Batch Machine Research Articles

Investigation on Effects of Alternative Process Routing in the Design of Cellular Manufacturing System

Background/Objectives: The adoption of cellular manufacturing becomes promising manufacturing philosophy to address the problems of today’s manufacturing plants such as an increasingly turbulent environment and rising customer requirements. Method/Statistical Analysis: Group Technology and Cellular Manufacturing System (CMS) have together paved way for the same through processing of similar parts groups as part families and the formation of a machine cell dedicated for the manufacture of the part family. The traditional CMS design methods do not incorporate many real-life manufacturing parameters such as batch size and machine flexibility, various cost factors at the design stage and also they are not taking the advantage of the machine flexibility in terms of coexistence of alternate process routing. Findings: In this work, a comprehensive mathematical model has been developed capturing these exact production parameters. An optimal solution is obtained using Lingo 8.0 software package and a solution methodology of best possible cell configurations is formed. Applications/Improvements: The effect of considering the alternate process routing in the design stage of CMS is evaluated and it is found that routing flexibility results in better cell configurations.

Integrated scheduling on a batch machine to minimize production, inventory and distribution costs

We consider the problem of scheduling a set of jobs on a single batch-processing machine. Each job has a size and a processing time. The jobs are batched together and scheduled on the batch-processing machine, provided that the total size does not exceed the machine capacity. The processing time of the batch is the longest processing time among all the jobs in the batch. There is a single vehicle to deliver the final products to the customer. If the vehicle has not returned, completed batches will be put into the inventory. In this paper, we consider the problem of minimizing the production, delivery and inventory costs. We show that if the jobs have the same size, there is an O(nlog n)-time algorithm to find an optimal solution. If the jobs have the same processing time, there is a fast approximation algorithm with an absolute worst-case ratio less than 1.783 and an asymptotic worst-case ratio equal to 11/9. When the jobs have arbitrary sizes and arbitrary processing times, there is a fast approximation algorithm with absolute and asymptotic worst-case ratios less than or equal to 2, respectively.

User Preference Learning for Online Social Recommendation

A social recommendation system has attracted a lot of attention recently in the research communities of information retrieval, machine learning, and data mining. Traditional social recommendation algorithms are often based on batch machine learning methods which suffer from several critical limitations, e.g., extremely expensive model retraining cost whenever new user ratings arrive, unable to capture the change of user preferences over time. Therefore, it is important to make social recommendation system suitable for real-world online applications where data often arrives sequentially and user preferences may change dynamically and rapidly. In this paper, we present a new framework of online social recommendation from the viewpoint of online graph regularized user preference learning (OGRPL), which incorporates both collaborative user-item relationship as well as item content features into an unified preference learning process. We further develop an efficient iterative procedure, OGRPL-FW which utilizes the Frank-Wolfe algorithm, to solve the proposed online optimization problem. We conduct extensive experiments on several large-scale datasets, in which the encouraging results demonstrate that the proposed algorithms obtain significantly lower errors (in terms of both RMSE and MAE) than the state-of-the-art online recommendation methods when receiving the same amount of training data in the online learning process.

Minimizing makespan for arbitrary size jobs with release times on P-batch machines with arbitrary capacities

We consider the problem of scheduling a set of arbitrary size jobs with dynamic arrival times on a set of parallel batch machines with arbitrary capacities; our goal is to minimize the makespan. We first give a mathematical model of the problem, and provide a lower bound for the objective function value. Based on different rules of batching the jobs and scheduling the batches on the machines, two meta-heuristics based on Ant Colony Optimization (ACO) are proposed to solve the problem. The performance of the proposed algorithms is evaluated and compared with existing heuristics by computational experiments. Our results show that one of the ACO algorithms consistently finds better solutions than all the others in a reasonable amount of time.

Sensitivity analysis–based dynamic process capability evaluation for small batch production runs

Quantifying the current and expected future performance of a machining process no doubt is essential for continuous improvement of product quality and productivity. However, process capability evaluation for small batch production runs is a challenging work, because the assumptions required by traditional evaluation approaches based on statistical process control techniques are commonly not satisfied in real world. In this article, a sensitivity analysis–based process capability evaluation method for small batch production runs is proposed, and a new capability index is also presented correspondingly. In this method, an error propagation model between machining errors and input errors is first established using weighted least squares support vector machine. Then, the sensitivity distribution of machining errors versus input errors is characterized by a set of eigenvalues and eigenvectors in the variation space of input errors. Third, the safe variation space of input errors is solved according to the specification limits of quality characteristics. Finally, the process capability is evaluated by comparing the fitness between the safe variation space and the tolerance space of input errors. A practical case is addressed to validate the feasibility and effectiveness of the proposed method, and the results demonstrate that the method can measure a real small batch machining process effectively and get rid of the common assumption of independent and identical distribution, which is needed by traditional methods.

Uniform parallel batch machines scheduling considering transportation using a hybrid DPSO-GA algorithm

This paper investigates coordinated scheduling on uniform parallel batch machines with batch transportation. Jobs are characterized by different processing time and sizes, and they are first delivered to manufacturers in batches and then processed on the uniform parallel batch machines. The manufacturers are distributed in different geographic zones and there exists one parallel batch machine in each manufacturer. A mixed integer programming model is developed for the studied problem, and its objective is to minimize the makespan. In addition, the structural properties of the problem are analyzed. A hybrid algorithm combining the merits of discrete particle swarm optimization (DPSO) and genetic algorithm (GA) is proposed to solve this problem. In the hybrid algorithm, a heuristic and a local search strategy are introduced. Finally, computational experiments are conducted and the results show that the proposed hybrid algorithm can effectively and efficiently solve the problem within a reasonable time, particularly in large-scale instances.

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.

Some Discussions on Parallel Bounded Batch Scheduling to Minimize the Sum of Squared Machine Loads

We study the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme (PTAS) and a fully polynomial time approximation scheme (FPTAS) for this problem.

Online scheduling on the unbounded drop-line batch machines to minimize the maximum delivery completion time

We consider the online scheduling on m unbounded drop-line batch machines with delivery times. Here a drop-line batch machine can process several jobs in a batch so that the processing time of a batch is equal to the longest processing time of the jobs in the batch, the jobs in a batch have the same starting time, and the completion time of a job is equal to the sum of its starting time and its processing time. Once the processing of a job is completed on the machine, we immediately deliver it to the destination. The objective is to minimize the time by which all jobs have been delivered. For this problem, we present a best possible online algorithm with a competitive ratio of 1+αm, where αm is the positive root of the equation α2+mα−1=0.

A hybrid coding SA method for multi-item capacity-constrained production and delivery scheduling problem with arbitrary job volumes and customer inventory considerations

This article deals with an integrated scheduling problem for a multi-item capacity-constrained production and delivery system. The compatible jobs are firstly processed on a batching machine, and then delivered to a customer by one capacitated transporter. Each job has to be delivered to the customer before its due date. It is assumed that the job which arrives to the customer before its due date will occur an earliness penalty. The problem is to find an integrated schedule such that the total logistics cost is minimised while guaranteeing a certain customer service level. We formulate the problem as a nonlinear model, and show that this problem is intractable. Then we develop a hybrid-coding simulated annealing algorithm for solving the problem. At last, we derive a lower bound to verify performance of this proposed algorithm. Experiments show the efficiency in terms of both solution quality and running time of the proposed algorithm.

Heuristics for Batch Machining at Reconfigurable Rotary Transfer Machines

A problem of design of reconfigurable rotary transfer machines is considered. Parts are divided into batches. Parts of a batch are located at the loading position of rotary table in a given sequence and they are processed simultaneously. Operations are partitioned into groups which are performed by spindle heads or by turrets. Constraints related to the design of spindle heads, turrets, and working positions, as well as precedence constraints related to operations, are given. The problem consists in minimizing the estimated cost of the transfer machine, while reaching a given output and satisfying all the constraints. The proposed methods to solve the problem are based on sequential assignment of operations to machining modules. Experimental results with different heuristics are reported.

The lockmaster’s problem

Inland waterways form a natural network infrastructure with capacity for more traffic. Transportation by ship is widely promoted as it is a reliable, efficient and environmental friendly way of transport. Nevertheless, locks managing the water level on waterways and within harbors sometimes constitute bottlenecks for transportation over water. The lockmaster’s problem concerns the optimal strategy for operating such a lock. In the lockmaster’s problem we are given a lock, a set of upstream-bound ships and another set of ships traveling in the opposite direction. We are given the arrival times of the ships and a constant lockage time; the goal is to minimize total waiting time of the ships. In this paper, a dynamic programming algorithm is proposed that solves the lockmaster’s problem in polynomial time. This algorithm can also be used to solve a single batching machine scheduling problem more efficiently than the current algorithms from the literature do. We extend the algorithm such that it can be applied in realistic settings, taking into account capacity, ship-dependent handling times, weights and water usage. In addition, we compare the performance of this new exact algorithm with the performance of some (straightforward) heuristics in a computational study.

An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan

This paper considers the large-scale mixed job shop scheduling problem with general number of jobs on each route. The problem includes ordinary machines, batch machines (with bounded or unbounded capacity), parallel machines, and machines with breakdowns. The objective is to find a schedule to minimize the makespan. For the problem, we define a virtual problem and a corresponding virtual schedule, based on which our algorithm TVSA is proposed. The performance analysis of the algorithm shows the gap between the obtained solution and the optimal solution is O(1), which indicates the algorithm is asymptotically optimal.

New results on the coordination of transportation and batching scheduling

We study a planning problem to coordinate production and transportation scheduling, where a set of jobs needs to be transported from a holding area to a single batch machine for further processing. A number of results for this combined transportation-and-scheduling environment have recently been published. They look into the complexity status of the minimization of the sum of total processing time and processing cost, and of the sum of makespan and processing cost, for a fixed number of transporters. In this paper, we add to these results in that (1) we show that the earlier complexity results are still valid when the processing cost is removed from the objective, thus reducing to more “classic” scheduling objectives; (2) we assess the complexity status of the relevant problem variants with free number of transporters; and (3) we prove that the weighted-completion-time objective leads to an intractable problem even with a single transporter, contrary to the unweighted case.

Scheduling a single machine with parallel batching to minimize makespan and total rejection cost

We consider the problem of scheduling a set of n jobs on a single machine with parallel batching and with rejection being allowed. Two bi-criteria problems are considered: (a) minimize the makespan subject to the constraint that the total rejection cost does not exceed a given threshold, and (b) minimize the total rejection cost subject to the constraint that the makespan does not exceed a given threshold. For the case of a batching machine with infinite capacity (i.e., the batch size allowed on the machine is larger than or equal to the number of jobs), we assume that the jobs have release dates. We present an O(n2)-time 2-approximation algorithm for problem (a) and, in addition, we present dynamic programming algorithms and fully polynomial-time approximation schemes for both problems (a) and (b). For the case of a batching machine with finite capacity (i.e., the batch size allowed on the machine is less than the number of jobs), we assume that the jobs have identical release dates. We propose approximation algorithms for (a) and present dynamic programming algorithms and fully polynomial-time approximation schemes for both problems (a) and (b).

An ACO algorithm for makespan minimization in parallel batch machines with non-identical job sizes and incompatible job families

We study the problem of scheduling a set of N jobs with non-identical job sizes from F different families on a set of M parallel batch machines; the objective is to minimize the makespan. The problem is known to be NP-hard. A meta-heuristic based on Max–Min Ant System (MMAS) is presented. The performance of the algorithm is compared with several previously studied algorithms by computational experiments. According to our results, the average distance between the solutions found by our proposed algorithm and the lower bounds is about 4% less than that of the best of all the compared algorithms, demonstrating that our algorithm outperforms the previously studied algorithms.

The single machine serial batch scheduling problems with rejection

We consider several serial batch scheduling problems with rejection. Each job is either processed on a single serial batching machine or rejected by paying a penalty. We analyze two models with rejection. The first model is to minimize the sum of the scheduling cost of the accepted jobs and the total penalty of the rejected jobs, where the scheduling costs are the total completion time, the makespan, the maximum lateness and the weighted number of tardy jobs, respectively. For the former two problems, we propose two polynomial time algorithms to solve them. For the last two problems, we derive efficient dynamic programming algorithms. The second model is to minimize the makespan, given an upper bound on the total rejection cost, we present a fully polynomial time approximation scheme.

Single batch machine scheduling with deliveries

AbstractWe consider the problem of scheduling a set of n jobs on a single batch machine, where several jobs can be processed simultaneously. Each job j has a processing time pj and a size sj. All jobs are available for processing at time 0. The batch machine has a capacity D. Several jobs can be batched together and processed simultaneously, provided that the total size of the jobs in the batch does not exceed D. The processing time of a batch is the largest processing time among all jobs in the batch. There is a single vehicle available for delivery of the finished products to the customer, and the vehicle has capacity K. We assume that K = rD, where and r is an integer. The travel time of the vehicle is T; that is, T is the time from the manufacturer to the customer. Our goal is to find a schedule of the jobs and a delivery plan so that the service span is minimized, where the service span is the time that the last job is delivered to the customer. We show that if the jobs have identical sizes, then we can find a schedule and delivery plan in time such that the service span is minimum. If the jobs have identical processing times, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most 11/9 times the optimal service span. When the jobs have arbitrary processing times and arbitrary sizes, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most twice the optimal service span. We also derive upper bounds of the absolute worst‐case ratios in both cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 470–482, 2015

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.

A note on unbounded parallel-batch scheduling

This paper revisits the scheduling problem on an unbounded parallel batch machine for minimizing a maximum cost fmax. It was reported in the literature that the decision version of the problem is solvable in O(n2+nlog⁡P) time, where n is the number of jobs and P is the total processing time of jobs. This implies that the optimization version for minimizing fmax can be solved in weakly polynomial time. But a strongly polynomial-time algorithm has not been provided for this problem. In this paper, we present an O(n4)-time algorithm for the Pareto optimization problem for minimizing Cmax and fmax, where Cmax is the maximum completion time of jobs. Consequently, the problem for minimizing fmax can also be solved in O(n4) time.