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Findings: The proposed algorithm achieves an average efficiency of 99.32% compared to the enumeration algorithm, with minimal deviation (0.4%). The results validate the main proposition for efficient scheduling, including prioritizing jobs based on due dates, allocating job demands based on machine capacity, and sequencing batches based on size to minimize delays.Research limitations/implications: The model assumes static machine conditions and predefined job parameters, limiting its applicability in dynamic environments. Future research can extend this approach to incorporate real-time job arrivals or machine breakdown scenarios.Practical implications: This algorithm provides a practical tool for industries to optimize batch scheduling on unrelated parallel machines, improving production efficiency and reducing operational costs.Social implications: By improving production scheduling, this model indirectly supports sustainable manufacturing practices through optimal resource utilization.Originality/value: This study introduces a novel integration of backward scheduling with resource constraints and sequence-dependent setup times, addressing gaps in scheduling research for unrelated parallel machines.

Purpose: This research develops a batch scheduling model for a three-stage flow shop with job processors in the first and second stages and a batch processor in the third stage. The model integrates production process activities and a product inspection activity to minimize the expected total actual flow time. Design/methodology/approach: The problem of batch scheduling for a three-stage flow shop is formulated as a mathematical model, and a heuristic algorithm is proposed to solve the problem. This model applies backward scheduling to accommodate the objective of minimizing the expected total actual flow time. Findings: This research has proposed a batch scheduling model for a three-stage flow shop with job and batch processors to produce multiple items and an algorithm to solve the model. The objective is to minimize total actual time. The resulting production batches can be sequenced between all types of products to minimize idle time, and the batch processor capacity affects the sample size and indirectly affects the production batch size. Originality/value: This research develops a batch scheduling model for a three-stage flow shop constituting job and batch processors and carrying out integrated production and inspection activities to minimize the expected total actual flow time.

Purpose: Today’s manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem has been addressed to enable on-time completion of customer orders in a lean manufacturing environment. The problem is optimizing the partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components. Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid excess final product inventory. The first model is a non-linear integer programming model whereas the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented. Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times compared to the other two models. It has also been showed that the alternative model is able to solve moderate sized real-world problems. Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature owing to the inclusion of new circumstances that are present in real-world applications. Those are: customer orders consisting of multi-products made of multi-parts, processing of all parts of the same product from different orders in the same batch, and delivering the orders only when all related products are completed. This research also contributes to the literature of batch scheduling problem by presenting new optimization models.

Purpose: This paper aims to investigate simultaneous problems of batch scheduling and operator assignment with time-changing effects caused by learning and forgetting.Design/methodology/approach: A number of parts will be processed in batches, each of which will be processed through a number of operations where there are alternative operators for each operation bringing different set up and processing times as operators experience different degree of learning and forgetting. A mathematical model is developed for the problems, and the decision variables are operator assignment, the number of batches, batch sizes and the schedule of the resulting batches. A proposed algorithm works by trying different number of batches, starting from one, and increasing the number of batches one by one until the objective function value does not improve anymore.Findings: We show both mathematically and numerically that the closest batch to the due date always becomes the largest batch in the schedule, and the faster operators learn, the larger the difference between the closest batch to the due date and the other batches, the lower optimal number of batches, and the lower the total actual flow time.Originality/value: Previous papers have considered the existence of alternative operators but have not considered learning and forgetting, or have considered learning and forgetting but only in a single-stage system and without considering alternative operators.

This study considers batch scheduling problem in the multi hybrid cell manufacturing system (MHCMS) taking into account worker resources. This problem consists of determining sequence of batches, finding the starting time of each batch, and assigning workers to the batches in accordance with some pre-determined objectives. Due to a lack of studies on the batch scheduling problem in the MHCMS, a binary integer linear goal programming mathematical model is developed for bi-objective batch scheduling problem in this study. The formulated model is difficult to solve for large sized problem instances. To solve the model, we develop an efficient heuristic method called the Hybrid Cells Batch Scheduling (HCBS) heuristic. The proposed HCBS heuristic permits integrating batch scheduling and employee (worker) timetabling. Furthermore, we construct upper and lower bounds for the average flow time and the total number of workers. For evaluation of the performance of the heuristic, computational experiments are performed on generated test instances based on real production data. Results of the experiments show that the suggested heuristic method is capable of solving large sized problem instances in a reasonable amount of CPU time.

This paper discusses a two-stage assembly-type flowshop scheduling problem with batching considerations subject to a fixed job sequence. The two-stage assembly flowshop consists of m stage-1 parallel dedicated machines and a stage-2 assembly machine which processes the jobs in batches. Four regular performance metrics, namely, the total completion time, maximum lateness, total tardiness, and number of tardy jobs, are considered. The goal is to obtain an optimal batching decision for the predetermined job sequence at stage 2. This study presents a two-phase algorithm, which is developed by coupling a problem-transformation procedure with a dynamic program. The running time of the proposed algorithm is O(mn+n 5 ), where n is the number of jobs.

This study is inspired by a batch scheduling problem in metal working industry which guarantees to satisfy a due date as a commitment to customers. Actual flowtime adopts the backward scheduling approach and considers the due date. Using the actual flowtime as the objective means that the solution  is oriented to satisfy the due date, and simultaneosly to minimize the length of time of the parts spending in the shop. This research is to address a problem of scheduling batches consisting of multiple items of parts processed on a batch processor where the completed parts must be delivered several time at different due dates. We propose an algorithm to solve the problem.

This paper, based on the parallel-sequence-transfer mode of batch jobs, aimed to implement research on the batch scheduling for work centers with multiple manufacturing machines in full detail. In order to arrange a precise product planning with batch jobs, obtain the maximum completing time with batch jobs, schedule manufacturing machines in each work center accurately, and get the actual number of manufacturing machines used to processing batch jobs in each work center, a new processing procedure of the processing time model under the parallel-sequence-transfer mode was designed. The new designed processing procedure was tested on a numeric example. The results show that the research in this thesis could not only arrange a precise production planning under the parallel-sequence-transfer mode, but also schedule manufacturing machines for each work center with multiple manufacturing machines accurately.

This paper addresses a parallel machine scheduling problem with non-anticipatory family setup times and batching, considering the task’s stochastic processing times and release dates. The problem arises from a real-life ship scheduling problem in the oil and gas industry. We developed an Iterated Greedy simheuristic with built-in Monte Carlo Simulation to sample the stochastic parameters. We conducted experiments on a set of instances from the literature, considering two simheuristic variants and three uncertainty levels for the stochastic parameters. To highlight the advantages of using simulation to tackle the stochastic problem, the simheuristics are compared against a regular Iterated Greedy metaheuristic, yielding an improvement of up to 16.5% on the objective function’s expected values, with a reduced impact on computational times. During a risk analysis, the Pareto set of solutions is generated to illustrate the trade-off between the expected objective value of the solutions and the conditional value at risk, providing decision-makers with a useful tool to select the schedules that better fit their risk profiles. We use an iterative mechanism to build confidence intervals within a certain confidence level during the method’s simulation step, interrupting the procedure when it reaches the desired error. This strategy’s advantage is highlighted in the computational experiments, which indicates that the number of replications of the simulation is instance and uncertainty level dependent. A periodic re-planning strategy is also used to evaluate the performance of the simheuristic, highlighting the advantages of using the proposed algorithm in a real-life usage situation.

The 1|s-batch(∞),rj|∑wjUj scheduling problem takes as input a batch setup time Δ and a set of n jobs, each having a processing time, a release date, a weight, and a due date; the task is to find a sequence of batches that minimizes the weighted number of tardy jobs. This problem was introduced by Hochbaum and Landy (Oper Res Lett 16(2):79–86, 1994); as a wide generalization of Knapsack, it is NP-hard. In this work, we provide a multivariate complexity analysis of the 1|s-batch(∞),rj|∑wjUj problem with respect to several natural parameters. That is, we establish a classification into fixed-parameter tractable and W[1]-hard problems, for parameter combinations of (i) #p = number of distinct processing times, (ii) #w = number of distinct weights, (iii) #d = number of distinct due dates, (iv) #r = number of distinct release dates. Thereby, we significantly extend the work of Hermelin et al. (Ann Oper Res 298:271–287, 2018) who analyzed the parameterized complexity of the non-batch variant of this problem without release dates. As one of our key results, we prove that 1|s-batch(∞),rj|∑wjUj is W[1]-hard parameterized by the number of distinct processing times and distinct due dates. To the best of our knowledge, these are the first parameterized intractability results for scheduling problems with few distinct processing times. Further, we show that 1|s-batch(∞),rj|∑wjUj is fixed-parameter tractable parameterized by #d+#p+#r, and parameterized by #d+#w if there is just a single release date. Both results hold even if the number of jobs per batch is limited by some integer b.