problem of scheduling a set of equal-processing-time jobs with arbitrary job sizes on a set of batch machines with different capacities. A job can only be assigned to a machine whose capacity is not smaller than the size of the job. Our goal is to minimize the schedule length (makespan). We show that there is no polynomial-time approximation algorithm with an absolute worst-case ratio less than 2, unless P=NP. We then give a polynomial-time approximation algorithm with an absolute worst-case ratio exactly 2. Moreover, we give a polynomial-time approximation algorithm with asymptotic worst-case ratio no more than 3/2. Finally, we perform a computational experiment and show that our approximation algorithm performs very well in practice.

Performance analysis of a multiple vehicle tandem system with inter-vehicle buffers and blocking

We analyze a new tandem system in which items are transported through a sequence of stations from an origin to a destination via a series of vehicles that move back and forth between consecutive stations. Each pair of consecutive stations is connected by a single vehicle with unit capacity that travels back and forth between the upstream and downstream station. Each vehicle travels with an item in the downstream direction and without an item in the upstream direction. The stations act as holding areas for items awaiting further transport within the system. Stations may have non-identical capacities. We model this system as a continuous time Markov chain and develop a recursive algorithm for generating the state transition matrix. After solving for the steady state probabilities using the Gauss–Seidel method, we compute the average throughput rate, average number of items in the system, and average sojourn time for various system configurations.

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 purpose Usually 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).