Batching decisions for assembly production systems

The two-stage assembly scheduling problem to minimize total completion time with setup times

This paper considers single-machine just-in-time scheduling of jobs that may be grouped into batches subject to a constraint on batches' weights. A job has a weight, due date, and earliness and tardiness penalties per unit time. A batch's processing time is determined by its jobs. Each job inherits its batch's completion time. The objective is to minimize the weighted sum of earliness and tardiness penalties of all jobs. This problem is challenging: Jobs-to-batch assignment changes the batch's processing time; thus, affects the structure of the entire solution and most importantly of its cost components. This problem is an excellent benchmark for testing linkage learning techniques, which exploit a problem's structure. We propose a matheuristic LTGA, which integrates evolutionary algorithms with mixed-integer programming (MIP). It builds a linkage tree that extracts the dependency among decision variables of MIP solutions. We compare its performance to a state of the art matheuristic CMSA, which combines the learning component of an ant colony system (ACS) with MIP within a construct, solve, merge, and adapt framework. It uses knowledge extracted from ACS' ants to construct a restricted MIP, solves it efficiently, and feeds it back to ACS. Computational tests indicate that LTGA outperforms MIP solvers and CMSA.

On the Capacity of a Process with Batch Processing and Setup times

The three-machine flowshop scheduling problem to minimize total completion time is studied where setup times are treated as separate from processing times. Setup and processing times of all jobs on all machines are unknown variables before the actual occurrence of these times. The lower and upper bounds for setup and processing times of each job on each machine is the only information that is available. In such a scheduling environment, there may not exist a unique schedule that remains optimal for all possible realizations of setup and processing times. Therefore, it is desired to obtain a set of dominating schedules (which dominate all other schedules) if possible. The objective for such a scheduling environment is to reduce the size of dominating schedule set. We obtain global and local dominance relations for a three-machine flowshop scheduling problem. Furthermore, we illustrate the use of dominance relations by numerical examples and conduct computational experiments on randomly generated problems to measure the effectiveness of the developed dominance relations. The computational experiments show that the developed dominance relations are quite helpful in reducing the size of dominating schedules.

We study a scheduling problem, in which jobs of two agents are performed in agent specific batches on the same serial unbounded batching machine. On this machine, jobs of the same batch complete simultaneously, and the batch processing time is equal to the total processing time of its jobs plus a setup time. Each agent aims at minimizing a function which depends only on the completion times of its jobs. The problem is to find a schedule that minimizes the objective function of one agent, subject to the objective function of the other agent does not exceed a given threshold. The problem appears in optimizing product consolidation operations of a cross-docking distribution center. Polynomial and pseudo-polynomial dynamic programming algorithms are derived for settings with various combinations of the objective functions.

The two-stage assembly scheduling problem (TASP) is widely existed in our real-life. Minimising the total tardiness of all jobs is important for increasing customers’ satisfaction. Although a few researchers have focused on such optimisation criterion, the performance of proposed algorithms depends on four or more fine-tuned parameters. This work focuses on TASPs with separated setup time. There are multiple and one machine at stages one and two, respectively. A branch and bound algorithm and a variable neighbourhood search (VNS) are proposed to minimise the total tardiness of all jobs. Both of them contain only one parameter, i.e. maximum CPU time, which needs no turning. In order to guide the search of the branch and bound algorithm, lower and upper bounds and dominance rules are proposed. In order to avoid VNS falling into local optima, three neighbourhoods and a novel shaking subroutine are proposed. Experimental results show that the proposed VNS outperforms all existing algorithms on thousands of large scale TASPs generated randomly. Branch and bound algorithm can not only ensure the optimal schedule for small scale TASPs but also enhance the search ability of the proposed VNS to some extent.

This paper deals with a single machine scheduling problem with general past-sequence-dependent (psd) setup time and log-linear learning in which the setup times and learning effects are job-dependent. The setup times are unique functions of the length of already processed jobs, and the learning effects show that processing times are unique decreasing functions of job positions. The goal is to find the optimal sequences that minimise objective functions such as the makespan, total completion time, total lateness, total waiting cost, total waiting time, total absolute differences in completion times, and the sum of earliness, tardiness and common due date penalty. Special cases of the resulting problems are solvable in polynomial time; however, the general problems are difficult to solve. We propose branch-and-bound (B&B) methods to derive the optimal sequences for such problems. Computational results show that the proposed methods can solve relatively large problem instances in reasonable amounts of time.

This article studies a submodular batch scheduling problem motivated by the vacuum heat treatment. The batch processing time is formulated by a monotone nondecreasing submodular function characterized by decreasing marginal gain property. The objective is to minimize the makespan. We show the NP‐hardness of the problem on a single machine and of finding a polynomial‐time approximation algorithm with the worst‐case performance ratio strictly less than for the problem on parallel machines. We introduce a bounded interval to model the batch processing time using two parameters, that is, the total curvature and the quantization indicator. Based on the decreasing marginal gain property and the two parameters, we make a systematic analysis of the full batch longest processing time algorithm and the longest processing time greedy algorithm, and propose the instances with the bound of batch capacity for these two algorithms for the submodular batch scheduling problem. Moreover, we prove the submodularity of batch processing time function of the existing batch models including the parallel batch, serial batch, and mixed batch models. We compare the worst‐case performance ratios in the existing batch models with those deduced from our work in the submodular batch model. In most situations, the worst‐case performance ratios deduced from our work are comparable to the best‐known worst‐case performance ratios with tailored examinations.

The paper deals with some single-machine scheduling problems with setup time considerations where the processing time of a job is given as a function of its starting times and position in a sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (\( \delta \geqslant 0 \)) power of job completion times, the total weighted completion time, the maximum lateness and the number of tardy jobs. We show that the makespan minimization problem, the total completion time minimization problem, and the sum of the δth power of job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.

Performance of manufacturing cells for group technology: a parametric analysis

Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect

Heuristics for an assembly flow-shop with non-identical assembly machines and sequence dependent setup times to minimize sum of holding and delay costs

Recent advances in CFD modeling of bioethanol production processes

Order review and release (ORR) in a job shop considering sequence-dependent setup time (SDST) is among the most challenging job shop problems. This study investigates the effect of varying setup times and workload trigger levels on ORR policies performance in a stochastic dynamic job shop considering SDST. It is essential to examine the effect of varying setup times and workload trigger levels on ORR policies, because, for different ORR policies, workload trigger level plays a major role to control the work-in-process on the shop floor. Further, in manufacturing industries, less setup time is required in some cases, but it can also be equal to or greater than the processing time in others. Promodel[Formula: see text] simulation software is used to develop the simulation model for conducting experiments. The performance of the system is evaluated in terms of mean lead time (MLT), mean throughput time (MTT), number of tardy jobs (NOTJ), and total setups (TS) performance measures. From results, it is found that for a given ORR policy and at a given setup time level, lower workload trigger level provides minimum MTT and maximum MLT, TS, and NOTJ performance measures. As the workload trigger level increases, MTT performance measure increases, whereas MLT, TS, and NOTJ performance measures decrease. Further, for a given ORR policy and workload trigger level, as the setup time level increases, MTT and MLT performance measures increase. In contrast, TS and NOTJ performance measures decrease. A stochastic dynamic job shop considering ORR and SDST where setup time is either less than, equal to or more than operation processing time is the novelty of the work.

Scheduling hybrid flowshop with parallel batching machines and compatibilities